idx int64 1 56k | question stringlengths 15 155 | answer stringlengths 2 29.2k ⌀ | question_cut stringlengths 15 100 | answer_cut stringlengths 2 200 ⌀ | conversation stringlengths 47 29.3k | conversation_cut stringlengths 47 301 |
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52,601 | Linear regression performing better than random forest in Caret | Check out caret's function findLinearCombos and run it on your data. The object returned is a list--the second element is a vector of indices which can safely be removed from your data set since they are linear combinations of other columns (which, now that I think about it makes total sense because you only had 500 ob... | Linear regression performing better than random forest in Caret | Check out caret's function findLinearCombos and run it on your data. The object returned is a list--the second element is a vector of indices which can safely be removed from your data set since they | Linear regression performing better than random forest in Caret
Check out caret's function findLinearCombos and run it on your data. The object returned is a list--the second element is a vector of indices which can safely be removed from your data set since they are linear combinations of other columns (which, now tha... | Linear regression performing better than random forest in Caret
Check out caret's function findLinearCombos and run it on your data. The object returned is a list--the second element is a vector of indices which can safely be removed from your data set since they |
52,602 | Etymology of "cluster" in the context of cluster analysis | "Cluster of rocks", "cluster of islands", "cluster of factories" etc. can easily be traced back to the 19th century (and probably much longer). Of course statistics early on started to look for a way to formalize this. So good luck, you will likely need to walk to a lot of libraries (the physical one, not the software ... | Etymology of "cluster" in the context of cluster analysis | "Cluster of rocks", "cluster of islands", "cluster of factories" etc. can easily be traced back to the 19th century (and probably much longer). Of course statistics early on started to look for a way | Etymology of "cluster" in the context of cluster analysis
"Cluster of rocks", "cluster of islands", "cluster of factories" etc. can easily be traced back to the 19th century (and probably much longer). Of course statistics early on started to look for a way to formalize this. So good luck, you will likely need to walk ... | Etymology of "cluster" in the context of cluster analysis
"Cluster of rocks", "cluster of islands", "cluster of factories" etc. can easily be traced back to the 19th century (and probably much longer). Of course statistics early on started to look for a way |
52,603 | Etymology of "cluster" in the context of cluster analysis | According to Oxford Dictionary the word cluster is derived from the Old English word 'clyster' and was "probably related to clot [or clott]" and is derived from the Germanic 'klotz'. | Etymology of "cluster" in the context of cluster analysis | According to Oxford Dictionary the word cluster is derived from the Old English word 'clyster' and was "probably related to clot [or clott]" and is derived from the Germanic 'klotz'. | Etymology of "cluster" in the context of cluster analysis
According to Oxford Dictionary the word cluster is derived from the Old English word 'clyster' and was "probably related to clot [or clott]" and is derived from the Germanic 'klotz'. | Etymology of "cluster" in the context of cluster analysis
According to Oxford Dictionary the word cluster is derived from the Old English word 'clyster' and was "probably related to clot [or clott]" and is derived from the Germanic 'klotz'. |
52,604 | What is a multivariate logistic regression | There is no reliable answer to your question in terms of standard usage in the medical literature. The paper cited by @DirkHorsten, in a comment on another answer here, examined articles published over the course of a year in a single high-quality public health journal that presumably has statistical expertise in its r... | What is a multivariate logistic regression | There is no reliable answer to your question in terms of standard usage in the medical literature. The paper cited by @DirkHorsten, in a comment on another answer here, examined articles published ove | What is a multivariate logistic regression
There is no reliable answer to your question in terms of standard usage in the medical literature. The paper cited by @DirkHorsten, in a comment on another answer here, examined articles published over the course of a year in a single high-quality public health journal that pr... | What is a multivariate logistic regression
There is no reliable answer to your question in terms of standard usage in the medical literature. The paper cited by @DirkHorsten, in a comment on another answer here, examined articles published ove |
52,605 | What is a multivariate logistic regression | In statistics, multivariate and multiple mean two different things all together. In a regression model, "multiple" denotes several predictors/independent variables. On the other hand, "multivariate" is used to mean several (2 or more) responses/ dependent variables. To this end, multivariate logistic regression is a l... | What is a multivariate logistic regression | In statistics, multivariate and multiple mean two different things all together. In a regression model, "multiple" denotes several predictors/independent variables. On the other hand, "multivariate" | What is a multivariate logistic regression
In statistics, multivariate and multiple mean two different things all together. In a regression model, "multiple" denotes several predictors/independent variables. On the other hand, "multivariate" is used to mean several (2 or more) responses/ dependent variables. To this e... | What is a multivariate logistic regression
In statistics, multivariate and multiple mean two different things all together. In a regression model, "multiple" denotes several predictors/independent variables. On the other hand, "multivariate" |
52,606 | What is a multivariate logistic regression | 'Standard logistic regression' (part of generalised linear models)
The logistic regression can be the 'standard' logistic regression with fixed coefficents, so in the univariate case (for simplicity I take one explanatory variable, but the reasoning holds also in the multivariate case), the logistic regression tries to... | What is a multivariate logistic regression | 'Standard logistic regression' (part of generalised linear models)
The logistic regression can be the 'standard' logistic regression with fixed coefficents, so in the univariate case (for simplicity I | What is a multivariate logistic regression
'Standard logistic regression' (part of generalised linear models)
The logistic regression can be the 'standard' logistic regression with fixed coefficents, so in the univariate case (for simplicity I take one explanatory variable, but the reasoning holds also in the multivari... | What is a multivariate logistic regression
'Standard logistic regression' (part of generalised linear models)
The logistic regression can be the 'standard' logistic regression with fixed coefficents, so in the univariate case (for simplicity I |
52,607 | What is a multivariate logistic regression | You may want to take a look at "Bahadur Model".
In Bahadur model, "multivariate" in "multivariate logistic regression" means multiple binary dependent variables, which may be correlated at second or higher order. See references from Verbeke and Molenberghs for a description of this model.
Best,
Rolando | What is a multivariate logistic regression | You may want to take a look at "Bahadur Model".
In Bahadur model, "multivariate" in "multivariate logistic regression" means multiple binary dependent variables, which may be correlated at second or h | What is a multivariate logistic regression
You may want to take a look at "Bahadur Model".
In Bahadur model, "multivariate" in "multivariate logistic regression" means multiple binary dependent variables, which may be correlated at second or higher order. See references from Verbeke and Molenberghs for a description of... | What is a multivariate logistic regression
You may want to take a look at "Bahadur Model".
In Bahadur model, "multivariate" in "multivariate logistic regression" means multiple binary dependent variables, which may be correlated at second or h |
52,608 | What is a multivariate logistic regression | Multivariate logistic regression is like simple logistic regression but with multiple predictors. Logistic regression is similar to linear regression but you can use it when your response variable is binary. This is common in medical research because with multiple logistic regression you can adjust for confounders. For... | What is a multivariate logistic regression | Multivariate logistic regression is like simple logistic regression but with multiple predictors. Logistic regression is similar to linear regression but you can use it when your response variable is | What is a multivariate logistic regression
Multivariate logistic regression is like simple logistic regression but with multiple predictors. Logistic regression is similar to linear regression but you can use it when your response variable is binary. This is common in medical research because with multiple logistic reg... | What is a multivariate logistic regression
Multivariate logistic regression is like simple logistic regression but with multiple predictors. Logistic regression is similar to linear regression but you can use it when your response variable is |
52,609 | Combining principal component regression and stepwise regression | Regression based on principal components analysis (PCA) of the independent variables is certainly a way to approach this problem; see this Cross Validated page for one extensive discussion of pros and cons, with links to further related topics. I don't see the point of the regression you propose after choosing the larg... | Combining principal component regression and stepwise regression | Regression based on principal components analysis (PCA) of the independent variables is certainly a way to approach this problem; see this Cross Validated page for one extensive discussion of pros and | Combining principal component regression and stepwise regression
Regression based on principal components analysis (PCA) of the independent variables is certainly a way to approach this problem; see this Cross Validated page for one extensive discussion of pros and cons, with links to further related topics. I don't se... | Combining principal component regression and stepwise regression
Regression based on principal components analysis (PCA) of the independent variables is certainly a way to approach this problem; see this Cross Validated page for one extensive discussion of pros and |
52,610 | Bootstrapping won't always return population statistics - so why say it does? | Heuristically, you can think that the motivation behind the bootstrap is that given a large sample, your sample should be distributed approximately equal to your population. If your sample is distributed approximately equal to your population, then re-sampling from your sample and calculating your statistic should be a... | Bootstrapping won't always return population statistics - so why say it does? | Heuristically, you can think that the motivation behind the bootstrap is that given a large sample, your sample should be distributed approximately equal to your population. If your sample is distribu | Bootstrapping won't always return population statistics - so why say it does?
Heuristically, you can think that the motivation behind the bootstrap is that given a large sample, your sample should be distributed approximately equal to your population. If your sample is distributed approximately equal to your population... | Bootstrapping won't always return population statistics - so why say it does?
Heuristically, you can think that the motivation behind the bootstrap is that given a large sample, your sample should be distributed approximately equal to your population. If your sample is distribu |
52,611 | Bootstrapping won't always return population statistics - so why say it does? | First, bootstrap cannot remedy a problem of an unrepresentative original sample. Thus I agree with @CliffAB.
The chances of randomly drawing a sample that is little representative diminish as the sample size grows. If there was just one coin throw, the outcome would always be "crippled": one element (either head or ta... | Bootstrapping won't always return population statistics - so why say it does? | First, bootstrap cannot remedy a problem of an unrepresentative original sample. Thus I agree with @CliffAB.
The chances of randomly drawing a sample that is little representative diminish as the sam | Bootstrapping won't always return population statistics - so why say it does?
First, bootstrap cannot remedy a problem of an unrepresentative original sample. Thus I agree with @CliffAB.
The chances of randomly drawing a sample that is little representative diminish as the sample size grows. If there was just one coin... | Bootstrapping won't always return population statistics - so why say it does?
First, bootstrap cannot remedy a problem of an unrepresentative original sample. Thus I agree with @CliffAB.
The chances of randomly drawing a sample that is little representative diminish as the sam |
52,612 | When does it makes sense to use Cross Validation? | Here are 2 different scenarios where cross-validation can be used.
1) You want to approximate your model's generalization error (how well it will do on inputs it hasn't seen before). Cross-validation can tell you that because it trains on one set of data, and tests on the other set of data. The error on the test set is... | When does it makes sense to use Cross Validation? | Here are 2 different scenarios where cross-validation can be used.
1) You want to approximate your model's generalization error (how well it will do on inputs it hasn't seen before). Cross-validation | When does it makes sense to use Cross Validation?
Here are 2 different scenarios where cross-validation can be used.
1) You want to approximate your model's generalization error (how well it will do on inputs it hasn't seen before). Cross-validation can tell you that because it trains on one set of data, and tests on t... | When does it makes sense to use Cross Validation?
Here are 2 different scenarios where cross-validation can be used.
1) You want to approximate your model's generalization error (how well it will do on inputs it hasn't seen before). Cross-validation |
52,613 | When does it makes sense to use Cross Validation? | In addition to @justin_credible's points:
When does it makes sense to use Cross Validation?
Whenever you cannot afford the independent test set you'd really want to have.
Iterated $k$-fold CV or out-of-bootstrap: in order to measure the stability of the predictions wrt. to slight changes in the training set.
(Note ... | When does it makes sense to use Cross Validation? | In addition to @justin_credible's points:
When does it makes sense to use Cross Validation?
Whenever you cannot afford the independent test set you'd really want to have.
Iterated $k$-fold CV or o | When does it makes sense to use Cross Validation?
In addition to @justin_credible's points:
When does it makes sense to use Cross Validation?
Whenever you cannot afford the independent test set you'd really want to have.
Iterated $k$-fold CV or out-of-bootstrap: in order to measure the stability of the predictions ... | When does it makes sense to use Cross Validation?
In addition to @justin_credible's points:
When does it makes sense to use Cross Validation?
Whenever you cannot afford the independent test set you'd really want to have.
Iterated $k$-fold CV or o |
52,614 | eliminating outliers in MARS regression | My suggestion is independent of the software used.
We need to clarify whether the outliers are outliers in Y, the dependent variable, or outliers in the predictor, X. Outliers in the predictor, X, are easily handled with the vast numbers of transformations available that would reshape the PDF (probability density func... | eliminating outliers in MARS regression | My suggestion is independent of the software used.
We need to clarify whether the outliers are outliers in Y, the dependent variable, or outliers in the predictor, X. Outliers in the predictor, X, ar | eliminating outliers in MARS regression
My suggestion is independent of the software used.
We need to clarify whether the outliers are outliers in Y, the dependent variable, or outliers in the predictor, X. Outliers in the predictor, X, are easily handled with the vast numbers of transformations available that would r... | eliminating outliers in MARS regression
My suggestion is independent of the software used.
We need to clarify whether the outliers are outliers in Y, the dependent variable, or outliers in the predictor, X. Outliers in the predictor, X, ar |
52,615 | eliminating outliers in MARS regression | From the R package documentation and from the original MARS paper, it looks like rsq and grsq are used for model selection within the package and it looks like your code is removing outliers until the fit of the model is maximized. This is usually not recommended. There are statistical tools to help identify potential ... | eliminating outliers in MARS regression | From the R package documentation and from the original MARS paper, it looks like rsq and grsq are used for model selection within the package and it looks like your code is removing outliers until the | eliminating outliers in MARS regression
From the R package documentation and from the original MARS paper, it looks like rsq and grsq are used for model selection within the package and it looks like your code is removing outliers until the fit of the model is maximized. This is usually not recommended. There are stati... | eliminating outliers in MARS regression
From the R package documentation and from the original MARS paper, it looks like rsq and grsq are used for model selection within the package and it looks like your code is removing outliers until the |
52,616 | eliminating outliers in MARS regression | To elaborate slightly on Eric Farng's comment that removing outliers until the fit of the model is maximized is not recommended:
The fundamental problem with tweaking the data until you get a good GRSq is that although you will build a model that gives a good fit to your selected data, your model will not give good ... | eliminating outliers in MARS regression | To elaborate slightly on Eric Farng's comment that removing outliers until the fit of the model is maximized is not recommended:
The fundamental problem with tweaking the data until you get a good G | eliminating outliers in MARS regression
To elaborate slightly on Eric Farng's comment that removing outliers until the fit of the model is maximized is not recommended:
The fundamental problem with tweaking the data until you get a good GRSq is that although you will build a model that gives a good fit to your select... | eliminating outliers in MARS regression
To elaborate slightly on Eric Farng's comment that removing outliers until the fit of the model is maximized is not recommended:
The fundamental problem with tweaking the data until you get a good G |
52,617 | bootstrapping vs. "repeated cross validation" | Q. 1. Is this bootstrapping without replacement or "repeated 2-fold cross validation"?
Q. 2. If the answer is both, what exactly is the difference between bootstrapping without replacement and "repeated cross validation"?
It is neither. But the differences between sampling methods are subtle.
It is not classic bootst... | bootstrapping vs. "repeated cross validation" | Q. 1. Is this bootstrapping without replacement or "repeated 2-fold cross validation"?
Q. 2. If the answer is both, what exactly is the difference between bootstrapping without replacement and "repeat | bootstrapping vs. "repeated cross validation"
Q. 1. Is this bootstrapping without replacement or "repeated 2-fold cross validation"?
Q. 2. If the answer is both, what exactly is the difference between bootstrapping without replacement and "repeated cross validation"?
It is neither. But the differences between sampling... | bootstrapping vs. "repeated cross validation"
Q. 1. Is this bootstrapping without replacement or "repeated 2-fold cross validation"?
Q. 2. If the answer is both, what exactly is the difference between bootstrapping without replacement and "repeat |
52,618 | bootstrapping vs. "repeated cross validation" | Bootstrapping always means that from your set of n samples you draw n samples with replacement. This means you will almost certainly have duplicates in your data set.
In n-fold cross validation you cleanly separate your data in n approximately equally large subsets, which do not overlap. What you are doing is indeed "... | bootstrapping vs. "repeated cross validation" | Bootstrapping always means that from your set of n samples you draw n samples with replacement. This means you will almost certainly have duplicates in your data set.
In n-fold cross validation you c | bootstrapping vs. "repeated cross validation"
Bootstrapping always means that from your set of n samples you draw n samples with replacement. This means you will almost certainly have duplicates in your data set.
In n-fold cross validation you cleanly separate your data in n approximately equally large subsets, which ... | bootstrapping vs. "repeated cross validation"
Bootstrapping always means that from your set of n samples you draw n samples with replacement. This means you will almost certainly have duplicates in your data set.
In n-fold cross validation you c |
52,619 | What is the name of this graph? | I didn't know before I saw your question but I remember that I saw such a graph in the d3.js gallery. This is called a chord diagram. | What is the name of this graph? | I didn't know before I saw your question but I remember that I saw such a graph in the d3.js gallery. This is called a chord diagram. | What is the name of this graph?
I didn't know before I saw your question but I remember that I saw such a graph in the d3.js gallery. This is called a chord diagram. | What is the name of this graph?
I didn't know before I saw your question but I remember that I saw such a graph in the d3.js gallery. This is called a chord diagram. |
52,620 | What is the name of this graph? | I saw this graph in some biological papers. It is called circos. Originally, it was proposed in this article:
Krzywinski, M. et al. Circos: an Information Aesthetic for Comparative Genomics. Genome Res (2009) 19:1639-1645. | What is the name of this graph? | I saw this graph in some biological papers. It is called circos. Originally, it was proposed in this article:
Krzywinski, M. et al. Circos: an Information Aesthetic for Comparative Genomics. Genome Re | What is the name of this graph?
I saw this graph in some biological papers. It is called circos. Originally, it was proposed in this article:
Krzywinski, M. et al. Circos: an Information Aesthetic for Comparative Genomics. Genome Res (2009) 19:1639-1645. | What is the name of this graph?
I saw this graph in some biological papers. It is called circos. Originally, it was proposed in this article:
Krzywinski, M. et al. Circos: an Information Aesthetic for Comparative Genomics. Genome Re |
52,621 | Distribution of the product of a gamma random variable and a beta random variable | Let random variable $X \sim \text{Gamma}(a,b)$ with pdf $f(x)$:
Let $Y \sim \text{Beta}(c, d)$ with pdf $g(y)$:
We seek the pdf of the product $Z = X*Y$, say $h(z)$, which is given by:
where I am using mathStatica's TransformProduct function to automate the nitty-gritties, and where Hypergeometric1F1 denotes the ... | Distribution of the product of a gamma random variable and a beta random variable | Let random variable $X \sim \text{Gamma}(a,b)$ with pdf $f(x)$:
Let $Y \sim \text{Beta}(c, d)$ with pdf $g(y)$:
We seek the pdf of the product $Z = X*Y$, say $h(z)$, which is given by:
where I a | Distribution of the product of a gamma random variable and a beta random variable
Let random variable $X \sim \text{Gamma}(a,b)$ with pdf $f(x)$:
Let $Y \sim \text{Beta}(c, d)$ with pdf $g(y)$:
We seek the pdf of the product $Z = X*Y$, say $h(z)$, which is given by:
where I am using mathStatica's TransformProduct... | Distribution of the product of a gamma random variable and a beta random variable
Let random variable $X \sim \text{Gamma}(a,b)$ with pdf $f(x)$:
Let $Y \sim \text{Beta}(c, d)$ with pdf $g(y)$:
We seek the pdf of the product $Z = X*Y$, say $h(z)$, which is given by:
where I a |
52,622 | Distribution of the product of a gamma random variable and a beta random variable | Let $X$ and $Y$ be absolutely continuous, independent, and non-negative random variables such that $X$ has bounded support. Then any two of the following 3 conditions imply the third:
(i) $X\sim{}\text{Beta}(a,b)$
(ii) $Y\sim{}\text{Gamma}(a+b,c)$
(iii) $XY\sim{}\text{Gamma}(a,c)$
see Yeo and Milne (1991) at https://w... | Distribution of the product of a gamma random variable and a beta random variable | Let $X$ and $Y$ be absolutely continuous, independent, and non-negative random variables such that $X$ has bounded support. Then any two of the following 3 conditions imply the third:
(i) $X\sim{}\tex | Distribution of the product of a gamma random variable and a beta random variable
Let $X$ and $Y$ be absolutely continuous, independent, and non-negative random variables such that $X$ has bounded support. Then any two of the following 3 conditions imply the third:
(i) $X\sim{}\text{Beta}(a,b)$
(ii) $Y\sim{}\text{Gamma... | Distribution of the product of a gamma random variable and a beta random variable
Let $X$ and $Y$ be absolutely continuous, independent, and non-negative random variables such that $X$ has bounded support. Then any two of the following 3 conditions imply the third:
(i) $X\sim{}\tex |
52,623 | Plotting distributions of variables across time | Something like these quartile bands may work. You can add more quantiles if more detail is needed, but sometimes less is more. The quartiles will be enough to get a sense of the spread and the skewness.
The downside is that the bands don't overlay well, so you lose direct comparison. I added a reference band around 0 t... | Plotting distributions of variables across time | Something like these quartile bands may work. You can add more quantiles if more detail is needed, but sometimes less is more. The quartiles will be enough to get a sense of the spread and the skewnes | Plotting distributions of variables across time
Something like these quartile bands may work. You can add more quantiles if more detail is needed, but sometimes less is more. The quartiles will be enough to get a sense of the spread and the skewness.
The downside is that the bands don't overlay well, so you lose direct... | Plotting distributions of variables across time
Something like these quartile bands may work. You can add more quantiles if more detail is needed, but sometimes less is more. The quartiles will be enough to get a sense of the spread and the skewnes |
52,624 | Plotting distributions of variables across time | Let's take $x$ first. Use the quantiles to construct a smooth distribution $x_j(\cdot)$ at each timestep $j$. Pick a 1D grid of values $a + bi$. Now plot the greyscale image $x_j(a+bi)$, where $i$ is the row coordinate and $j$ is the column coordinate, and the $x$-values are normalized to 0-255.
Now do the same for $y$... | Plotting distributions of variables across time | Let's take $x$ first. Use the quantiles to construct a smooth distribution $x_j(\cdot)$ at each timestep $j$. Pick a 1D grid of values $a + bi$. Now plot the greyscale image $x_j(a+bi)$, where $i$ is | Plotting distributions of variables across time
Let's take $x$ first. Use the quantiles to construct a smooth distribution $x_j(\cdot)$ at each timestep $j$. Pick a 1D grid of values $a + bi$. Now plot the greyscale image $x_j(a+bi)$, where $i$ is the row coordinate and $j$ is the column coordinate, and the $x$-values ... | Plotting distributions of variables across time
Let's take $x$ first. Use the quantiles to construct a smooth distribution $x_j(\cdot)$ at each timestep $j$. Pick a 1D grid of values $a + bi$. Now plot the greyscale image $x_j(a+bi)$, where $i$ is |
52,625 | How to build a predictive model with a billion of sparse features? | An alternative to dimensionality reduction is to use the hashing trick to train a classifier on the entire feature set without reduction beforehand.* The Vowpal Wabbit pwoject--er, project--is an implementation of various learning algorithms using the hashing trick to speed up computation:
VW is the essence of speed i... | How to build a predictive model with a billion of sparse features? | An alternative to dimensionality reduction is to use the hashing trick to train a classifier on the entire feature set without reduction beforehand.* The Vowpal Wabbit pwoject--er, project--is an impl | How to build a predictive model with a billion of sparse features?
An alternative to dimensionality reduction is to use the hashing trick to train a classifier on the entire feature set without reduction beforehand.* The Vowpal Wabbit pwoject--er, project--is an implementation of various learning algorithms using the h... | How to build a predictive model with a billion of sparse features?
An alternative to dimensionality reduction is to use the hashing trick to train a classifier on the entire feature set without reduction beforehand.* The Vowpal Wabbit pwoject--er, project--is an impl |
52,626 | How to build a predictive model with a billion of sparse features? | Traditionally, principal components analysis (PCA) is used for dimensionality reduction (in a mathematical sense). However, if you care about latent constructs (factors) that your features (indicators or items, in factor analysis and latent variable modeling terminology) represent and measure, then exploratory factor a... | How to build a predictive model with a billion of sparse features? | Traditionally, principal components analysis (PCA) is used for dimensionality reduction (in a mathematical sense). However, if you care about latent constructs (factors) that your features (indicators | How to build a predictive model with a billion of sparse features?
Traditionally, principal components analysis (PCA) is used for dimensionality reduction (in a mathematical sense). However, if you care about latent constructs (factors) that your features (indicators or items, in factor analysis and latent variable mod... | How to build a predictive model with a billion of sparse features?
Traditionally, principal components analysis (PCA) is used for dimensionality reduction (in a mathematical sense). However, if you care about latent constructs (factors) that your features (indicators |
52,627 | Balanced datasets in Naive Bayes | There are two types of classification model, generative model and discriminative model.
Naive Bayes is a generative model, and to train Naive Bayes, your training data should be generated by the true process, and future data will be generated by that process as well. Balancing the data isn't part of the true process, s... | Balanced datasets in Naive Bayes | There are two types of classification model, generative model and discriminative model.
Naive Bayes is a generative model, and to train Naive Bayes, your training data should be generated by the true | Balanced datasets in Naive Bayes
There are two types of classification model, generative model and discriminative model.
Naive Bayes is a generative model, and to train Naive Bayes, your training data should be generated by the true process, and future data will be generated by that process as well. Balancing the data ... | Balanced datasets in Naive Bayes
There are two types of classification model, generative model and discriminative model.
Naive Bayes is a generative model, and to train Naive Bayes, your training data should be generated by the true |
52,628 | Balanced datasets in Naive Bayes | Getting balanced data sets is not the only option you've got for the Naive Bayes classifier.
The paper Tackling the Poor Assumptions of Naive Bayes Text Classifiers contains a discussion of this point plus some ways to overcome that difficulty. The paper is focused on text classification though.
Concretely, it shows wi... | Balanced datasets in Naive Bayes | Getting balanced data sets is not the only option you've got for the Naive Bayes classifier.
The paper Tackling the Poor Assumptions of Naive Bayes Text Classifiers contains a discussion of this point | Balanced datasets in Naive Bayes
Getting balanced data sets is not the only option you've got for the Naive Bayes classifier.
The paper Tackling the Poor Assumptions of Naive Bayes Text Classifiers contains a discussion of this point plus some ways to overcome that difficulty. The paper is focused on text classificatio... | Balanced datasets in Naive Bayes
Getting balanced data sets is not the only option you've got for the Naive Bayes classifier.
The paper Tackling the Poor Assumptions of Naive Bayes Text Classifiers contains a discussion of this point |
52,629 | How to implement model in R? | Here is one way to fit the model that you describe.
# sample series
x <- AirPassengers
# to illustrate a more general case,
# take a subsample that does not start in the first season
# and ends in the last season
x <- window(x, start=c(1949,2), end=c(1959,4))
Indicator variables for the seasonal intercepts can be cre... | How to implement model in R? | Here is one way to fit the model that you describe.
# sample series
x <- AirPassengers
# to illustrate a more general case,
# take a subsample that does not start in the first season
# and ends in th | How to implement model in R?
Here is one way to fit the model that you describe.
# sample series
x <- AirPassengers
# to illustrate a more general case,
# take a subsample that does not start in the first season
# and ends in the last season
x <- window(x, start=c(1949,2), end=c(1959,4))
Indicator variables for the s... | How to implement model in R?
Here is one way to fit the model that you describe.
# sample series
x <- AirPassengers
# to illustrate a more general case,
# take a subsample that does not start in the first season
# and ends in th |
52,630 | Gower distance with R functions; "gower.dist" and "daisy" | They in fact do give the same results. I am not sure how you are comparing them but here is an example:
# Create example data
set.seed(123)
# create nominal variable
nom <- factor(rep(letters[1:3], each=10))
# create numeric variables
vars <- as.matrix(replicate(17, rnorm(30)))
df <- data.frame(nom, vars)
library(clu... | Gower distance with R functions; "gower.dist" and "daisy" | They in fact do give the same results. I am not sure how you are comparing them but here is an example:
# Create example data
set.seed(123)
# create nominal variable
nom <- factor(rep(letters[1:3], e | Gower distance with R functions; "gower.dist" and "daisy"
They in fact do give the same results. I am not sure how you are comparing them but here is an example:
# Create example data
set.seed(123)
# create nominal variable
nom <- factor(rep(letters[1:3], each=10))
# create numeric variables
vars <- as.matrix(replicat... | Gower distance with R functions; "gower.dist" and "daisy"
They in fact do give the same results. I am not sure how you are comparing them but here is an example:
# Create example data
set.seed(123)
# create nominal variable
nom <- factor(rep(letters[1:3], e |
52,631 | Gower distance with R functions; "gower.dist" and "daisy" | Yes, They give the same result, just as proven by cdeterman.
One different I want to mention here is "gower.dist" actually use some kind of equal weights method (what they called weights in the function documents can only be 0 or 1), but "daisy" allow you to pass your weight vector by argument 'weights'.
Conclusion:
... | Gower distance with R functions; "gower.dist" and "daisy" | Yes, They give the same result, just as proven by cdeterman.
One different I want to mention here is "gower.dist" actually use some kind of equal weights method (what they called weights in the funct | Gower distance with R functions; "gower.dist" and "daisy"
Yes, They give the same result, just as proven by cdeterman.
One different I want to mention here is "gower.dist" actually use some kind of equal weights method (what they called weights in the function documents can only be 0 or 1), but "daisy" allow you to pa... | Gower distance with R functions; "gower.dist" and "daisy"
Yes, They give the same result, just as proven by cdeterman.
One different I want to mention here is "gower.dist" actually use some kind of equal weights method (what they called weights in the funct |
52,632 | Should we remove axis and use direct label on scientific chart? | It depends on your goals.
Who is reading the graph? In print or on screen? Web or PDF? Are the numbers important, or just the relative magnitudes?
I'd say that, in this kind of plot, the number labels are fine and the axis label is probably unnecessary. That's because there are only a few bars and the scale is linear.
... | Should we remove axis and use direct label on scientific chart? | It depends on your goals.
Who is reading the graph? In print or on screen? Web or PDF? Are the numbers important, or just the relative magnitudes?
I'd say that, in this kind of plot, the number labels | Should we remove axis and use direct label on scientific chart?
It depends on your goals.
Who is reading the graph? In print or on screen? Web or PDF? Are the numbers important, or just the relative magnitudes?
I'd say that, in this kind of plot, the number labels are fine and the axis label is probably unnecessary. Th... | Should we remove axis and use direct label on scientific chart?
It depends on your goals.
Who is reading the graph? In print or on screen? Web or PDF? Are the numbers important, or just the relative magnitudes?
I'd say that, in this kind of plot, the number labels |
52,633 | Should we remove axis and use direct label on scientific chart? | Here's some sage advice from Jane Miller:
Data labels are typed numeric values adjacent to the pertinent slice,
point, or bar in a chart ... To keep charts simple and readable, use data labels sparingly. Again, the main advantage of a chart is that it can illustrate general
levels or patterns, which will be eviden... | Should we remove axis and use direct label on scientific chart? | Here's some sage advice from Jane Miller:
Data labels are typed numeric values adjacent to the pertinent slice,
point, or bar in a chart ... To keep charts simple and readable, use data labels spar | Should we remove axis and use direct label on scientific chart?
Here's some sage advice from Jane Miller:
Data labels are typed numeric values adjacent to the pertinent slice,
point, or bar in a chart ... To keep charts simple and readable, use data labels sparingly. Again, the main advantage of a chart is that it c... | Should we remove axis and use direct label on scientific chart?
Here's some sage advice from Jane Miller:
Data labels are typed numeric values adjacent to the pertinent slice,
point, or bar in a chart ... To keep charts simple and readable, use data labels spar |
52,634 | Why use upper triangular Cholesky? | Traditionally, and in most of the "world" (literature), the convention that the Cholesky factor is lower triangular is the most common, i.e., $LL^T$.
In MATLAB and Octave, among others (R's chol), Cholesky factor is defined to be upper triangular, i.e., $R^TR$. This convention was inherited by MATLAB from LINPACK, bec... | Why use upper triangular Cholesky? | Traditionally, and in most of the "world" (literature), the convention that the Cholesky factor is lower triangular is the most common, i.e., $LL^T$.
In MATLAB and Octave, among others (R's chol), Cho | Why use upper triangular Cholesky?
Traditionally, and in most of the "world" (literature), the convention that the Cholesky factor is lower triangular is the most common, i.e., $LL^T$.
In MATLAB and Octave, among others (R's chol), Cholesky factor is defined to be upper triangular, i.e., $R^TR$. This convention was in... | Why use upper triangular Cholesky?
Traditionally, and in most of the "world" (literature), the convention that the Cholesky factor is lower triangular is the most common, i.e., $LL^T$.
In MATLAB and Octave, among others (R's chol), Cho |
52,635 | Why use upper triangular Cholesky? | It's really a matter of preference. Also $U'z$ will give you the same sample from a multivariate normal. Why? I'll leave this as an exercise for you.
For me it is more natural the upper Cholesky factorization $A = U'U$ as I am more used to the `jik' algorithm, which takes the name from the ordering of the indices in th... | Why use upper triangular Cholesky? | It's really a matter of preference. Also $U'z$ will give you the same sample from a multivariate normal. Why? I'll leave this as an exercise for you.
For me it is more natural the upper Cholesky facto | Why use upper triangular Cholesky?
It's really a matter of preference. Also $U'z$ will give you the same sample from a multivariate normal. Why? I'll leave this as an exercise for you.
For me it is more natural the upper Cholesky factorization $A = U'U$ as I am more used to the `jik' algorithm, which takes the name fro... | Why use upper triangular Cholesky?
It's really a matter of preference. Also $U'z$ will give you the same sample from a multivariate normal. Why? I'll leave this as an exercise for you.
For me it is more natural the upper Cholesky facto |
52,636 | Calculate $\mathbb{E}[Z_i]$ where $Z_i = \min(X_i, Y_{i-1})$, $X \sim Beta(\alpha,1)$ | Explicit computation of these expectations appears to be out of the question once the index exceeds two or three, so I will focus on issues that had been emphasized in earlier versions of the question:
What happens (asymptotically) as $i$ increases?
What happens as $\alpha$ increases?
The answers turn out to be int... | Calculate $\mathbb{E}[Z_i]$ where $Z_i = \min(X_i, Y_{i-1})$, $X \sim Beta(\alpha,1)$ | Explicit computation of these expectations appears to be out of the question once the index exceeds two or three, so I will focus on issues that had been emphasized in earlier versions of the question | Calculate $\mathbb{E}[Z_i]$ where $Z_i = \min(X_i, Y_{i-1})$, $X \sim Beta(\alpha,1)$
Explicit computation of these expectations appears to be out of the question once the index exceeds two or three, so I will focus on issues that had been emphasized in earlier versions of the question:
What happens (asymptotically) a... | Calculate $\mathbb{E}[Z_i]$ where $Z_i = \min(X_i, Y_{i-1})$, $X \sim Beta(\alpha,1)$
Explicit computation of these expectations appears to be out of the question once the index exceeds two or three, so I will focus on issues that had been emphasized in earlier versions of the question |
52,637 | Calculate $\mathbb{E}[Z_i]$ where $Z_i = \min(X_i, Y_{i-1})$, $X \sim Beta(\alpha,1)$ | A conditional approach appears possibly helpful here.
The variable $Z_{i+1}$ can be written using indicator functions,
$$Z_{i+1} = X_{i+1}\cdot I_{\{X_{i+1} \leq Y_i\}}+Y_i\cdot [1-I_{\{X_{i+1} \leq Y_i\}}] $$
Denote $\mathcal F_i$ the sigma-algebra at time $i$, that includes $Z_i$ and hence $Y_i$ and consider the con... | Calculate $\mathbb{E}[Z_i]$ where $Z_i = \min(X_i, Y_{i-1})$, $X \sim Beta(\alpha,1)$ | A conditional approach appears possibly helpful here.
The variable $Z_{i+1}$ can be written using indicator functions,
$$Z_{i+1} = X_{i+1}\cdot I_{\{X_{i+1} \leq Y_i\}}+Y_i\cdot [1-I_{\{X_{i+1} \leq | Calculate $\mathbb{E}[Z_i]$ where $Z_i = \min(X_i, Y_{i-1})$, $X \sim Beta(\alpha,1)$
A conditional approach appears possibly helpful here.
The variable $Z_{i+1}$ can be written using indicator functions,
$$Z_{i+1} = X_{i+1}\cdot I_{\{X_{i+1} \leq Y_i\}}+Y_i\cdot [1-I_{\{X_{i+1} \leq Y_i\}}] $$
Denote $\mathcal F_i$ t... | Calculate $\mathbb{E}[Z_i]$ where $Z_i = \min(X_i, Y_{i-1})$, $X \sim Beta(\alpha,1)$
A conditional approach appears possibly helpful here.
The variable $Z_{i+1}$ can be written using indicator functions,
$$Z_{i+1} = X_{i+1}\cdot I_{\{X_{i+1} \leq Y_i\}}+Y_i\cdot [1-I_{\{X_{i+1} \leq |
52,638 | Common name for distributions that are bounded on one side | I would say no, as there are quite a few distributions in addition to log-normal that have support on $[ 0, \infty)$, such as the $\chi^2$ or gamma. (Wikipedia even has a list devoted to this criterion.)
In practice there are different circumstances in which such distributions are useful to approximate actually observe... | Common name for distributions that are bounded on one side | I would say no, as there are quite a few distributions in addition to log-normal that have support on $[ 0, \infty)$, such as the $\chi^2$ or gamma. (Wikipedia even has a list devoted to this criterio | Common name for distributions that are bounded on one side
I would say no, as there are quite a few distributions in addition to log-normal that have support on $[ 0, \infty)$, such as the $\chi^2$ or gamma. (Wikipedia even has a list devoted to this criterion.)
In practice there are different circumstances in which su... | Common name for distributions that are bounded on one side
I would say no, as there are quite a few distributions in addition to log-normal that have support on $[ 0, \infty)$, such as the $\chi^2$ or gamma. (Wikipedia even has a list devoted to this criterio |
52,639 | Common name for distributions that are bounded on one side | There seems to be no standard term, based on my experience. Some people refer to them as "one-sided", or "of one-sided support". I'd say "supported on [the positive half-line]", even though that is clunky.
Edit: related to Andy W's comment- "truncated" rather than "censored" more appropriate if the values outside a c... | Common name for distributions that are bounded on one side | There seems to be no standard term, based on my experience. Some people refer to them as "one-sided", or "of one-sided support". I'd say "supported on [the positive half-line]", even though that is | Common name for distributions that are bounded on one side
There seems to be no standard term, based on my experience. Some people refer to them as "one-sided", or "of one-sided support". I'd say "supported on [the positive half-line]", even though that is clunky.
Edit: related to Andy W's comment- "truncated" rather... | Common name for distributions that are bounded on one side
There seems to be no standard term, based on my experience. Some people refer to them as "one-sided", or "of one-sided support". I'd say "supported on [the positive half-line]", even though that is |
52,640 | Automatic identification of distribution of data | Identifying the distribution of data is essentially impossible.
The class of distribution functions is very large; it must be at least as large as the cardinality of $\mathbb{R}$ (e.g. consider only the unit step functions, corresponding to a constant value at some $x$ - there are as many of those as the cardinality of... | Automatic identification of distribution of data | Identifying the distribution of data is essentially impossible.
The class of distribution functions is very large; it must be at least as large as the cardinality of $\mathbb{R}$ (e.g. consider only t | Automatic identification of distribution of data
Identifying the distribution of data is essentially impossible.
The class of distribution functions is very large; it must be at least as large as the cardinality of $\mathbb{R}$ (e.g. consider only the unit step functions, corresponding to a constant value at some $x$ -... | Automatic identification of distribution of data
Identifying the distribution of data is essentially impossible.
The class of distribution functions is very large; it must be at least as large as the cardinality of $\mathbb{R}$ (e.g. consider only t |
52,641 | Automatic identification of distribution of data | The problem with this approach in practice is that most data sets are small enough that many distributions will adequately fit the data. If you arbitrarily pick a distribution that happens to fit the data and then proceed to do calculations or a simulation under this assumption, you can be badly mislead.
This proble... | Automatic identification of distribution of data | The problem with this approach in practice is that most data sets are small enough that many distributions will adequately fit the data. If you arbitrarily pick a distribution that happens to fit the | Automatic identification of distribution of data
The problem with this approach in practice is that most data sets are small enough that many distributions will adequately fit the data. If you arbitrarily pick a distribution that happens to fit the data and then proceed to do calculations or a simulation under this as... | Automatic identification of distribution of data
The problem with this approach in practice is that most data sets are small enough that many distributions will adequately fit the data. If you arbitrarily pick a distribution that happens to fit the |
52,642 | Why is the true (test) error rate of any classifier 50%? | That's not a general statement about classifiers. In this particular case where the class frequencies are half & half, & none of the predictors are any use, the true error rate, of any classifier, is 50%. Imagine trying to predict the result of coin tosses from denomination, year of issue, metal content, &c.—in the lo... | Why is the true (test) error rate of any classifier 50%? | That's not a general statement about classifiers. In this particular case where the class frequencies are half & half, & none of the predictors are any use, the true error rate, of any classifier, is | Why is the true (test) error rate of any classifier 50%?
That's not a general statement about classifiers. In this particular case where the class frequencies are half & half, & none of the predictors are any use, the true error rate, of any classifier, is 50%. Imagine trying to predict the result of coin tosses from ... | Why is the true (test) error rate of any classifier 50%?
That's not a general statement about classifiers. In this particular case where the class frequencies are half & half, & none of the predictors are any use, the true error rate, of any classifier, is |
52,643 | Why is the true (test) error rate of any classifier 50%? | To expand on the answer above, the key point is that the predictors are independent of the class labels (of no use) i.e. any forecast using these predictors is equivalent to a random draw from the class labels. | Why is the true (test) error rate of any classifier 50%? | To expand on the answer above, the key point is that the predictors are independent of the class labels (of no use) i.e. any forecast using these predictors is equivalent to a random draw from the cla | Why is the true (test) error rate of any classifier 50%?
To expand on the answer above, the key point is that the predictors are independent of the class labels (of no use) i.e. any forecast using these predictors is equivalent to a random draw from the class labels. | Why is the true (test) error rate of any classifier 50%?
To expand on the answer above, the key point is that the predictors are independent of the class labels (of no use) i.e. any forecast using these predictors is equivalent to a random draw from the cla |
52,644 | Should there be an "i" in a regression equation? | The $i$'s usually index the observations in the sample used to fit the model, so if you simply want to present the predictive equation for a single new observation, there's no need for them. Also be careful not to confuse the random variable, its observed values, & the fitted values: if you've previously defined $Y_i$ ... | Should there be an "i" in a regression equation? | The $i$'s usually index the observations in the sample used to fit the model, so if you simply want to present the predictive equation for a single new observation, there's no need for them. Also be c | Should there be an "i" in a regression equation?
The $i$'s usually index the observations in the sample used to fit the model, so if you simply want to present the predictive equation for a single new observation, there's no need for them. Also be careful not to confuse the random variable, its observed values, & the f... | Should there be an "i" in a regression equation?
The $i$'s usually index the observations in the sample used to fit the model, so if you simply want to present the predictive equation for a single new observation, there's no need for them. Also be c |
52,645 | Should there be an "i" in a regression equation? | Both are correct, but if you use the i 's they should preferably be subscripts:
$Y_i = .432 + .320Age_i + .520WE_i + .300JP1_i + .210JP2_i$
If you don't use the i's then the equation is about vectors. | Should there be an "i" in a regression equation? | Both are correct, but if you use the i 's they should preferably be subscripts:
$Y_i = .432 + .320Age_i + .520WE_i + .300JP1_i + .210JP2_i$
If you don't use the i's then the equation is about vectors. | Should there be an "i" in a regression equation?
Both are correct, but if you use the i 's they should preferably be subscripts:
$Y_i = .432 + .320Age_i + .520WE_i + .300JP1_i + .210JP2_i$
If you don't use the i's then the equation is about vectors. | Should there be an "i" in a regression equation?
Both are correct, but if you use the i 's they should preferably be subscripts:
$Y_i = .432 + .320Age_i + .520WE_i + .300JP1_i + .210JP2_i$
If you don't use the i's then the equation is about vectors. |
52,646 | Unequal variances t-test or U Mann-Whitney test? | The Mann-Whitney doesn't require equal variances unless you're specifically looking for location-shift alternatives.
In particular, it is able to test whether the probability of values in the first group are larger than the values in the second group, which is quite a general alternative that sounds like it's related ... | Unequal variances t-test or U Mann-Whitney test? | The Mann-Whitney doesn't require equal variances unless you're specifically looking for location-shift alternatives.
In particular, it is able to test whether the probability of values in the first g | Unequal variances t-test or U Mann-Whitney test?
The Mann-Whitney doesn't require equal variances unless you're specifically looking for location-shift alternatives.
In particular, it is able to test whether the probability of values in the first group are larger than the values in the second group, which is quite a g... | Unequal variances t-test or U Mann-Whitney test?
The Mann-Whitney doesn't require equal variances unless you're specifically looking for location-shift alternatives.
In particular, it is able to test whether the probability of values in the first g |
52,647 | Unequal variances t-test or U Mann-Whitney test? | If the sample sizes are unequal, we should use the unpooled variances t-test. If they're equal, use the pooled. Here's an excerpt from "Understanding and Using Statistics in Psychology" (which I co-authored, with Phil Banyard).
"There are a number of different ways to decide if your variances (or standard deviations) ... | Unequal variances t-test or U Mann-Whitney test? | If the sample sizes are unequal, we should use the unpooled variances t-test. If they're equal, use the pooled. Here's an excerpt from "Understanding and Using Statistics in Psychology" (which I co-au | Unequal variances t-test or U Mann-Whitney test?
If the sample sizes are unequal, we should use the unpooled variances t-test. If they're equal, use the pooled. Here's an excerpt from "Understanding and Using Statistics in Psychology" (which I co-authored, with Phil Banyard).
"There are a number of different ways to d... | Unequal variances t-test or U Mann-Whitney test?
If the sample sizes are unequal, we should use the unpooled variances t-test. If they're equal, use the pooled. Here's an excerpt from "Understanding and Using Statistics in Psychology" (which I co-au |
52,648 | Unequal variances t-test or U Mann-Whitney test? | You haven't said exactly what you are measuring. If it is count data then this paper is very helpful. I am curious about the nature of your measurements, since if you have a mean of 10 and a SD of 11, a negative number for a value one standard deviation below the mean may or may not be meaningful.
Review: analysis of p... | Unequal variances t-test or U Mann-Whitney test? | You haven't said exactly what you are measuring. If it is count data then this paper is very helpful. I am curious about the nature of your measurements, since if you have a mean of 10 and a SD of 11, | Unequal variances t-test or U Mann-Whitney test?
You haven't said exactly what you are measuring. If it is count data then this paper is very helpful. I am curious about the nature of your measurements, since if you have a mean of 10 and a SD of 11, a negative number for a value one standard deviation below the mean ma... | Unequal variances t-test or U Mann-Whitney test?
You haven't said exactly what you are measuring. If it is count data then this paper is very helpful. I am curious about the nature of your measurements, since if you have a mean of 10 and a SD of 11, |
52,649 | Unequal variances t-test or U Mann-Whitney test? | Before using any test see if a log transform will make the variances more similar and if so then apply the test to the transformed values. Any conclusion that you might draw form log-transformed data will be equally applicable to the raw untransformed data. See my answeer to this question and the comments elicited for ... | Unequal variances t-test or U Mann-Whitney test? | Before using any test see if a log transform will make the variances more similar and if so then apply the test to the transformed values. Any conclusion that you might draw form log-transformed data | Unequal variances t-test or U Mann-Whitney test?
Before using any test see if a log transform will make the variances more similar and if so then apply the test to the transformed values. Any conclusion that you might draw form log-transformed data will be equally applicable to the raw untransformed data. See my answee... | Unequal variances t-test or U Mann-Whitney test?
Before using any test see if a log transform will make the variances more similar and if so then apply the test to the transformed values. Any conclusion that you might draw form log-transformed data |
52,650 | statsmodels: error in kde on a list of repeated values | I've never used the Python statsmodels package, and I'm not familiar with it, but based upon the error messages, I think I have a pretty good guess as to what is probably going on, and it's not a bug--the problem is with your input. According to wikipedia, a key step in Kernal Density Estimation is bandwidth estimatio... | statsmodels: error in kde on a list of repeated values | I've never used the Python statsmodels package, and I'm not familiar with it, but based upon the error messages, I think I have a pretty good guess as to what is probably going on, and it's not a bug- | statsmodels: error in kde on a list of repeated values
I've never used the Python statsmodels package, and I'm not familiar with it, but based upon the error messages, I think I have a pretty good guess as to what is probably going on, and it's not a bug--the problem is with your input. According to wikipedia, a key s... | statsmodels: error in kde on a list of repeated values
I've never used the Python statsmodels package, and I'm not familiar with it, but based upon the error messages, I think I have a pretty good guess as to what is probably going on, and it's not a bug- |
52,651 | statsmodels: error in kde on a list of repeated values | Float32 only has 1e-6 precision in numpy, therefore, if you are manipulating small numbers, similar instances could become identical (or very close) therefore producing singular or badly scaled matrices. This issue is particularly tricky to as there are no algebric reason for the desired inversion not to be possible. T... | statsmodels: error in kde on a list of repeated values | Float32 only has 1e-6 precision in numpy, therefore, if you are manipulating small numbers, similar instances could become identical (or very close) therefore producing singular or badly scaled matric | statsmodels: error in kde on a list of repeated values
Float32 only has 1e-6 precision in numpy, therefore, if you are manipulating small numbers, similar instances could become identical (or very close) therefore producing singular or badly scaled matrices. This issue is particularly tricky to as there are no algebric... | statsmodels: error in kde on a list of repeated values
Float32 only has 1e-6 precision in numpy, therefore, if you are manipulating small numbers, similar instances could become identical (or very close) therefore producing singular or badly scaled matric |
52,652 | What is the purpose of precision variables? | Regression coefficient is often characterisized as a partial correlation coefficient which means it will show effect of particular variable X to the outcome variable Y after effects of other variables, Z, are controlled.
What happens when you omit Z and leave only X? Do coefficient for X change?
If variables Z and... | What is the purpose of precision variables? | Regression coefficient is often characterisized as a partial correlation coefficient which means it will show effect of particular variable X to the outcome variable Y after effects of other variables | What is the purpose of precision variables?
Regression coefficient is often characterisized as a partial correlation coefficient which means it will show effect of particular variable X to the outcome variable Y after effects of other variables, Z, are controlled.
What happens when you omit Z and leave only X? Do co... | What is the purpose of precision variables?
Regression coefficient is often characterisized as a partial correlation coefficient which means it will show effect of particular variable X to the outcome variable Y after effects of other variables |
52,653 | What is the purpose of precision variables? | Here is my contribution to Anscombe's Quartet.
The below image shows a regression line on some imaginary data. The estimated regession line is $\hat{y}_{i} = 3 + .5x$, the p-value for the t-test of $H_{0}: \beta=0$ equals 0.002, and the $R^{2}$ for my regression model is 0.67 (just as for the four graphs in Anscombe, 1... | What is the purpose of precision variables? | Here is my contribution to Anscombe's Quartet.
The below image shows a regression line on some imaginary data. The estimated regession line is $\hat{y}_{i} = 3 + .5x$, the p-value for the t-test of $H | What is the purpose of precision variables?
Here is my contribution to Anscombe's Quartet.
The below image shows a regression line on some imaginary data. The estimated regession line is $\hat{y}_{i} = 3 + .5x$, the p-value for the t-test of $H_{0}: \beta=0$ equals 0.002, and the $R^{2}$ for my regression model is 0.67... | What is the purpose of precision variables?
Here is my contribution to Anscombe's Quartet.
The below image shows a regression line on some imaginary data. The estimated regession line is $\hat{y}_{i} = 3 + .5x$, the p-value for the t-test of $H |
52,654 | What is the purpose of precision variables? | Precision variables would help to reduce the standard errors and hence shrink confidence intervals on the coefficients that you are interested in, and hence make it easier to find significant effects of the variables you are interested in. | What is the purpose of precision variables? | Precision variables would help to reduce the standard errors and hence shrink confidence intervals on the coefficients that you are interested in, and hence make it easier to find significant effects | What is the purpose of precision variables?
Precision variables would help to reduce the standard errors and hence shrink confidence intervals on the coefficients that you are interested in, and hence make it easier to find significant effects of the variables you are interested in. | What is the purpose of precision variables?
Precision variables would help to reduce the standard errors and hence shrink confidence intervals on the coefficients that you are interested in, and hence make it easier to find significant effects |
52,655 | Regression for really small data with high degree of multicollinearity and outliers | My advice is "don't try to do this".
25 observations with 15 variables is very overfit, even if it satisfies all the assumptions of linear regression. Collinearity will mess up your standard errors and make the output highly sensitive to small changes in input. Outliers may well be influential points (although they m... | Regression for really small data with high degree of multicollinearity and outliers | My advice is "don't try to do this".
25 observations with 15 variables is very overfit, even if it satisfies all the assumptions of linear regression. Collinearity will mess up your standard errors | Regression for really small data with high degree of multicollinearity and outliers
My advice is "don't try to do this".
25 observations with 15 variables is very overfit, even if it satisfies all the assumptions of linear regression. Collinearity will mess up your standard errors and make the output highly sensitive... | Regression for really small data with high degree of multicollinearity and outliers
My advice is "don't try to do this".
25 observations with 15 variables is very overfit, even if it satisfies all the assumptions of linear regression. Collinearity will mess up your standard errors |
52,656 | Regression for really small data with high degree of multicollinearity and outliers | To begin in terms of an analytical framework...I would say you have 15 independent variables to choose from. You don't have 15 independent variables you have to include in your model. Given that, I have a couple of ideas. Hopefully one of them will be helpful. Before trying any of the following ideas, I would scrutini... | Regression for really small data with high degree of multicollinearity and outliers | To begin in terms of an analytical framework...I would say you have 15 independent variables to choose from. You don't have 15 independent variables you have to include in your model. Given that, I ha | Regression for really small data with high degree of multicollinearity and outliers
To begin in terms of an analytical framework...I would say you have 15 independent variables to choose from. You don't have 15 independent variables you have to include in your model. Given that, I have a couple of ideas. Hopefully one ... | Regression for really small data with high degree of multicollinearity and outliers
To begin in terms of an analytical framework...I would say you have 15 independent variables to choose from. You don't have 15 independent variables you have to include in your model. Given that, I ha |
52,657 | Regression for really small data with high degree of multicollinearity and outliers | if this is a survey analysis, then you might want to try something called "structural equation modeling". it's an entire field in qualitative analysis, but you can get it working quickly with software like Stata.
the fact that you say your data is collinear is exactly the problem with which SEM deals with. | Regression for really small data with high degree of multicollinearity and outliers | if this is a survey analysis, then you might want to try something called "structural equation modeling". it's an entire field in qualitative analysis, but you can get it working quickly with software | Regression for really small data with high degree of multicollinearity and outliers
if this is a survey analysis, then you might want to try something called "structural equation modeling". it's an entire field in qualitative analysis, but you can get it working quickly with software like Stata.
the fact that you say y... | Regression for really small data with high degree of multicollinearity and outliers
if this is a survey analysis, then you might want to try something called "structural equation modeling". it's an entire field in qualitative analysis, but you can get it working quickly with software |
52,658 | How can I interpret this scatterplot? | Assuming the dots are your observations, the vectors seem to express upper and lower bounds on the range of $y$ as a function of $x$. The correlation appears weakly negative at a glance, but I wouldn't really trust my eyeballs to estimate Pearson's $r$. What does seem clear enough is that $y$ exhibits heteroscedasticit... | How can I interpret this scatterplot? | Assuming the dots are your observations, the vectors seem to express upper and lower bounds on the range of $y$ as a function of $x$. The correlation appears weakly negative at a glance, but I wouldn' | How can I interpret this scatterplot?
Assuming the dots are your observations, the vectors seem to express upper and lower bounds on the range of $y$ as a function of $x$. The correlation appears weakly negative at a glance, but I wouldn't really trust my eyeballs to estimate Pearson's $r$. What does seem clear enough ... | How can I interpret this scatterplot?
Assuming the dots are your observations, the vectors seem to express upper and lower bounds on the range of $y$ as a function of $x$. The correlation appears weakly negative at a glance, but I wouldn' |
52,659 | Can nonstationarity be told from the autocorrelation function? | It is possible to get a general formula for stationary ARMA(p,q) autocovariance function. Suppose $X_t$ is a (zero mean) stationary solution of an ARMA(p,q) equation:
$$\phi(B)X_t=\theta(B)Z_t$$
Multiply this equation by $X_{t-h}$, $h>q$, take expectations and you will get
$$r(h)-\phi_1r(h-1)-...-\phi_pr(h-p)=0$$
This ... | Can nonstationarity be told from the autocorrelation function? | It is possible to get a general formula for stationary ARMA(p,q) autocovariance function. Suppose $X_t$ is a (zero mean) stationary solution of an ARMA(p,q) equation:
$$\phi(B)X_t=\theta(B)Z_t$$
Multi | Can nonstationarity be told from the autocorrelation function?
It is possible to get a general formula for stationary ARMA(p,q) autocovariance function. Suppose $X_t$ is a (zero mean) stationary solution of an ARMA(p,q) equation:
$$\phi(B)X_t=\theta(B)Z_t$$
Multiply this equation by $X_{t-h}$, $h>q$, take expectations ... | Can nonstationarity be told from the autocorrelation function?
It is possible to get a general formula for stationary ARMA(p,q) autocovariance function. Suppose $X_t$ is a (zero mean) stationary solution of an ARMA(p,q) equation:
$$\phi(B)X_t=\theta(B)Z_t$$
Multi |
52,660 | Can nonstationarity be told from the autocorrelation function? | (1) A stationary ARMA process has a "rapidly" decaying acf because the acf shows the extent to which previous observations predict the current observation. An AR(1) model would have one significant lag, and AR(2) would have two significant lags....and so on.
Strictly speaking, an ACF cannot tell you whether the time s... | Can nonstationarity be told from the autocorrelation function? | (1) A stationary ARMA process has a "rapidly" decaying acf because the acf shows the extent to which previous observations predict the current observation. An AR(1) model would have one significant la | Can nonstationarity be told from the autocorrelation function?
(1) A stationary ARMA process has a "rapidly" decaying acf because the acf shows the extent to which previous observations predict the current observation. An AR(1) model would have one significant lag, and AR(2) would have two significant lags....and so on... | Can nonstationarity be told from the autocorrelation function?
(1) A stationary ARMA process has a "rapidly" decaying acf because the acf shows the extent to which previous observations predict the current observation. An AR(1) model would have one significant la |
52,661 | Can nonstationarity be told from the autocorrelation function? | As @Clayton pointed out sample autocorrelation function cannot tell if series is non-stationary.
Problem is that there is various levels of non-stationarity, deterministic OR stochastic trends are just one way time series to be non-stationary.
Non-constant variance can be also problem even when expected value is inde... | Can nonstationarity be told from the autocorrelation function? | As @Clayton pointed out sample autocorrelation function cannot tell if series is non-stationary.
Problem is that there is various levels of non-stationarity, deterministic OR stochastic trends are ju | Can nonstationarity be told from the autocorrelation function?
As @Clayton pointed out sample autocorrelation function cannot tell if series is non-stationary.
Problem is that there is various levels of non-stationarity, deterministic OR stochastic trends are just one way time series to be non-stationary.
Non-constan... | Can nonstationarity be told from the autocorrelation function?
As @Clayton pointed out sample autocorrelation function cannot tell if series is non-stationary.
Problem is that there is various levels of non-stationarity, deterministic OR stochastic trends are ju |
52,662 | Cholesky update for removing row | The usual approach involves interchanging the position of the column you want removed and the last one, and returning the Cholesky to triangular form via either Givens rotations or Householder transforms, whereupon you can simply drop the last one.
Similarly you can update an additional column into any position by add... | Cholesky update for removing row | The usual approach involves interchanging the position of the column you want removed and the last one, and returning the Cholesky to triangular form via either Givens rotations or Householder transfo | Cholesky update for removing row
The usual approach involves interchanging the position of the column you want removed and the last one, and returning the Cholesky to triangular form via either Givens rotations or Householder transforms, whereupon you can simply drop the last one.
Similarly you can update an additiona... | Cholesky update for removing row
The usual approach involves interchanging the position of the column you want removed and the last one, and returning the Cholesky to triangular form via either Givens rotations or Householder transfo |
52,663 | Is it possible to train a one-class SVM to have zero training error? | As @Joe already mentioned, $\nu$:
sets an upper bound on the fraction of outliers (training examples regarded out-of-class) and,
serves as a lower bound on the number of training examples used as Support Vector.
Mathematically, the quadratic programming minimization function is:
So if $\nu$ is too small, the problem... | Is it possible to train a one-class SVM to have zero training error? | As @Joe already mentioned, $\nu$:
sets an upper bound on the fraction of outliers (training examples regarded out-of-class) and,
serves as a lower bound on the number of training examples used as Sup | Is it possible to train a one-class SVM to have zero training error?
As @Joe already mentioned, $\nu$:
sets an upper bound on the fraction of outliers (training examples regarded out-of-class) and,
serves as a lower bound on the number of training examples used as Support Vector.
Mathematically, the quadratic program... | Is it possible to train a one-class SVM to have zero training error?
As @Joe already mentioned, $\nu$:
sets an upper bound on the fraction of outliers (training examples regarded out-of-class) and,
serves as a lower bound on the number of training examples used as Sup |
52,664 | Is it possible to train a one-class SVM to have zero training error? | Can I achieve zero training error in an SVM?
Yes, but only if the data is separable. The separability of a dataset might depend on the kernel function you're using (e.g., if you're using the dot product, then "separable" = "linearly separable"), but some data sets aren't separable under any kernel function, for example... | Is it possible to train a one-class SVM to have zero training error? | Can I achieve zero training error in an SVM?
Yes, but only if the data is separable. The separability of a dataset might depend on the kernel function you're using (e.g., if you're using the dot produ | Is it possible to train a one-class SVM to have zero training error?
Can I achieve zero training error in an SVM?
Yes, but only if the data is separable. The separability of a dataset might depend on the kernel function you're using (e.g., if you're using the dot product, then "separable" = "linearly separable"), but s... | Is it possible to train a one-class SVM to have zero training error?
Can I achieve zero training error in an SVM?
Yes, but only if the data is separable. The separability of a dataset might depend on the kernel function you're using (e.g., if you're using the dot produ |
52,665 | Non-Stationary Time Series Forecasting | I don't know what "non-stationary limited data" means. So I will assume you mean "non-stationary data".
Exponential smoothing methods including Holt-Winters methods are appropriate for (some kinds of) non-stationary data. In fact, they are only really appropriate if the data are non-stationary. Using an exponential smo... | Non-Stationary Time Series Forecasting | I don't know what "non-stationary limited data" means. So I will assume you mean "non-stationary data".
Exponential smoothing methods including Holt-Winters methods are appropriate for (some kinds of) | Non-Stationary Time Series Forecasting
I don't know what "non-stationary limited data" means. So I will assume you mean "non-stationary data".
Exponential smoothing methods including Holt-Winters methods are appropriate for (some kinds of) non-stationary data. In fact, they are only really appropriate if the data are n... | Non-Stationary Time Series Forecasting
I don't know what "non-stationary limited data" means. So I will assume you mean "non-stationary data".
Exponential smoothing methods including Holt-Winters methods are appropriate for (some kinds of) |
52,666 | Non-Stationary Time Series Forecasting | There is no problem with forecasting nonstationary data directly. Take the random walk
$$Y_t=Y_{t-1}+\epsilon_t$$
The best predictor of $Y_{t+1}$ given the information set $\{Y_t,Y_{t-1},...\}$ simply is
$$E(Y_{t+1}|Y_t)=E(Y_t|Y_{t})+E(\epsilon_{t+1}|Y_t)=Y_t$$ | Non-Stationary Time Series Forecasting | There is no problem with forecasting nonstationary data directly. Take the random walk
$$Y_t=Y_{t-1}+\epsilon_t$$
The best predictor of $Y_{t+1}$ given the information set $\{Y_t,Y_{t-1},...\}$ simply | Non-Stationary Time Series Forecasting
There is no problem with forecasting nonstationary data directly. Take the random walk
$$Y_t=Y_{t-1}+\epsilon_t$$
The best predictor of $Y_{t+1}$ given the information set $\{Y_t,Y_{t-1},...\}$ simply is
$$E(Y_{t+1}|Y_t)=E(Y_t|Y_{t})+E(\epsilon_{t+1}|Y_t)=Y_t$$ | Non-Stationary Time Series Forecasting
There is no problem with forecasting nonstationary data directly. Take the random walk
$$Y_t=Y_{t-1}+\epsilon_t$$
The best predictor of $Y_{t+1}$ given the information set $\{Y_t,Y_{t-1},...\}$ simply |
52,667 | Non-Stationary Time Series Forecasting | Stationarity refers to uniformity in the properties of the data. If you know that the data is non-stationary, it means that the useful properties of the data cannot be assumed to be the same for the entire series. Under such an assumption, why do you want to apply the same filter or model to the entire series ?
My sugg... | Non-Stationary Time Series Forecasting | Stationarity refers to uniformity in the properties of the data. If you know that the data is non-stationary, it means that the useful properties of the data cannot be assumed to be the same for the e | Non-Stationary Time Series Forecasting
Stationarity refers to uniformity in the properties of the data. If you know that the data is non-stationary, it means that the useful properties of the data cannot be assumed to be the same for the entire series. Under such an assumption, why do you want to apply the same filter ... | Non-Stationary Time Series Forecasting
Stationarity refers to uniformity in the properties of the data. If you know that the data is non-stationary, it means that the useful properties of the data cannot be assumed to be the same for the e |
52,668 | Updating variance of a dataset [duplicate] | In the absence of information to the contrary I assume you want univariate calculations and you want the $n-1$-denominator version of variance.
One useful way is to update the sums of squares of deviations from the mean, which I'll call SSE.
Let's say that at time $t$ you have $\bar x$, $\text{SSE}$ and $s^2$, and an ... | Updating variance of a dataset [duplicate] | In the absence of information to the contrary I assume you want univariate calculations and you want the $n-1$-denominator version of variance.
One useful way is to update the sums of squares of devia | Updating variance of a dataset [duplicate]
In the absence of information to the contrary I assume you want univariate calculations and you want the $n-1$-denominator version of variance.
One useful way is to update the sums of squares of deviations from the mean, which I'll call SSE.
Let's say that at time $t$ you hav... | Updating variance of a dataset [duplicate]
In the absence of information to the contrary I assume you want univariate calculations and you want the $n-1$-denominator version of variance.
One useful way is to update the sums of squares of devia |
52,669 | Updating variance of a dataset [duplicate] | That is not really a question for CrossValidated, but here it comes: you only need to store three values:
current number of variables,
current sum of squares of the variables
current sum of the variables.
That's because variance can be expressed in terms of $\sum x_i^2$ and $(\sum x_i)^2$.
$var(X) = \frac{\sum (\b... | Updating variance of a dataset [duplicate] | That is not really a question for CrossValidated, but here it comes: you only need to store three values:
current number of variables,
current sum of squares of the variables
current sum of the var | Updating variance of a dataset [duplicate]
That is not really a question for CrossValidated, but here it comes: you only need to store three values:
current number of variables,
current sum of squares of the variables
current sum of the variables.
That's because variance can be expressed in terms of $\sum x_i^2$ a... | Updating variance of a dataset [duplicate]
That is not really a question for CrossValidated, but here it comes: you only need to store three values:
current number of variables,
current sum of squares of the variables
current sum of the var |
52,670 | Bernoulli random variable parameter estimation | Instead of tedious derivations, simply invoke the invariance property of MLEs. Then solve for $x$ using basic algebra. However, note that this approach will lead to the same estimator you derived, i.e., $\hat{x}=-\log(2m/n -1)$.
So what to do? First, ignore estimation for the moment. Look at what the true value of $x$ ... | Bernoulli random variable parameter estimation | Instead of tedious derivations, simply invoke the invariance property of MLEs. Then solve for $x$ using basic algebra. However, note that this approach will lead to the same estimator you derived, i.e | Bernoulli random variable parameter estimation
Instead of tedious derivations, simply invoke the invariance property of MLEs. Then solve for $x$ using basic algebra. However, note that this approach will lead to the same estimator you derived, i.e., $\hat{x}=-\log(2m/n -1)$.
So what to do? First, ignore estimation for ... | Bernoulli random variable parameter estimation
Instead of tedious derivations, simply invoke the invariance property of MLEs. Then solve for $x$ using basic algebra. However, note that this approach will lead to the same estimator you derived, i.e |
52,671 | Bernoulli random variable parameter estimation | Since your knowledge about $\theta$ restricts the parameter space to $\Theta = (\tfrac{1}{2}, 1)$, you need to respect that when solving for the maximum likelihood. In other words, the maximum likelihood estimator is the solution to the constrained maximization problem, not the unconstrained maximization problem you've... | Bernoulli random variable parameter estimation | Since your knowledge about $\theta$ restricts the parameter space to $\Theta = (\tfrac{1}{2}, 1)$, you need to respect that when solving for the maximum likelihood. In other words, the maximum likelih | Bernoulli random variable parameter estimation
Since your knowledge about $\theta$ restricts the parameter space to $\Theta = (\tfrac{1}{2}, 1)$, you need to respect that when solving for the maximum likelihood. In other words, the maximum likelihood estimator is the solution to the constrained maximization problem, no... | Bernoulli random variable parameter estimation
Since your knowledge about $\theta$ restricts the parameter space to $\Theta = (\tfrac{1}{2}, 1)$, you need to respect that when solving for the maximum likelihood. In other words, the maximum likelih |
52,672 | Is the model wrong if a coefficient changes from minus in correlation table to plus in OLS? | No, this doesn't imply 'the model is wrong' in the least. It's telling you that you should be wary of interpreting raw correlations when other important variables exist.
Here's a set of data I just generated (in R). The sample correlation between y and x1 is negative:
print(cor(cbind(y,x1,x2)),d=3)
y x1 ... | Is the model wrong if a coefficient changes from minus in correlation table to plus in OLS? | No, this doesn't imply 'the model is wrong' in the least. It's telling you that you should be wary of interpreting raw correlations when other important variables exist.
Here's a set of data I just ge | Is the model wrong if a coefficient changes from minus in correlation table to plus in OLS?
No, this doesn't imply 'the model is wrong' in the least. It's telling you that you should be wary of interpreting raw correlations when other important variables exist.
Here's a set of data I just generated (in R). The sample c... | Is the model wrong if a coefficient changes from minus in correlation table to plus in OLS?
No, this doesn't imply 'the model is wrong' in the least. It's telling you that you should be wary of interpreting raw correlations when other important variables exist.
Here's a set of data I just ge |
52,673 | Is the model wrong if a coefficient changes from minus in correlation table to plus in OLS? | In addition to looking at the coefficients, you should also look at their confidence intervals. If the interval is quite wide then a change from $0.351$ to $-0.150$ could be explained by random chance. Even if the intervals are narrow (and show significant difference) a change in sign is not uncommon.
Remember that t... | Is the model wrong if a coefficient changes from minus in correlation table to plus in OLS? | In addition to looking at the coefficients, you should also look at their confidence intervals. If the interval is quite wide then a change from $0.351$ to $-0.150$ could be explained by random chanc | Is the model wrong if a coefficient changes from minus in correlation table to plus in OLS?
In addition to looking at the coefficients, you should also look at their confidence intervals. If the interval is quite wide then a change from $0.351$ to $-0.150$ could be explained by random chance. Even if the intervals ar... | Is the model wrong if a coefficient changes from minus in correlation table to plus in OLS?
In addition to looking at the coefficients, you should also look at their confidence intervals. If the interval is quite wide then a change from $0.351$ to $-0.150$ could be explained by random chanc |
52,674 | Strange outcome when performing nonlinear least squares fit to a power law | It would be fairly unusual to find power law data for which the variance is actually constant across $x$ values. However, let's take that constant variance as given and proceed with the analysis as a least squares problem.
The easy way to fit this particular model is actually to use GLMs, not NLS! No need for starting ... | Strange outcome when performing nonlinear least squares fit to a power law | It would be fairly unusual to find power law data for which the variance is actually constant across $x$ values. However, let's take that constant variance as given and proceed with the analysis as a | Strange outcome when performing nonlinear least squares fit to a power law
It would be fairly unusual to find power law data for which the variance is actually constant across $x$ values. However, let's take that constant variance as given and proceed with the analysis as a least squares problem.
The easy way to fit th... | Strange outcome when performing nonlinear least squares fit to a power law
It would be fairly unusual to find power law data for which the variance is actually constant across $x$ values. However, let's take that constant variance as given and proceed with the analysis as a |
52,675 | Strange outcome when performing nonlinear least squares fit to a power law | Now that you have explored a couple ways of fitting a power-law, why not try out the recommended way. For the continuous case, the MLE for the scaling parameter is:
$$\hat \alpha = 1 + n \left[ \sum_{i=1}^n ln \frac{x_i}{x_{min}} \right]$$
One of the authors offers additional (somewhat acerbic) advice in his blog; he s... | Strange outcome when performing nonlinear least squares fit to a power law | Now that you have explored a couple ways of fitting a power-law, why not try out the recommended way. For the continuous case, the MLE for the scaling parameter is:
$$\hat \alpha = 1 + n \left[ \sum_{ | Strange outcome when performing nonlinear least squares fit to a power law
Now that you have explored a couple ways of fitting a power-law, why not try out the recommended way. For the continuous case, the MLE for the scaling parameter is:
$$\hat \alpha = 1 + n \left[ \sum_{i=1}^n ln \frac{x_i}{x_{min}} \right]$$
One o... | Strange outcome when performing nonlinear least squares fit to a power law
Now that you have explored a couple ways of fitting a power-law, why not try out the recommended way. For the continuous case, the MLE for the scaling parameter is:
$$\hat \alpha = 1 + n \left[ \sum_{ |
52,676 | Strange outcome when performing nonlinear least squares fit to a power law | The problem with your nonlinear regression is your initial estimate of A. You say you set the initial value to 1.0 "because it doesn't seem to matter". Try plotting a curve using your initial values, and you'll see that it is very far away from your data points, so far that the nonlinear regression algorithm is stuck a... | Strange outcome when performing nonlinear least squares fit to a power law | The problem with your nonlinear regression is your initial estimate of A. You say you set the initial value to 1.0 "because it doesn't seem to matter". Try plotting a curve using your initial values, | Strange outcome when performing nonlinear least squares fit to a power law
The problem with your nonlinear regression is your initial estimate of A. You say you set the initial value to 1.0 "because it doesn't seem to matter". Try plotting a curve using your initial values, and you'll see that it is very far away from ... | Strange outcome when performing nonlinear least squares fit to a power law
The problem with your nonlinear regression is your initial estimate of A. You say you set the initial value to 1.0 "because it doesn't seem to matter". Try plotting a curve using your initial values, |
52,677 | Why is the k-means algorithm minimizing the within cluster variance? | Within-cluster-variance is a simple to understand measure of compactness (there are others, too).
So basically, the objective is to find the most compact partitioning of the data set into $k$ partitions.
K-Means, in the Lloyd version, actually originated from 1d PCM data as far as I know. So assuming you have a really ... | Why is the k-means algorithm minimizing the within cluster variance? | Within-cluster-variance is a simple to understand measure of compactness (there are others, too).
So basically, the objective is to find the most compact partitioning of the data set into $k$ partitio | Why is the k-means algorithm minimizing the within cluster variance?
Within-cluster-variance is a simple to understand measure of compactness (there are others, too).
So basically, the objective is to find the most compact partitioning of the data set into $k$ partitions.
K-Means, in the Lloyd version, actually origina... | Why is the k-means algorithm minimizing the within cluster variance?
Within-cluster-variance is a simple to understand measure of compactness (there are others, too).
So basically, the objective is to find the most compact partitioning of the data set into $k$ partitio |
52,678 | Why is the k-means algorithm minimizing the within cluster variance? | There are several questions here at very different levels. In essence every text on cluster analysis is an answer. You have to keep reading!
Variance is at one level just one statistical standard which statistical people find convenient to think about. Roughly, minimising variance encourages -- nay, enforces -- cluste... | Why is the k-means algorithm minimizing the within cluster variance? | There are several questions here at very different levels. In essence every text on cluster analysis is an answer. You have to keep reading!
Variance is at one level just one statistical standard whi | Why is the k-means algorithm minimizing the within cluster variance?
There are several questions here at very different levels. In essence every text on cluster analysis is an answer. You have to keep reading!
Variance is at one level just one statistical standard which statistical people find convenient to think abou... | Why is the k-means algorithm minimizing the within cluster variance?
There are several questions here at very different levels. In essence every text on cluster analysis is an answer. You have to keep reading!
Variance is at one level just one statistical standard whi |
52,679 | Which glm algorithm to use when predictors are numerical as well as categorical? | When your dependent variable is binary ($1$ vs. $0$, "dead" vs. "alive"), the you might use logistic regression which is a glm with a binomial error distribution and a logit link function. When your dependent variable is ordinal (e.g. "bad"> "good" > "best"), you can use ordinal logistic regression. For a nominal (e.g.... | Which glm algorithm to use when predictors are numerical as well as categorical? | When your dependent variable is binary ($1$ vs. $0$, "dead" vs. "alive"), the you might use logistic regression which is a glm with a binomial error distribution and a logit link function. When your d | Which glm algorithm to use when predictors are numerical as well as categorical?
When your dependent variable is binary ($1$ vs. $0$, "dead" vs. "alive"), the you might use logistic regression which is a glm with a binomial error distribution and a logit link function. When your dependent variable is ordinal (e.g. "bad... | Which glm algorithm to use when predictors are numerical as well as categorical?
When your dependent variable is binary ($1$ vs. $0$, "dead" vs. "alive"), the you might use logistic regression which is a glm with a binomial error distribution and a logit link function. When your d |
52,680 | Which glm algorithm to use when predictors are numerical as well as categorical? | The algorithm used by any implementation of generalised linear models is immaterial here -- or at least if there are grounds to choose one algorithm rather than another they don't hinge on any detail you mention.
Typically you present categorical predictors to GLM commands or functions as indicator variables (dummy va... | Which glm algorithm to use when predictors are numerical as well as categorical? | The algorithm used by any implementation of generalised linear models is immaterial here -- or at least if there are grounds to choose one algorithm rather than another they don't hinge on any detail | Which glm algorithm to use when predictors are numerical as well as categorical?
The algorithm used by any implementation of generalised linear models is immaterial here -- or at least if there are grounds to choose one algorithm rather than another they don't hinge on any detail you mention.
Typically you present cat... | Which glm algorithm to use when predictors are numerical as well as categorical?
The algorithm used by any implementation of generalised linear models is immaterial here -- or at least if there are grounds to choose one algorithm rather than another they don't hinge on any detail |
52,681 | Which glm algorithm to use when predictors are numerical as well as categorical? | glm requires that all variables be numeric. Typically, you convert categorical variables to numeric variables using dummy variables. | Which glm algorithm to use when predictors are numerical as well as categorical? | glm requires that all variables be numeric. Typically, you convert categorical variables to numeric variables using dummy variables. | Which glm algorithm to use when predictors are numerical as well as categorical?
glm requires that all variables be numeric. Typically, you convert categorical variables to numeric variables using dummy variables. | Which glm algorithm to use when predictors are numerical as well as categorical?
glm requires that all variables be numeric. Typically, you convert categorical variables to numeric variables using dummy variables. |
52,682 | Homogeneity testing of baseline characteristics in medical trials | It is generally thought nowadays that testing for baseline differences in randomized experiments is misleading. Stephen Senn's book Statistical Issues in Drug Development discusses this. One of the many issues involved is that you never know when to stop. How many uncollected variables do you go back and collect in ... | Homogeneity testing of baseline characteristics in medical trials | It is generally thought nowadays that testing for baseline differences in randomized experiments is misleading. Stephen Senn's book Statistical Issues in Drug Development discusses this. One of the | Homogeneity testing of baseline characteristics in medical trials
It is generally thought nowadays that testing for baseline differences in randomized experiments is misleading. Stephen Senn's book Statistical Issues in Drug Development discusses this. One of the many issues involved is that you never know when to st... | Homogeneity testing of baseline characteristics in medical trials
It is generally thought nowadays that testing for baseline differences in randomized experiments is misleading. Stephen Senn's book Statistical Issues in Drug Development discusses this. One of the |
52,683 | Homogeneity testing of baseline characteristics in medical trials | This is not actually an answer to your question but the logic behind such tests seems fundamentally misguided, no matter what the specifics are.
If treatment assignment is not or cannot be properly randomized, showing that both groups have approximately the same characteristics on some arbitrary set of variables is not... | Homogeneity testing of baseline characteristics in medical trials | This is not actually an answer to your question but the logic behind such tests seems fundamentally misguided, no matter what the specifics are.
If treatment assignment is not or cannot be properly ra | Homogeneity testing of baseline characteristics in medical trials
This is not actually an answer to your question but the logic behind such tests seems fundamentally misguided, no matter what the specifics are.
If treatment assignment is not or cannot be properly randomized, showing that both groups have approximately ... | Homogeneity testing of baseline characteristics in medical trials
This is not actually an answer to your question but the logic behind such tests seems fundamentally misguided, no matter what the specifics are.
If treatment assignment is not or cannot be properly ra |
52,684 | Is there a simple rule for interpretation of Interactions (and their directions) in binary logistic regression? [duplicate] | A positive interaction effect between A and B means that when A increases, the effect (in this case log odds ratio) of B increases. A negative interaction effect means that when A increases, the effect of B decreases.
When interpreting the results, I often find it easiest to work in the odds metric rather than the log... | Is there a simple rule for interpretation of Interactions (and their directions) in binary logistic | A positive interaction effect between A and B means that when A increases, the effect (in this case log odds ratio) of B increases. A negative interaction effect means that when A increases, the effec | Is there a simple rule for interpretation of Interactions (and their directions) in binary logistic regression? [duplicate]
A positive interaction effect between A and B means that when A increases, the effect (in this case log odds ratio) of B increases. A negative interaction effect means that when A increases, the e... | Is there a simple rule for interpretation of Interactions (and their directions) in binary logistic
A positive interaction effect between A and B means that when A increases, the effect (in this case log odds ratio) of B increases. A negative interaction effect means that when A increases, the effec |
52,685 | Is there a simple rule for interpretation of Interactions (and their directions) in binary logistic regression? [duplicate] | I'm not familiar with binary logistic regression, but in interaction effects in general, the way you understand them is by plotting (usually means, perhaps different in this case?). That will allow you to see the relationship between different levels and state the interaction effect specifically. | Is there a simple rule for interpretation of Interactions (and their directions) in binary logistic | I'm not familiar with binary logistic regression, but in interaction effects in general, the way you understand them is by plotting (usually means, perhaps different in this case?). That will allow y | Is there a simple rule for interpretation of Interactions (and their directions) in binary logistic regression? [duplicate]
I'm not familiar with binary logistic regression, but in interaction effects in general, the way you understand them is by plotting (usually means, perhaps different in this case?). That will all... | Is there a simple rule for interpretation of Interactions (and their directions) in binary logistic
I'm not familiar with binary logistic regression, but in interaction effects in general, the way you understand them is by plotting (usually means, perhaps different in this case?). That will allow y |
52,686 | Paired t-test and two-sample t-test | It would be bad -- very bad. If you ignore the pairing and use a two-sample t-test where you should have used the paired, chances are that you will not be able to detect the effect of interest. In this case, between subject variation is included in the estimate of variance used to measure the effect of interest. The va... | Paired t-test and two-sample t-test | It would be bad -- very bad. If you ignore the pairing and use a two-sample t-test where you should have used the paired, chances are that you will not be able to detect the effect of interest. In thi | Paired t-test and two-sample t-test
It would be bad -- very bad. If you ignore the pairing and use a two-sample t-test where you should have used the paired, chances are that you will not be able to detect the effect of interest. In this case, between subject variation is included in the estimate of variance used to me... | Paired t-test and two-sample t-test
It would be bad -- very bad. If you ignore the pairing and use a two-sample t-test where you should have used the paired, chances are that you will not be able to detect the effect of interest. In thi |
52,687 | Paired t-test and two-sample t-test | I thought I'd post R code here to illustrate the point that I made in the comments to Placidia's answer above (which I like, but I wanted to go into more detail on this particular point.) This is the working that went into that comment.
The following code imposes random pairings of observations from two independent sam... | Paired t-test and two-sample t-test | I thought I'd post R code here to illustrate the point that I made in the comments to Placidia's answer above (which I like, but I wanted to go into more detail on this particular point.) This is the | Paired t-test and two-sample t-test
I thought I'd post R code here to illustrate the point that I made in the comments to Placidia's answer above (which I like, but I wanted to go into more detail on this particular point.) This is the working that went into that comment.
The following code imposes random pairings of o... | Paired t-test and two-sample t-test
I thought I'd post R code here to illustrate the point that I made in the comments to Placidia's answer above (which I like, but I wanted to go into more detail on this particular point.) This is the |
52,688 | Who are some famous USSR/Russian Statistics/probability academic researchers? [closed] | It is hard to underestimate the contribution of Andrey Kolmogorov, for putting probability theory on a rigorous mathematical footing during the Soviet era.
Also, Andrey Markov, for his contribution to stochastic processes and Markov chains in particular, though most of his work was in the pre-Soviet era.
Possibly worth... | Who are some famous USSR/Russian Statistics/probability academic researchers? [closed] | It is hard to underestimate the contribution of Andrey Kolmogorov, for putting probability theory on a rigorous mathematical footing during the Soviet era.
Also, Andrey Markov, for his contribution to | Who are some famous USSR/Russian Statistics/probability academic researchers? [closed]
It is hard to underestimate the contribution of Andrey Kolmogorov, for putting probability theory on a rigorous mathematical footing during the Soviet era.
Also, Andrey Markov, for his contribution to stochastic processes and Markov ... | Who are some famous USSR/Russian Statistics/probability academic researchers? [closed]
It is hard to underestimate the contribution of Andrey Kolmogorov, for putting probability theory on a rigorous mathematical footing during the Soviet era.
Also, Andrey Markov, for his contribution to |
52,689 | Who are some famous USSR/Russian Statistics/probability academic researchers? [closed] | Vladimir Vapnik - important contributions to computational learning theory (e.g. VC theory) and an inventor of the support vector machine. | Who are some famous USSR/Russian Statistics/probability academic researchers? [closed] | Vladimir Vapnik - important contributions to computational learning theory (e.g. VC theory) and an inventor of the support vector machine. | Who are some famous USSR/Russian Statistics/probability academic researchers? [closed]
Vladimir Vapnik - important contributions to computational learning theory (e.g. VC theory) and an inventor of the support vector machine. | Who are some famous USSR/Russian Statistics/probability academic researchers? [closed]
Vladimir Vapnik - important contributions to computational learning theory (e.g. VC theory) and an inventor of the support vector machine. |
52,690 | Who are some famous USSR/Russian Statistics/probability academic researchers? [closed] | As @PSellaz mentions, Kolmogorov's contributions are very fundamental and include the standard axiomatization of the notion of probability (there are other ways to define a probability, but they aren't as well known as Kolmogorov's definition.) You might have also heard of Kolmogorov-Smirnov test and Kolmogorov's 0-1 T... | Who are some famous USSR/Russian Statistics/probability academic researchers? [closed] | As @PSellaz mentions, Kolmogorov's contributions are very fundamental and include the standard axiomatization of the notion of probability (there are other ways to define a probability, but they aren' | Who are some famous USSR/Russian Statistics/probability academic researchers? [closed]
As @PSellaz mentions, Kolmogorov's contributions are very fundamental and include the standard axiomatization of the notion of probability (there are other ways to define a probability, but they aren't as well known as Kolmogorov's d... | Who are some famous USSR/Russian Statistics/probability academic researchers? [closed]
As @PSellaz mentions, Kolmogorov's contributions are very fundamental and include the standard axiomatization of the notion of probability (there are other ways to define a probability, but they aren' |
52,691 | Who are some famous USSR/Russian Statistics/probability academic researchers? [closed] | USSR was strong in both probability and statistics, but after breakdown of USSR many of the most prominent scientists leaved Russia and have worked during a long term in Western Universities. However, some of them now work partially in Russia.
I don't say that I mention all of prominent statistics with deep connection... | Who are some famous USSR/Russian Statistics/probability academic researchers? [closed] | USSR was strong in both probability and statistics, but after breakdown of USSR many of the most prominent scientists leaved Russia and have worked during a long term in Western Universities. However, | Who are some famous USSR/Russian Statistics/probability academic researchers? [closed]
USSR was strong in both probability and statistics, but after breakdown of USSR many of the most prominent scientists leaved Russia and have worked during a long term in Western Universities. However, some of them now work partially ... | Who are some famous USSR/Russian Statistics/probability academic researchers? [closed]
USSR was strong in both probability and statistics, but after breakdown of USSR many of the most prominent scientists leaved Russia and have worked during a long term in Western Universities. However, |
52,692 | Partitioning data for k-fold cross validation that will not have equal partitions | Usually the $k$-fold cross validation subsets have approximately equal size. It is just crucial that they don't overlap.
For example I just had a look at what WEKA does. Say that you have $N$ instances and $k$ folds, then
$$ r = N \mod k $$
(the remainder of $N$ divided by $k$) is the number of surplus records. The f... | Partitioning data for k-fold cross validation that will not have equal partitions | Usually the $k$-fold cross validation subsets have approximately equal size. It is just crucial that they don't overlap.
For example I just had a look at what WEKA does. Say that you have $N$ instanc | Partitioning data for k-fold cross validation that will not have equal partitions
Usually the $k$-fold cross validation subsets have approximately equal size. It is just crucial that they don't overlap.
For example I just had a look at what WEKA does. Say that you have $N$ instances and $k$ folds, then
$$ r = N \mod k... | Partitioning data for k-fold cross validation that will not have equal partitions
Usually the $k$-fold cross validation subsets have approximately equal size. It is just crucial that they don't overlap.
For example I just had a look at what WEKA does. Say that you have $N$ instanc |
52,693 | Partitioning data for k-fold cross validation that will not have equal partitions | As Simone said, it's usually not essential for each fold to be exactly the same size. It'd be perfectly reasonable to have six folds containing eight records and four containing seven records each. That's probably a better solution than having nine folds of size seven and shoving the excess into the last one.
10-fold c... | Partitioning data for k-fold cross validation that will not have equal partitions | As Simone said, it's usually not essential for each fold to be exactly the same size. It'd be perfectly reasonable to have six folds containing eight records and four containing seven records each. Th | Partitioning data for k-fold cross validation that will not have equal partitions
As Simone said, it's usually not essential for each fold to be exactly the same size. It'd be perfectly reasonable to have six folds containing eight records and four containing seven records each. That's probably a better solution than h... | Partitioning data for k-fold cross validation that will not have equal partitions
As Simone said, it's usually not essential for each fold to be exactly the same size. It'd be perfectly reasonable to have six folds containing eight records and four containing seven records each. Th |
52,694 | Partitioning data for k-fold cross validation that will not have equal partitions | You may want to use kfoldcv function to calculate sample sizes for the k groups.
kfoldcv(k, N, nlevel=NULL)
Arguments:
k number of groups.
N total sample size.
nlevel a vector of sample sizes for stratified sampling.
You will have to install the ipred package. | Partitioning data for k-fold cross validation that will not have equal partitions | You may want to use kfoldcv function to calculate sample sizes for the k groups.
kfoldcv(k, N, nlevel=NULL)
Arguments:
k number of groups.
N total sample size.
nlevel a vector of sample sizes | Partitioning data for k-fold cross validation that will not have equal partitions
You may want to use kfoldcv function to calculate sample sizes for the k groups.
kfoldcv(k, N, nlevel=NULL)
Arguments:
k number of groups.
N total sample size.
nlevel a vector of sample sizes for stratified sampling.
You will ha... | Partitioning data for k-fold cross validation that will not have equal partitions
You may want to use kfoldcv function to calculate sample sizes for the k groups.
kfoldcv(k, N, nlevel=NULL)
Arguments:
k number of groups.
N total sample size.
nlevel a vector of sample sizes |
52,695 | Robust standard errors in econometrics | If the assumption of homoskedasticity is truly valid, the simple estimator of the VCE is more efficient than the robust sandwich version. That means it has smaller variance, so your estimates are less uncertain.
Of course, you can always do a heteroskedasticity test first and estimate accordingly. | Robust standard errors in econometrics | If the assumption of homoskedasticity is truly valid, the simple estimator of the VCE is more efficient than the robust sandwich version. That means it has smaller variance, so your estimates are less | Robust standard errors in econometrics
If the assumption of homoskedasticity is truly valid, the simple estimator of the VCE is more efficient than the robust sandwich version. That means it has smaller variance, so your estimates are less uncertain.
Of course, you can always do a heteroskedasticity test first and esti... | Robust standard errors in econometrics
If the assumption of homoskedasticity is truly valid, the simple estimator of the VCE is more efficient than the robust sandwich version. That means it has smaller variance, so your estimates are less |
52,696 | Robust standard errors in econometrics | There's also an interesting point raised by King & Roberts (2014): if your classical and robust standard errors diverge, your model suffers from misspecification that need to be fixed. "Settling" for the misspecified model and just correcting the standard errors will lead to "biased estimators of all but a few quantiti... | Robust standard errors in econometrics | There's also an interesting point raised by King & Roberts (2014): if your classical and robust standard errors diverge, your model suffers from misspecification that need to be fixed. "Settling" for | Robust standard errors in econometrics
There's also an interesting point raised by King & Roberts (2014): if your classical and robust standard errors diverge, your model suffers from misspecification that need to be fixed. "Settling" for the misspecified model and just correcting the standard errors will lead to "bias... | Robust standard errors in econometrics
There's also an interesting point raised by King & Roberts (2014): if your classical and robust standard errors diverge, your model suffers from misspecification that need to be fixed. "Settling" for |
52,697 | How do I compute sales forecasts? | I would have a look at Holt-Winters exponential smoothing. You can implement this fairly easily in R.
It picks up quite easily on trend and seasonality, and it will often (according to Colin Chatfield) give as good results as more complicated techniques such as ARIMA modelling.
Are you familiar with R?
You can download... | How do I compute sales forecasts? | I would have a look at Holt-Winters exponential smoothing. You can implement this fairly easily in R.
It picks up quite easily on trend and seasonality, and it will often (according to Colin Chatfield | How do I compute sales forecasts?
I would have a look at Holt-Winters exponential smoothing. You can implement this fairly easily in R.
It picks up quite easily on trend and seasonality, and it will often (according to Colin Chatfield) give as good results as more complicated techniques such as ARIMA modelling.
Are you... | How do I compute sales forecasts?
I would have a look at Holt-Winters exponential smoothing. You can implement this fairly easily in R.
It picks up quite easily on trend and seasonality, and it will often (according to Colin Chatfield |
52,698 | How do I compute sales forecasts? | Chris Chatfield's comments came about 10-15 years and were based on his experiences with Box-Jenkins methods that did not include features commonly available today as his software was inadequate as compared to today's software.
Holt-Winters model may be adequate if and only if
1) You assume that the parameters of the m... | How do I compute sales forecasts? | Chris Chatfield's comments came about 10-15 years and were based on his experiences with Box-Jenkins methods that did not include features commonly available today as his software was inadequate as co | How do I compute sales forecasts?
Chris Chatfield's comments came about 10-15 years and were based on his experiences with Box-Jenkins methods that did not include features commonly available today as his software was inadequate as compared to today's software.
Holt-Winters model may be adequate if and only if
1) You a... | How do I compute sales forecasts?
Chris Chatfield's comments came about 10-15 years and were based on his experiences with Box-Jenkins methods that did not include features commonly available today as his software was inadequate as co |
52,699 | How do I compute sales forecasts? | Since this question cannot possibly be answered with the best answer because it deals with simulations and it's only speculation, I thought I'd also include what another friend told me to consider as well. He suggested looking at Monte Carlo simulations.
http://en.wikipedia.org/wiki/Monte_Carlo_method | How do I compute sales forecasts? | Since this question cannot possibly be answered with the best answer because it deals with simulations and it's only speculation, I thought I'd also include what another friend told me to consider as | How do I compute sales forecasts?
Since this question cannot possibly be answered with the best answer because it deals with simulations and it's only speculation, I thought I'd also include what another friend told me to consider as well. He suggested looking at Monte Carlo simulations.
http://en.wikipedia.org/wiki/Mo... | How do I compute sales forecasts?
Since this question cannot possibly be answered with the best answer because it deals with simulations and it's only speculation, I thought I'd also include what another friend told me to consider as |
52,700 | Comparing coefficients in logistic regression | What you need is a postestimation test, which tests for significance of difference between two regression models, one of which is nested, i.e., it results from the first regression model plus some restrictions. In your case, the restriction would be $β₁ > β₂$, Null Hypothesis is $β₁ − β₂ = 0$.
Examples for such postes... | Comparing coefficients in logistic regression | What you need is a postestimation test, which tests for significance of difference between two regression models, one of which is nested, i.e., it results from the first regression model plus some res | Comparing coefficients in logistic regression
What you need is a postestimation test, which tests for significance of difference between two regression models, one of which is nested, i.e., it results from the first regression model plus some restrictions. In your case, the restriction would be $β₁ > β₂$, Null Hypothes... | Comparing coefficients in logistic regression
What you need is a postestimation test, which tests for significance of difference between two regression models, one of which is nested, i.e., it results from the first regression model plus some res |
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