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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48,701 | R latent class multinomial logit model [closed] | Have you tried the brms package? Its brm function supports multinomial logistic models and category-specific variables as well. Not sure if it will do what you want, though. Something like:
mod <- brm (choice ~ agentVar1 + agentVar2 + cse (choiceVar1),
family="categorical", data=yourData,
prior... | R latent class multinomial logit model [closed] | Have you tried the brms package? Its brm function supports multinomial logistic models and category-specific variables as well. Not sure if it will do what you want, though. Something like:
mod <- br | R latent class multinomial logit model [closed]
Have you tried the brms package? Its brm function supports multinomial logistic models and category-specific variables as well. Not sure if it will do what you want, though. Something like:
mod <- brm (choice ~ agentVar1 + agentVar2 + cse (choiceVar1),
family... | R latent class multinomial logit model [closed]
Have you tried the brms package? Its brm function supports multinomial logistic models and category-specific variables as well. Not sure if it will do what you want, though. Something like:
mod <- br |
48,702 | R latent class multinomial logit model [closed] | I have used both mlogit and flexmix. But there is a more general package in R called RSGHB that can easily implement the functions of those packages, as well as some things which are more difficult, such as latent class models. (I don't have enough reputation points to add as comment--strange that one needs more point... | R latent class multinomial logit model [closed] | I have used both mlogit and flexmix. But there is a more general package in R called RSGHB that can easily implement the functions of those packages, as well as some things which are more difficult, | R latent class multinomial logit model [closed]
I have used both mlogit and flexmix. But there is a more general package in R called RSGHB that can easily implement the functions of those packages, as well as some things which are more difficult, such as latent class models. (I don't have enough reputation points to a... | R latent class multinomial logit model [closed]
I have used both mlogit and flexmix. But there is a more general package in R called RSGHB that can easily implement the functions of those packages, as well as some things which are more difficult, |
48,703 | Plot Pareto tails in QQ-plot for log-normal distributions | If you take logs, it should be normal with exponential tail
Just do a normal and an exponential qq plot of the data, the first should be roughly linear before the kink, the second roughly linear after the kink:
(In this case the change point was at 5.5, and we see what we should - a kink near 5.5, and the first plot r... | Plot Pareto tails in QQ-plot for log-normal distributions | If you take logs, it should be normal with exponential tail
Just do a normal and an exponential qq plot of the data, the first should be roughly linear before the kink, the second roughly linear after | Plot Pareto tails in QQ-plot for log-normal distributions
If you take logs, it should be normal with exponential tail
Just do a normal and an exponential qq plot of the data, the first should be roughly linear before the kink, the second roughly linear after the kink:
(In this case the change point was at 5.5, and we ... | Plot Pareto tails in QQ-plot for log-normal distributions
If you take logs, it should be normal with exponential tail
Just do a normal and an exponential qq plot of the data, the first should be roughly linear before the kink, the second roughly linear after |
48,704 | Plot Pareto tails in QQ-plot for log-normal distributions | Here we go. Normal QQ plot and Exponential QQ plot. | Plot Pareto tails in QQ-plot for log-normal distributions | Here we go. Normal QQ plot and Exponential QQ plot. | Plot Pareto tails in QQ-plot for log-normal distributions
Here we go. Normal QQ plot and Exponential QQ plot. | Plot Pareto tails in QQ-plot for log-normal distributions
Here we go. Normal QQ plot and Exponential QQ plot. |
48,705 | Plot Pareto tails in QQ-plot for log-normal distributions | If you are interested in testing the Pareto tail, this answer would help you. If you are interested in visualizing the Pareto tail, this gist can plot the empirical CCDF of your data in log scale. A Pareto tail would manifest itself in a straight line. | Plot Pareto tails in QQ-plot for log-normal distributions | If you are interested in testing the Pareto tail, this answer would help you. If you are interested in visualizing the Pareto tail, this gist can plot the empirical CCDF of your data in log scale. A P | Plot Pareto tails in QQ-plot for log-normal distributions
If you are interested in testing the Pareto tail, this answer would help you. If you are interested in visualizing the Pareto tail, this gist can plot the empirical CCDF of your data in log scale. A Pareto tail would manifest itself in a straight line. | Plot Pareto tails in QQ-plot for log-normal distributions
If you are interested in testing the Pareto tail, this answer would help you. If you are interested in visualizing the Pareto tail, this gist can plot the empirical CCDF of your data in log scale. A P |
48,706 | I want to learn about ROC curve -- what is the canonical textbook? | I would start from this practically canonical paper by Davis and Goadrich The relationship between Precision-Recall and ROC curves.
Through this, the ROC origins can be tracked to this book: Evaluation of Diagnostic Systems:
Methods from Signal Detection Theory which is unfortunately hardly accessible. | I want to learn about ROC curve -- what is the canonical textbook? | I would start from this practically canonical paper by Davis and Goadrich The relationship between Precision-Recall and ROC curves.
Through this, the ROC origins can be tracked to this book: Evaluatio | I want to learn about ROC curve -- what is the canonical textbook?
I would start from this practically canonical paper by Davis and Goadrich The relationship between Precision-Recall and ROC curves.
Through this, the ROC origins can be tracked to this book: Evaluation of Diagnostic Systems:
Methods from Signal Detectio... | I want to learn about ROC curve -- what is the canonical textbook?
I would start from this practically canonical paper by Davis and Goadrich The relationship between Precision-Recall and ROC curves.
Through this, the ROC origins can be tracked to this book: Evaluatio |
48,707 | R rpart cross validation and 1 SE rule, why is the column in cptable called "xstd"? | 'xstd' is simply a poor label, it should say 'xse' since it's actually outputting the standard error, as opposed to the standard deviation. If you select row 7 in the above, then you are properly applying the '1SE Rule' as you intended. | R rpart cross validation and 1 SE rule, why is the column in cptable called "xstd"? | 'xstd' is simply a poor label, it should say 'xse' since it's actually outputting the standard error, as opposed to the standard deviation. If you select row 7 in the above, then you are properly appl | R rpart cross validation and 1 SE rule, why is the column in cptable called "xstd"?
'xstd' is simply a poor label, it should say 'xse' since it's actually outputting the standard error, as opposed to the standard deviation. If you select row 7 in the above, then you are properly applying the '1SE Rule' as you intended. | R rpart cross validation and 1 SE rule, why is the column in cptable called "xstd"?
'xstd' is simply a poor label, it should say 'xse' since it's actually outputting the standard error, as opposed to the standard deviation. If you select row 7 in the above, then you are properly appl |
48,708 | Posterior variance reduction | As you point out, $$H(X|Y)\le H(X)$$ is generally true, and can be interpreted from a Bayesian perspective as the entropy decrease in $X$ going from the prior to posterior distributions upon incorporating the additional information provided by observation of the data $Y$.
It is also generally true that
$\mathbb{V}ar_X[... | Posterior variance reduction | As you point out, $$H(X|Y)\le H(X)$$ is generally true, and can be interpreted from a Bayesian perspective as the entropy decrease in $X$ going from the prior to posterior distributions upon incorpora | Posterior variance reduction
As you point out, $$H(X|Y)\le H(X)$$ is generally true, and can be interpreted from a Bayesian perspective as the entropy decrease in $X$ going from the prior to posterior distributions upon incorporating the additional information provided by observation of the data $Y$.
It is also general... | Posterior variance reduction
As you point out, $$H(X|Y)\le H(X)$$ is generally true, and can be interpreted from a Bayesian perspective as the entropy decrease in $X$ going from the prior to posterior distributions upon incorpora |
48,709 | How to handle underdispersion in GLMM (binomial outcome variable) | For binary outcomes, overdispersion or underdispersion are only identifiable (i.e., can only be meaningfully measured) if sets of individuals with identical predictors can be grouped. For example, if the data look like
response fac1 fac2
0 A A
0 A A
1 A B
0 A B
(a ridi... | How to handle underdispersion in GLMM (binomial outcome variable) | For binary outcomes, overdispersion or underdispersion are only identifiable (i.e., can only be meaningfully measured) if sets of individuals with identical predictors can be grouped. For example, if | How to handle underdispersion in GLMM (binomial outcome variable)
For binary outcomes, overdispersion or underdispersion are only identifiable (i.e., can only be meaningfully measured) if sets of individuals with identical predictors can be grouped. For example, if the data look like
response fac1 fac2
0 A ... | How to handle underdispersion in GLMM (binomial outcome variable)
For binary outcomes, overdispersion or underdispersion are only identifiable (i.e., can only be meaningfully measured) if sets of individuals with identical predictors can be grouped. For example, if |
48,710 | What does the "different populations" result of a significant group t-test mean exactly? | It certainly doesn't "have to be equivalent to the two groups coming from different underlying populations", hypothesis testing is a probabilistic endeavor. It could be a type I error. To use your example, if the students were randomized into the two groups and nothing else was done except to give them all a math tes... | What does the "different populations" result of a significant group t-test mean exactly? | It certainly doesn't "have to be equivalent to the two groups coming from different underlying populations", hypothesis testing is a probabilistic endeavor. It could be a type I error. To use your e | What does the "different populations" result of a significant group t-test mean exactly?
It certainly doesn't "have to be equivalent to the two groups coming from different underlying populations", hypothesis testing is a probabilistic endeavor. It could be a type I error. To use your example, if the students were ra... | What does the "different populations" result of a significant group t-test mean exactly?
It certainly doesn't "have to be equivalent to the two groups coming from different underlying populations", hypothesis testing is a probabilistic endeavor. It could be a type I error. To use your e |
48,711 | Fourier bases for a stationary signal & relation to PCA for natural images | I am afraid this will not fully answer your question, but I would still like to write it to give you some keywords and mainly hoping to sparkle further discussion. I will be happy if anybody provides a better answer.
Having said that, I disagree with what @whuber wrote in the comments above ("in no circumstances does a... | Fourier bases for a stationary signal & relation to PCA for natural images | I am afraid this will not fully answer your question, but I would still like to write it to give you some keywords and mainly hoping to sparkle further discussion. I will be happy if anybody provides | Fourier bases for a stationary signal & relation to PCA for natural images
I am afraid this will not fully answer your question, but I would still like to write it to give you some keywords and mainly hoping to sparkle further discussion. I will be happy if anybody provides a better answer.
Having said that, I disagree... | Fourier bases for a stationary signal & relation to PCA for natural images
I am afraid this will not fully answer your question, but I would still like to write it to give you some keywords and mainly hoping to sparkle further discussion. I will be happy if anybody provides |
48,712 | Expected standard deviation for a sample from a uniform distribution? | The integration is difficult even with as few as $3$ values. Why not estimate the bias in the sample SD by using a surrogate measure of spread? One set of choices is afforded by differences in the order statistics.
Consider, for instance, Tukey's H-spread. For a data set of $n$ values, let $m = \lfloor\frac{n+1}{2}\... | Expected standard deviation for a sample from a uniform distribution? | The integration is difficult even with as few as $3$ values. Why not estimate the bias in the sample SD by using a surrogate measure of spread? One set of choices is afforded by differences in the o | Expected standard deviation for a sample from a uniform distribution?
The integration is difficult even with as few as $3$ values. Why not estimate the bias in the sample SD by using a surrogate measure of spread? One set of choices is afforded by differences in the order statistics.
Consider, for instance, Tukey's H... | Expected standard deviation for a sample from a uniform distribution?
The integration is difficult even with as few as $3$ values. Why not estimate the bias in the sample SD by using a surrogate measure of spread? One set of choices is afforded by differences in the o |
48,713 | Comparing estimators in Cauchy distribution | Yes, this is the right approach. Let's see where it can go.
Getting Off to a Fast Start
You can usually sneak up on to a full-blown simulation by working from the inside out. The R command
x <- rcauchy(10, location=0, scale=1)
generates a sample of $10$ and stores it in the variable x. The next step is to compute t... | Comparing estimators in Cauchy distribution | Yes, this is the right approach. Let's see where it can go.
Getting Off to a Fast Start
You can usually sneak up on to a full-blown simulation by working from the inside out. The R command
x <- rcau | Comparing estimators in Cauchy distribution
Yes, this is the right approach. Let's see where it can go.
Getting Off to a Fast Start
You can usually sneak up on to a full-blown simulation by working from the inside out. The R command
x <- rcauchy(10, location=0, scale=1)
generates a sample of $10$ and stores it in th... | Comparing estimators in Cauchy distribution
Yes, this is the right approach. Let's see where it can go.
Getting Off to a Fast Start
You can usually sneak up on to a full-blown simulation by working from the inside out. The R command
x <- rcau |
48,714 | ML vs WLSMV: which is better for categorical data and why? | In one medical research paper, Proitsi et al. (2009) write:
"The WLSMV is a robust estimator which does not assume normally
distributed variables and provides the best option for modelling
categorical or ordered data (Brown, 2006)".
For your convenience, I'm including the cited reference in the reference list bel... | ML vs WLSMV: which is better for categorical data and why? | In one medical research paper, Proitsi et al. (2009) write:
"The WLSMV is a robust estimator which does not assume normally
distributed variables and provides the best option for modelling
catego | ML vs WLSMV: which is better for categorical data and why?
In one medical research paper, Proitsi et al. (2009) write:
"The WLSMV is a robust estimator which does not assume normally
distributed variables and provides the best option for modelling
categorical or ordered data (Brown, 2006)".
For your convenience, ... | ML vs WLSMV: which is better for categorical data and why?
In one medical research paper, Proitsi et al. (2009) write:
"The WLSMV is a robust estimator which does not assume normally
distributed variables and provides the best option for modelling
catego |
48,715 | ML vs WLSMV: which is better for categorical data and why? | The most obvious reason for choosing one over the other would be the kind of fit indices you need. The WLSMV will give you CFI, TLI and RMSEA, which will help you evaluate the fit of a given model. If you need to compare non-nested models, you would need AIC and/or BIC, which aren't available with WLSMV and categorical... | ML vs WLSMV: which is better for categorical data and why? | The most obvious reason for choosing one over the other would be the kind of fit indices you need. The WLSMV will give you CFI, TLI and RMSEA, which will help you evaluate the fit of a given model. If | ML vs WLSMV: which is better for categorical data and why?
The most obvious reason for choosing one over the other would be the kind of fit indices you need. The WLSMV will give you CFI, TLI and RMSEA, which will help you evaluate the fit of a given model. If you need to compare non-nested models, you would need AIC an... | ML vs WLSMV: which is better for categorical data and why?
The most obvious reason for choosing one over the other would be the kind of fit indices you need. The WLSMV will give you CFI, TLI and RMSEA, which will help you evaluate the fit of a given model. If |
48,716 | When is the standard error of the mean impossibly large for a given data range, when we know the sample size? | I'm looking at the paper now (figures are at the end).
I may have missed something, but so far I see nothing in the paper that states that the 2.9 is intended to be a standard error (I can't find "SE" or "standard error" in the paper, for example).
Edit: Mattias points out in comments that (unlike the html version I li... | When is the standard error of the mean impossibly large for a given data range, when we know the sam | I'm looking at the paper now (figures are at the end).
I may have missed something, but so far I see nothing in the paper that states that the 2.9 is intended to be a standard error (I can't find "SE" | When is the standard error of the mean impossibly large for a given data range, when we know the sample size?
I'm looking at the paper now (figures are at the end).
I may have missed something, but so far I see nothing in the paper that states that the 2.9 is intended to be a standard error (I can't find "SE" or "stand... | When is the standard error of the mean impossibly large for a given data range, when we know the sam
I'm looking at the paper now (figures are at the end).
I may have missed something, but so far I see nothing in the paper that states that the 2.9 is intended to be a standard error (I can't find "SE" |
48,717 | Data input uncertainty + Monte Carlo simulation + forecasting | You have two sources of uncertainty: the uncertainty in the historical data, and the uncertainty in producing the forecasts given the historical data. The simulation distribution of point forecasts is capturing the uncertainty in the historical data only.
To capture the joint uncertainty, I suggest you simulate a futu... | Data input uncertainty + Monte Carlo simulation + forecasting | You have two sources of uncertainty: the uncertainty in the historical data, and the uncertainty in producing the forecasts given the historical data. The simulation distribution of point forecasts is | Data input uncertainty + Monte Carlo simulation + forecasting
You have two sources of uncertainty: the uncertainty in the historical data, and the uncertainty in producing the forecasts given the historical data. The simulation distribution of point forecasts is capturing the uncertainty in the historical data only.
T... | Data input uncertainty + Monte Carlo simulation + forecasting
You have two sources of uncertainty: the uncertainty in the historical data, and the uncertainty in producing the forecasts given the historical data. The simulation distribution of point forecasts is |
48,718 | T-tests for power-law distributed data? | Actually with 4 groups, you'd normally compare means using one ANOVA, not six t-tests (though t-tests would still come in with multiple comparisons or planned contrasts).
If one assumes Pareto distributions, then there are a number of possible approaches. I'll mention only a few, starting with one I think is perhaps ea... | T-tests for power-law distributed data? | Actually with 4 groups, you'd normally compare means using one ANOVA, not six t-tests (though t-tests would still come in with multiple comparisons or planned contrasts).
If one assumes Pareto distrib | T-tests for power-law distributed data?
Actually with 4 groups, you'd normally compare means using one ANOVA, not six t-tests (though t-tests would still come in with multiple comparisons or planned contrasts).
If one assumes Pareto distributions, then there are a number of possible approaches. I'll mention only a few,... | T-tests for power-law distributed data?
Actually with 4 groups, you'd normally compare means using one ANOVA, not six t-tests (though t-tests would still come in with multiple comparisons or planned contrasts).
If one assumes Pareto distrib |
48,719 | Sample mean of random walk | From
$$\bar{y}_T = \frac{1}{T}\sum_{i=1}^T y_t = \frac{T}{T} u_1 + \frac{T-1}{T} u_2 + \cdots + \frac{1}{T}u_T$$
the independence of the $u_i$ implies (along with their unit variance) that
$$\text{Var}(\bar{y}_T) = \left(\frac{T}{T}\right)^2 + \left(\frac{T-1}{T} \right)^2 + \cdots + \left(\frac{1}{T}\right)^2 = \frac{... | Sample mean of random walk | From
$$\bar{y}_T = \frac{1}{T}\sum_{i=1}^T y_t = \frac{T}{T} u_1 + \frac{T-1}{T} u_2 + \cdots + \frac{1}{T}u_T$$
the independence of the $u_i$ implies (along with their unit variance) that
$$\text{Var | Sample mean of random walk
From
$$\bar{y}_T = \frac{1}{T}\sum_{i=1}^T y_t = \frac{T}{T} u_1 + \frac{T-1}{T} u_2 + \cdots + \frac{1}{T}u_T$$
the independence of the $u_i$ implies (along with their unit variance) that
$$\text{Var}(\bar{y}_T) = \left(\frac{T}{T}\right)^2 + \left(\frac{T-1}{T} \right)^2 + \cdots + \left(\f... | Sample mean of random walk
From
$$\bar{y}_T = \frac{1}{T}\sum_{i=1}^T y_t = \frac{T}{T} u_1 + \frac{T-1}{T} u_2 + \cdots + \frac{1}{T}u_T$$
the independence of the $u_i$ implies (along with their unit variance) that
$$\text{Var |
48,720 | Regression discontinuity design parametric versus non-parametric different result | This is happening because you are restricting the effect of Democratic vote share to be the same on both sides of the cutoff in your third specification, which is a slightly different model. As the magnitude and significance of the interaction term in (2) tells you, the slopes are actually somewhat different:
Graph co... | Regression discontinuity design parametric versus non-parametric different result | This is happening because you are restricting the effect of Democratic vote share to be the same on both sides of the cutoff in your third specification, which is a slightly different model. As the ma | Regression discontinuity design parametric versus non-parametric different result
This is happening because you are restricting the effect of Democratic vote share to be the same on both sides of the cutoff in your third specification, which is a slightly different model. As the magnitude and significance of the intera... | Regression discontinuity design parametric versus non-parametric different result
This is happening because you are restricting the effect of Democratic vote share to be the same on both sides of the cutoff in your third specification, which is a slightly different model. As the ma |
48,721 | Corrected AIC (AICC) for k-means | The form of $AICc$ of
$$
AICc = AIC + \frac{2k(k+1)}{n-k-1}
$$
was proposed by
Hurvich, C. M.; Tsai, C.-L. (1989), "Regression and time series model selection in small samples", Biometrika 76: 297–307
specifically for a linear regression model with normally distributed errors. For different models, a different correcti... | Corrected AIC (AICC) for k-means | The form of $AICc$ of
$$
AICc = AIC + \frac{2k(k+1)}{n-k-1}
$$
was proposed by
Hurvich, C. M.; Tsai, C.-L. (1989), "Regression and time series model selection in small samples", Biometrika 76: 297–307 | Corrected AIC (AICC) for k-means
The form of $AICc$ of
$$
AICc = AIC + \frac{2k(k+1)}{n-k-1}
$$
was proposed by
Hurvich, C. M.; Tsai, C.-L. (1989), "Regression and time series model selection in small samples", Biometrika 76: 297–307
specifically for a linear regression model with normally distributed errors. For diffe... | Corrected AIC (AICC) for k-means
The form of $AICc$ of
$$
AICc = AIC + \frac{2k(k+1)}{n-k-1}
$$
was proposed by
Hurvich, C. M.; Tsai, C.-L. (1989), "Regression and time series model selection in small samples", Biometrika 76: 297–307 |
48,722 | Estimate population quantiles from subpopulations' quantiles | Because the subpopulations are arbitrary and not random, the best you can do is to use interval arithmetic.
Let the quantiles of a subpopulation be $x_{[1]} \le x_{[2]} \le \cdots \le x_{[m]}$ corresponding to percentiles $100 q_1, 100 q_2, \ldots, 100 q_m,$ respectively. This information means that
$100 q_i \%$ of ... | Estimate population quantiles from subpopulations' quantiles | Because the subpopulations are arbitrary and not random, the best you can do is to use interval arithmetic.
Let the quantiles of a subpopulation be $x_{[1]} \le x_{[2]} \le \cdots \le x_{[m]}$ corresp | Estimate population quantiles from subpopulations' quantiles
Because the subpopulations are arbitrary and not random, the best you can do is to use interval arithmetic.
Let the quantiles of a subpopulation be $x_{[1]} \le x_{[2]} \le \cdots \le x_{[m]}$ corresponding to percentiles $100 q_1, 100 q_2, \ldots, 100 q_m,$ ... | Estimate population quantiles from subpopulations' quantiles
Because the subpopulations are arbitrary and not random, the best you can do is to use interval arithmetic.
Let the quantiles of a subpopulation be $x_{[1]} \le x_{[2]} \le \cdots \le x_{[m]}$ corresp |
48,723 | Estimate population quantiles from subpopulations' quantiles | Since your samples collectivey constitiute the entire population, you can re-aggregate to get some ideas about the overall distribution.
Let $N_s$ be the number of subpopulations, $n_i$ be the size of subpopulation $i$,$N_q$ be the number of quantiles, and $q_{ij}$ be the set of quantiles for subpopulation $i$, and let... | Estimate population quantiles from subpopulations' quantiles | Since your samples collectivey constitiute the entire population, you can re-aggregate to get some ideas about the overall distribution.
Let $N_s$ be the number of subpopulations, $n_i$ be the size of | Estimate population quantiles from subpopulations' quantiles
Since your samples collectivey constitiute the entire population, you can re-aggregate to get some ideas about the overall distribution.
Let $N_s$ be the number of subpopulations, $n_i$ be the size of subpopulation $i$,$N_q$ be the number of quantiles, and $q... | Estimate population quantiles from subpopulations' quantiles
Since your samples collectivey constitiute the entire population, you can re-aggregate to get some ideas about the overall distribution.
Let $N_s$ be the number of subpopulations, $n_i$ be the size of |
48,724 | How to summarize and understand the reults of DBSCAN clustering on big data? | Are you sure that clustering big data is actually used anywhere?
As far as I can tell, it is not used. Everybody uses classification, nobody uses clustering. Because the clustering problem is much harder, and will require manual analysis of the results.
K-means: the usual Lloyd algorithm is naive parallel, and thus tri... | How to summarize and understand the reults of DBSCAN clustering on big data? | Are you sure that clustering big data is actually used anywhere?
As far as I can tell, it is not used. Everybody uses classification, nobody uses clustering. Because the clustering problem is much har | How to summarize and understand the reults of DBSCAN clustering on big data?
Are you sure that clustering big data is actually used anywhere?
As far as I can tell, it is not used. Everybody uses classification, nobody uses clustering. Because the clustering problem is much harder, and will require manual analysis of th... | How to summarize and understand the reults of DBSCAN clustering on big data?
Are you sure that clustering big data is actually used anywhere?
As far as I can tell, it is not used. Everybody uses classification, nobody uses clustering. Because the clustering problem is much har |
48,725 | How to summarize and understand the reults of DBSCAN clustering on big data? | It is not true that we need to understand the clusters in every application. Actually if you have few well established clusters, probably you will soon end up doing some supervised learning rather than clustering: do the clustering of choice, check results, assign labels to cluster members, train using a supervised met... | How to summarize and understand the reults of DBSCAN clustering on big data? | It is not true that we need to understand the clusters in every application. Actually if you have few well established clusters, probably you will soon end up doing some supervised learning rather tha | How to summarize and understand the reults of DBSCAN clustering on big data?
It is not true that we need to understand the clusters in every application. Actually if you have few well established clusters, probably you will soon end up doing some supervised learning rather than clustering: do the clustering of choice, ... | How to summarize and understand the reults of DBSCAN clustering on big data?
It is not true that we need to understand the clusters in every application. Actually if you have few well established clusters, probably you will soon end up doing some supervised learning rather tha |
48,726 | Minimizing number of questions of questionnaire from past binary responses | Sounds a lot like a computerized adaptive testing (CAT) application. This is just one small hint, not an attempt at a comprehensive solution, so I hope others will keep the answers coming.
I'm assuming that you're hoping to predict responses to the unasked questions from an optimally small subset of questions to such ... | Minimizing number of questions of questionnaire from past binary responses | Sounds a lot like a computerized adaptive testing (CAT) application. This is just one small hint, not an attempt at a comprehensive solution, so I hope others will keep the answers coming.
I'm assumi | Minimizing number of questions of questionnaire from past binary responses
Sounds a lot like a computerized adaptive testing (CAT) application. This is just one small hint, not an attempt at a comprehensive solution, so I hope others will keep the answers coming.
I'm assuming that you're hoping to predict responses to... | Minimizing number of questions of questionnaire from past binary responses
Sounds a lot like a computerized adaptive testing (CAT) application. This is just one small hint, not an attempt at a comprehensive solution, so I hope others will keep the answers coming.
I'm assumi |
48,727 | Can I use a z-test on heteroscedastic data? | Note that the $\beta$'s in your $z$ formula should be $\hat \beta$'s (both in the numerator and denominator).
The short answer is 'yes'; as long as (a) the sample sizes are sufficiently large that (i) the $\hat \beta$ terms are close to normal (i.e. the CLT 'kicks in'), and (ii) the two $\hat\sigma$ terms (on which the... | Can I use a z-test on heteroscedastic data? | Note that the $\beta$'s in your $z$ formula should be $\hat \beta$'s (both in the numerator and denominator).
The short answer is 'yes'; as long as (a) the sample sizes are sufficiently large that (i) | Can I use a z-test on heteroscedastic data?
Note that the $\beta$'s in your $z$ formula should be $\hat \beta$'s (both in the numerator and denominator).
The short answer is 'yes'; as long as (a) the sample sizes are sufficiently large that (i) the $\hat \beta$ terms are close to normal (i.e. the CLT 'kicks in'), and (... | Can I use a z-test on heteroscedastic data?
Note that the $\beta$'s in your $z$ formula should be $\hat \beta$'s (both in the numerator and denominator).
The short answer is 'yes'; as long as (a) the sample sizes are sufficiently large that (i) |
48,728 | Confusion about hidden Markov models definition and graphical notation? | I think the problem is a misinterpretation of the notation. $X_1$ stands for $X(t)=1$, not for $X(t=1)$, and $a_{ij}=P(X(t)=j| X(t-1)=i)$. $X_1, X_2$ and $X_3$ are the three possible values of the variable $X$ at a time $t$, not three variables a $t=1, t=2$ and $t=3$.
So at time $t=1$ you have an initial value. Let's t... | Confusion about hidden Markov models definition and graphical notation? | I think the problem is a misinterpretation of the notation. $X_1$ stands for $X(t)=1$, not for $X(t=1)$, and $a_{ij}=P(X(t)=j| X(t-1)=i)$. $X_1, X_2$ and $X_3$ are the three possible values of the var | Confusion about hidden Markov models definition and graphical notation?
I think the problem is a misinterpretation of the notation. $X_1$ stands for $X(t)=1$, not for $X(t=1)$, and $a_{ij}=P(X(t)=j| X(t-1)=i)$. $X_1, X_2$ and $X_3$ are the three possible values of the variable $X$ at a time $t$, not three variables a $... | Confusion about hidden Markov models definition and graphical notation?
I think the problem is a misinterpretation of the notation. $X_1$ stands for $X(t)=1$, not for $X(t=1)$, and $a_{ij}=P(X(t)=j| X(t-1)=i)$. $X_1, X_2$ and $X_3$ are the three possible values of the var |
48,729 | Confusion about hidden Markov models definition and graphical notation? | Your confusion is coming from different graphical notations about HMM. Specifically, there are two types of notations.
Type 1 is using nodes to represent possible values of random variables and use arrows to represent transitions
Type 2 is using nodes to represent random variables, and use errors to represent conditio... | Confusion about hidden Markov models definition and graphical notation? | Your confusion is coming from different graphical notations about HMM. Specifically, there are two types of notations.
Type 1 is using nodes to represent possible values of random variables and use a | Confusion about hidden Markov models definition and graphical notation?
Your confusion is coming from different graphical notations about HMM. Specifically, there are two types of notations.
Type 1 is using nodes to represent possible values of random variables and use arrows to represent transitions
Type 2 is using n... | Confusion about hidden Markov models definition and graphical notation?
Your confusion is coming from different graphical notations about HMM. Specifically, there are two types of notations.
Type 1 is using nodes to represent possible values of random variables and use a |
48,730 | Confusion about hidden Markov models definition and graphical notation? | Transition probability is a potential for switching between any 2 states, not a statement about the relationship of events that have happened. These transition probabilities are independent of each other, as shown in the diagram by the fact that $a_{12}$ has no explicit relationship to $a_{21}$ or $a_{23}$.
The diagra... | Confusion about hidden Markov models definition and graphical notation? | Transition probability is a potential for switching between any 2 states, not a statement about the relationship of events that have happened. These transition probabilities are independent of each o | Confusion about hidden Markov models definition and graphical notation?
Transition probability is a potential for switching between any 2 states, not a statement about the relationship of events that have happened. These transition probabilities are independent of each other, as shown in the diagram by the fact that $... | Confusion about hidden Markov models definition and graphical notation?
Transition probability is a potential for switching between any 2 states, not a statement about the relationship of events that have happened. These transition probabilities are independent of each o |
48,731 | CDF for uncorrelated bivariate normal | If $X \sim N(0, \sigma_1^2)$ and $Y \sim N(0, \sigma_2^2)$ are independent random variables, then the joint pdf of $(X,Y)$ is say $f(x,y)$:
Given $Z = \sqrt{X^2 + Y^2}$, you seek $\text{Var}(Z)$:
where Var is the Variance function from the mathStatica add-on to Mathematica (to compute the pleasantries), and Elliptic... | CDF for uncorrelated bivariate normal | If $X \sim N(0, \sigma_1^2)$ and $Y \sim N(0, \sigma_2^2)$ are independent random variables, then the joint pdf of $(X,Y)$ is say $f(x,y)$:
Given $Z = \sqrt{X^2 + Y^2}$, you seek $\text{Var}(Z)$:
w | CDF for uncorrelated bivariate normal
If $X \sim N(0, \sigma_1^2)$ and $Y \sim N(0, \sigma_2^2)$ are independent random variables, then the joint pdf of $(X,Y)$ is say $f(x,y)$:
Given $Z = \sqrt{X^2 + Y^2}$, you seek $\text{Var}(Z)$:
where Var is the Variance function from the mathStatica add-on to Mathematica (to c... | CDF for uncorrelated bivariate normal
If $X \sim N(0, \sigma_1^2)$ and $Y \sim N(0, \sigma_2^2)$ are independent random variables, then the joint pdf of $(X,Y)$ is say $f(x,y)$:
Given $Z = \sqrt{X^2 + Y^2}$, you seek $\text{Var}(Z)$:
w |
48,732 | Difference of two random variable distributions | Are the two random variables $X$ and $Y$ supposed to be independent? If so, it is easy to prove that the distribution function of $Z=X-Y$ is given by the convolution
$$
F_Z(z) = P(X-Y\leq z) = \int F_X(z+y) \, dF_Y(y) \, .
$$
Hence, one idea is to compute the empirical distribution functions $\hat{F}_m$ of $(x_1,\dot... | Difference of two random variable distributions | Are the two random variables $X$ and $Y$ supposed to be independent? If so, it is easy to prove that the distribution function of $Z=X-Y$ is given by the convolution
$$
F_Z(z) = P(X-Y\leq z) = \int | Difference of two random variable distributions
Are the two random variables $X$ and $Y$ supposed to be independent? If so, it is easy to prove that the distribution function of $Z=X-Y$ is given by the convolution
$$
F_Z(z) = P(X-Y\leq z) = \int F_X(z+y) \, dF_Y(y) \, .
$$
Hence, one idea is to compute the empirical ... | Difference of two random variable distributions
Are the two random variables $X$ and $Y$ supposed to be independent? If so, it is easy to prove that the distribution function of $Z=X-Y$ is given by the convolution
$$
F_Z(z) = P(X-Y\leq z) = \int |
48,733 | Difference of two random variable distributions | I don't think you need a special package to do this; ordinary numpy is enough. I've appended example code and its output below. Note that the cdf of (A-B) looks very similar to the cdfs of A and B separately, but actually it's not. You can see a subtle difference at around +/- 2 or 3 sigma. The cdf of (A-B) is a li... | Difference of two random variable distributions | I don't think you need a special package to do this; ordinary numpy is enough. I've appended example code and its output below. Note that the cdf of (A-B) looks very similar to the cdfs of A and B s | Difference of two random variable distributions
I don't think you need a special package to do this; ordinary numpy is enough. I've appended example code and its output below. Note that the cdf of (A-B) looks very similar to the cdfs of A and B separately, but actually it's not. You can see a subtle difference at ar... | Difference of two random variable distributions
I don't think you need a special package to do this; ordinary numpy is enough. I've appended example code and its output below. Note that the cdf of (A-B) looks very similar to the cdfs of A and B s |
48,734 | Getting the units right for the Pareto distribution of wealth: x = people, dollars, dollars per person? | I elaborate on @stachyra answer, trying to explain how the Lorenz
curve emerges.
We can regard the wealth of an individual chosen at random in the
population as a r.v. $X$ having density $f(x)$ over $(x_{\text{min}},
\,\infty)$ and survival $S(x):= \Pr\{X>x\}$. Assume that $n$
independent individuals $X_i$ are chosen ... | Getting the units right for the Pareto distribution of wealth: x = people, dollars, dollars per pers | I elaborate on @stachyra answer, trying to explain how the Lorenz
curve emerges.
We can regard the wealth of an individual chosen at random in the
population as a r.v. $X$ having density $f(x)$ over $ | Getting the units right for the Pareto distribution of wealth: x = people, dollars, dollars per person?
I elaborate on @stachyra answer, trying to explain how the Lorenz
curve emerges.
We can regard the wealth of an individual chosen at random in the
population as a r.v. $X$ having density $f(x)$ over $(x_{\text{min}},... | Getting the units right for the Pareto distribution of wealth: x = people, dollars, dollars per pers
I elaborate on @stachyra answer, trying to explain how the Lorenz
curve emerges.
We can regard the wealth of an individual chosen at random in the
population as a r.v. $X$ having density $f(x)$ over $ |
48,735 | Getting the units right for the Pareto distribution of wealth: x = people, dollars, dollars per person? | I believe the concept that you are grasping for is the Lorenz curve. As stated in the link, it plots percentage of people vs. percentage of wealth, and points along the Lorenz curve represent statements such as "the bottom 20% of all households have 10% of the total income."
If you want to understand explicitly the re... | Getting the units right for the Pareto distribution of wealth: x = people, dollars, dollars per pers | I believe the concept that you are grasping for is the Lorenz curve. As stated in the link, it plots percentage of people vs. percentage of wealth, and points along the Lorenz curve represent stateme | Getting the units right for the Pareto distribution of wealth: x = people, dollars, dollars per person?
I believe the concept that you are grasping for is the Lorenz curve. As stated in the link, it plots percentage of people vs. percentage of wealth, and points along the Lorenz curve represent statements such as "the... | Getting the units right for the Pareto distribution of wealth: x = people, dollars, dollars per pers
I believe the concept that you are grasping for is the Lorenz curve. As stated in the link, it plots percentage of people vs. percentage of wealth, and points along the Lorenz curve represent stateme |
48,736 | How to measure test set error with logistic regression | There is no standard way to define goodness-of-fit. It depends on your application and what the problem you are going to solve. As in classification, you may define the goodness-of-fit as 0-1 loss.
For a logistic regression, you can compute the likelihood function. I would use a McFadden pseudo-$R^2$, which is defined... | How to measure test set error with logistic regression | There is no standard way to define goodness-of-fit. It depends on your application and what the problem you are going to solve. As in classification, you may define the goodness-of-fit as 0-1 loss.
F | How to measure test set error with logistic regression
There is no standard way to define goodness-of-fit. It depends on your application and what the problem you are going to solve. As in classification, you may define the goodness-of-fit as 0-1 loss.
For a logistic regression, you can compute the likelihood function... | How to measure test set error with logistic regression
There is no standard way to define goodness-of-fit. It depends on your application and what the problem you are going to solve. As in classification, you may define the goodness-of-fit as 0-1 loss.
F |
48,737 | How to measure test set error with logistic regression | (1) You're describing split sample internal validation that has become less popular (in favor of bootstrapping) given the large dataset size you need to produce reliable estimates.
(2) You don't have to choose 0.5 as your classification cut-point. You can choose anything, depending on what suits your objective/utility ... | How to measure test set error with logistic regression | (1) You're describing split sample internal validation that has become less popular (in favor of bootstrapping) given the large dataset size you need to produce reliable estimates.
(2) You don't have | How to measure test set error with logistic regression
(1) You're describing split sample internal validation that has become less popular (in favor of bootstrapping) given the large dataset size you need to produce reliable estimates.
(2) You don't have to choose 0.5 as your classification cut-point. You can choose an... | How to measure test set error with logistic regression
(1) You're describing split sample internal validation that has become less popular (in favor of bootstrapping) given the large dataset size you need to produce reliable estimates.
(2) You don't have |
48,738 | How to measure test set error with logistic regression | Besides data splitting sometimes requiring $n > 10,000$ to be reliable, you are using an "error" measure that is unnatural to probability models. Besides a generalized $R^2$ as mentioned above, consider the Brier score and the $c$-index (concordance probability) or the related Somers' $D_{xy}$ rank correlation between... | How to measure test set error with logistic regression | Besides data splitting sometimes requiring $n > 10,000$ to be reliable, you are using an "error" measure that is unnatural to probability models. Besides a generalized $R^2$ as mentioned above, consi | How to measure test set error with logistic regression
Besides data splitting sometimes requiring $n > 10,000$ to be reliable, you are using an "error" measure that is unnatural to probability models. Besides a generalized $R^2$ as mentioned above, consider the Brier score and the $c$-index (concordance probability) o... | How to measure test set error with logistic regression
Besides data splitting sometimes requiring $n > 10,000$ to be reliable, you are using an "error" measure that is unnatural to probability models. Besides a generalized $R^2$ as mentioned above, consi |
48,739 | How to measure test set error with logistic regression | Measure the F statistic or proportion of explained variation. Also consider the covariate measurement error as it was performed by this study: S Rabe-Hesketh et al.,Correcting for covariate measurement error in logistic regression using nonparametric maximum likelihood estimation, 2003 | How to measure test set error with logistic regression | Measure the F statistic or proportion of explained variation. Also consider the covariate measurement error as it was performed by this study: S Rabe-Hesketh et al.,Correcting for covariate measuremen | How to measure test set error with logistic regression
Measure the F statistic or proportion of explained variation. Also consider the covariate measurement error as it was performed by this study: S Rabe-Hesketh et al.,Correcting for covariate measurement error in logistic regression using nonparametric maximum likeli... | How to measure test set error with logistic regression
Measure the F statistic or proportion of explained variation. Also consider the covariate measurement error as it was performed by this study: S Rabe-Hesketh et al.,Correcting for covariate measuremen |
48,740 | How to measure test set error with logistic regression | There isn't a perfect analogy to say R squared for a binary GLM though there are a few approximations using residual deviance and such.
Another way to approach measuring performance is to look at the AUC of the ROC curve which looks more at the ability of the model to separate goods and bads as probabilities increase.
... | How to measure test set error with logistic regression | There isn't a perfect analogy to say R squared for a binary GLM though there are a few approximations using residual deviance and such.
Another way to approach measuring performance is to look at the | How to measure test set error with logistic regression
There isn't a perfect analogy to say R squared for a binary GLM though there are a few approximations using residual deviance and such.
Another way to approach measuring performance is to look at the AUC of the ROC curve which looks more at the ability of the model... | How to measure test set error with logistic regression
There isn't a perfect analogy to say R squared for a binary GLM though there are a few approximations using residual deviance and such.
Another way to approach measuring performance is to look at the |
48,741 | scikit-learn score metric on the coefficient of determination $R^2$ | Actually there are two different measures that are called correlations. Let us then call them little $r$, which is the Pearson correlation coefficient, and big $R$, which is what you have; a correlation (usually as $R^2$) adjusted for a generalized residual. Now $|r|=|R|$ only when we restrict ourselves to ordinary lea... | scikit-learn score metric on the coefficient of determination $R^2$ | Actually there are two different measures that are called correlations. Let us then call them little $r$, which is the Pearson correlation coefficient, and big $R$, which is what you have; a correlati | scikit-learn score metric on the coefficient of determination $R^2$
Actually there are two different measures that are called correlations. Let us then call them little $r$, which is the Pearson correlation coefficient, and big $R$, which is what you have; a correlation (usually as $R^2$) adjusted for a generalized res... | scikit-learn score metric on the coefficient of determination $R^2$
Actually there are two different measures that are called correlations. Let us then call them little $r$, which is the Pearson correlation coefficient, and big $R$, which is what you have; a correlati |
48,742 | scikit-learn score metric on the coefficient of determination $R^2$ | Consider using the precision and recall scores of scikit-learn: http://scikit-learn.org/stable/modules/generated/sklearn.metrics.precision_recall_fscore_support.html. It may give you a more tangible number to consider.
Precision and recall are defined as:
The precision is the ratio tp / (tp + fp) where tp is the number... | scikit-learn score metric on the coefficient of determination $R^2$ | Consider using the precision and recall scores of scikit-learn: http://scikit-learn.org/stable/modules/generated/sklearn.metrics.precision_recall_fscore_support.html. It may give you a more tangible n | scikit-learn score metric on the coefficient of determination $R^2$
Consider using the precision and recall scores of scikit-learn: http://scikit-learn.org/stable/modules/generated/sklearn.metrics.precision_recall_fscore_support.html. It may give you a more tangible number to consider.
Precision and recall are defined ... | scikit-learn score metric on the coefficient of determination $R^2$
Consider using the precision and recall scores of scikit-learn: http://scikit-learn.org/stable/modules/generated/sklearn.metrics.precision_recall_fscore_support.html. It may give you a more tangible n |
48,743 | scikit-learn score metric on the coefficient of determination $R^2$ | The Coefficient of Determination (R^2) generalizes the correlation coefficient (r) to multiple predictors, and is often summarized as the proportion of variance explained by the model. It will be quite comfortable for anyone used to analyzing linear regression models, and will be discussed in any text or course you mi... | scikit-learn score metric on the coefficient of determination $R^2$ | The Coefficient of Determination (R^2) generalizes the correlation coefficient (r) to multiple predictors, and is often summarized as the proportion of variance explained by the model. It will be qui | scikit-learn score metric on the coefficient of determination $R^2$
The Coefficient of Determination (R^2) generalizes the correlation coefficient (r) to multiple predictors, and is often summarized as the proportion of variance explained by the model. It will be quite comfortable for anyone used to analyzing linear r... | scikit-learn score metric on the coefficient of determination $R^2$
The Coefficient of Determination (R^2) generalizes the correlation coefficient (r) to multiple predictors, and is often summarized as the proportion of variance explained by the model. It will be qui |
48,744 | Bayesian Aproach: Infering the N and $\theta$ values from a binomial distribution | The hierarchical model seems to be
$$
\begin{eqnarray}
X_i\mid N=n,\Theta=\theta,\Lambda=\lambda &\sim& \mathrm{Bin}(n,\theta) \qquad\qquad\qquad i=1,\dots,m \\
N\mid\Theta=\theta,\Lambda=\lambda &\sim& \mathrm{Poisson}(\lambda/\theta) \\
\Theta &\sim& \mathrm{Beta}(\alpha,\beta) \\
\Lambda &\sim& \mathrm{Gamm... | Bayesian Aproach: Infering the N and $\theta$ values from a binomial distribution | The hierarchical model seems to be
$$
\begin{eqnarray}
X_i\mid N=n,\Theta=\theta,\Lambda=\lambda &\sim& \mathrm{Bin}(n,\theta) \qquad\qquad\qquad i=1,\dots,m \\
N\mid\Theta=\theta,\Lambda=\lambda | Bayesian Aproach: Infering the N and $\theta$ values from a binomial distribution
The hierarchical model seems to be
$$
\begin{eqnarray}
X_i\mid N=n,\Theta=\theta,\Lambda=\lambda &\sim& \mathrm{Bin}(n,\theta) \qquad\qquad\qquad i=1,\dots,m \\
N\mid\Theta=\theta,\Lambda=\lambda &\sim& \mathrm{Poisson}(\lambda/\thet... | Bayesian Aproach: Infering the N and $\theta$ values from a binomial distribution
The hierarchical model seems to be
$$
\begin{eqnarray}
X_i\mid N=n,\Theta=\theta,\Lambda=\lambda &\sim& \mathrm{Bin}(n,\theta) \qquad\qquad\qquad i=1,\dots,m \\
N\mid\Theta=\theta,\Lambda=\lambda |
48,745 | Why does correlation come out the same on raw data and z-scored (standardized) data? | Two facts:
(i) Correlation is the covariance of the z-scores.
(e.g. see here about four-fifths of the way down the page; alternatively, try
zx = scale(x) # this returns z-scores directly, but you can use your form instead
zy = scale(y)
cov(zx,zy);cor(x,y)
to see that covariance of z-scores and correlation are the s... | Why does correlation come out the same on raw data and z-scored (standardized) data? | Two facts:
(i) Correlation is the covariance of the z-scores.
(e.g. see here about four-fifths of the way down the page; alternatively, try
zx = scale(x) # this returns z-scores directly, but you c | Why does correlation come out the same on raw data and z-scored (standardized) data?
Two facts:
(i) Correlation is the covariance of the z-scores.
(e.g. see here about four-fifths of the way down the page; alternatively, try
zx = scale(x) # this returns z-scores directly, but you can use your form instead
zy = scale... | Why does correlation come out the same on raw data and z-scored (standardized) data?
Two facts:
(i) Correlation is the covariance of the z-scores.
(e.g. see here about four-fifths of the way down the page; alternatively, try
zx = scale(x) # this returns z-scores directly, but you c |
48,746 | Why does correlation come out the same on raw data and z-scored (standardized) data? | Correlation is scale-invariant. Try
> cor(zx, y)
and you'll see that the correlation between the raw and z scored data is also the same. | Why does correlation come out the same on raw data and z-scored (standardized) data? | Correlation is scale-invariant. Try
> cor(zx, y)
and you'll see that the correlation between the raw and z scored data is also the same. | Why does correlation come out the same on raw data and z-scored (standardized) data?
Correlation is scale-invariant. Try
> cor(zx, y)
and you'll see that the correlation between the raw and z scored data is also the same. | Why does correlation come out the same on raw data and z-scored (standardized) data?
Correlation is scale-invariant. Try
> cor(zx, y)
and you'll see that the correlation between the raw and z scored data is also the same. |
48,747 | Comparing means with unequal variance and very different sample sizes | The traditional test for comparing two sample means is the t-test. There are no assumptions about the sizes of the samples, so it is OK if they are different.
However, you touch upon the normality assumption. Even if the population is not normally distributed, the Central Limit Theorem allows us to infer normality as ... | Comparing means with unequal variance and very different sample sizes | The traditional test for comparing two sample means is the t-test. There are no assumptions about the sizes of the samples, so it is OK if they are different.
However, you touch upon the normality as | Comparing means with unequal variance and very different sample sizes
The traditional test for comparing two sample means is the t-test. There are no assumptions about the sizes of the samples, so it is OK if they are different.
However, you touch upon the normality assumption. Even if the population is not normally d... | Comparing means with unequal variance and very different sample sizes
The traditional test for comparing two sample means is the t-test. There are no assumptions about the sizes of the samples, so it is OK if they are different.
However, you touch upon the normality as |
48,748 | Comparing means with unequal variance and very different sample sizes | Taking logs and testing the mean on the log scale would normally not correspond to a difference in means on the original scale.
However:
[Edit: my comments apply to an earlier version of the data, and don't apply to the data that are presently in the question. As such, my comments really apply to the situation where th... | Comparing means with unequal variance and very different sample sizes | Taking logs and testing the mean on the log scale would normally not correspond to a difference in means on the original scale.
However:
[Edit: my comments apply to an earlier version of the data, and | Comparing means with unequal variance and very different sample sizes
Taking logs and testing the mean on the log scale would normally not correspond to a difference in means on the original scale.
However:
[Edit: my comments apply to an earlier version of the data, and don't apply to the data that are presently in the... | Comparing means with unequal variance and very different sample sizes
Taking logs and testing the mean on the log scale would normally not correspond to a difference in means on the original scale.
However:
[Edit: my comments apply to an earlier version of the data, and |
48,749 | Comparing means with unequal variance and very different sample sizes | From the data you cannot infer that the variance between males and females is same, in fact the opposite is almost certainly true. Also, since 50 is indeed a bit low, suppose you cannot assume normality.
Compare each female's value with the median of men's values. If median female is neither better nor worse than a m... | Comparing means with unequal variance and very different sample sizes | From the data you cannot infer that the variance between males and females is same, in fact the opposite is almost certainly true. Also, since 50 is indeed a bit low, suppose you cannot assume normal | Comparing means with unequal variance and very different sample sizes
From the data you cannot infer that the variance between males and females is same, in fact the opposite is almost certainly true. Also, since 50 is indeed a bit low, suppose you cannot assume normality.
Compare each female's value with the median o... | Comparing means with unequal variance and very different sample sizes
From the data you cannot infer that the variance between males and females is same, in fact the opposite is almost certainly true. Also, since 50 is indeed a bit low, suppose you cannot assume normal |
48,750 | Goodness of fit tests for quantile regression in R | quantreg includes several AIC functions: "AIC.nlrq", "AIC.rq", "AIC.rqs" and "AIC.rqss" and similar log likelihood functions.
It also has a vignette at vignette("rq",package="quantreg").
Do these do what you want? | Goodness of fit tests for quantile regression in R | quantreg includes several AIC functions: "AIC.nlrq", "AIC.rq", "AIC.rqs" and "AIC.rqss" and similar log likelihood functions.
It also has a vignette at vignette("rq",package="quantreg").
Do these do | Goodness of fit tests for quantile regression in R
quantreg includes several AIC functions: "AIC.nlrq", "AIC.rq", "AIC.rqs" and "AIC.rqss" and similar log likelihood functions.
It also has a vignette at vignette("rq",package="quantreg").
Do these do what you want? | Goodness of fit tests for quantile regression in R
quantreg includes several AIC functions: "AIC.nlrq", "AIC.rq", "AIC.rqs" and "AIC.rqss" and similar log likelihood functions.
It also has a vignette at vignette("rq",package="quantreg").
Do these do |
48,751 | Large scale ridge regression | I've found that LSQR is ideal for problems like this - I've used it successfully for operators of about 3e5 * 1e6 or so. Check http://www.stanford.edu/group/SOL/software/lsqr.html for details. I've used Friedlander's (I think) C port and the python port, which I have (hastily and sloppily) ported to R. | Large scale ridge regression | I've found that LSQR is ideal for problems like this - I've used it successfully for operators of about 3e5 * 1e6 or so. Check http://www.stanford.edu/group/SOL/software/lsqr.html for details. I've | Large scale ridge regression
I've found that LSQR is ideal for problems like this - I've used it successfully for operators of about 3e5 * 1e6 or so. Check http://www.stanford.edu/group/SOL/software/lsqr.html for details. I've used Friedlander's (I think) C port and the python port, which I have (hastily and sloppily... | Large scale ridge regression
I've found that LSQR is ideal for problems like this - I've used it successfully for operators of about 3e5 * 1e6 or so. Check http://www.stanford.edu/group/SOL/software/lsqr.html for details. I've |
48,752 | Optimal orthogonal polynomial chaos basis functions for log-normally distributed random variables | There's no optimal polynomial basis for the log-normal distribution, because it's not determinate in the Hamburger sense. The approach indicated by Xiu and Karniadakis (Generalized Polynomial Chaos) doesn't always work. I'll be a bit informal here. For a rigorous treatement, see here.
Let $X$ denote a continuous random... | Optimal orthogonal polynomial chaos basis functions for log-normally distributed random variables | There's no optimal polynomial basis for the log-normal distribution, because it's not determinate in the Hamburger sense. The approach indicated by Xiu and Karniadakis (Generalized Polynomial Chaos) d | Optimal orthogonal polynomial chaos basis functions for log-normally distributed random variables
There's no optimal polynomial basis for the log-normal distribution, because it's not determinate in the Hamburger sense. The approach indicated by Xiu and Karniadakis (Generalized Polynomial Chaos) doesn't always work. I'... | Optimal orthogonal polynomial chaos basis functions for log-normally distributed random variables
There's no optimal polynomial basis for the log-normal distribution, because it's not determinate in the Hamburger sense. The approach indicated by Xiu and Karniadakis (Generalized Polynomial Chaos) d |
48,753 | Understanding tail dependence coefficients | The tail dependence coefficients $\lambda_U$ and $\lambda_L$ are measures of extremal dependence that quantify the dependence in the upper and lower tails of a bivariate distribution with continuous margins $F$ and $G$.
The coefficients $\lambda_U$ and $\lambda_L$ are defined in terms of quantile exceedences.
For the u... | Understanding tail dependence coefficients | The tail dependence coefficients $\lambda_U$ and $\lambda_L$ are measures of extremal dependence that quantify the dependence in the upper and lower tails of a bivariate distribution with continuous m | Understanding tail dependence coefficients
The tail dependence coefficients $\lambda_U$ and $\lambda_L$ are measures of extremal dependence that quantify the dependence in the upper and lower tails of a bivariate distribution with continuous margins $F$ and $G$.
The coefficients $\lambda_U$ and $\lambda_L$ are defined ... | Understanding tail dependence coefficients
The tail dependence coefficients $\lambda_U$ and $\lambda_L$ are measures of extremal dependence that quantify the dependence in the upper and lower tails of a bivariate distribution with continuous m |
48,754 | Mean difference for count data | A t-test has already been proposed, a Poisson-like generalized linear regression has been proposed. With > 1000 sample size, how about bootstrapping the difference between both samples? It's easy, it's fast, it gives not only a point estimate but also a distribution an it gets rid of all assumptions of normality or poi... | Mean difference for count data | A t-test has already been proposed, a Poisson-like generalized linear regression has been proposed. With > 1000 sample size, how about bootstrapping the difference between both samples? It's easy, it' | Mean difference for count data
A t-test has already been proposed, a Poisson-like generalized linear regression has been proposed. With > 1000 sample size, how about bootstrapping the difference between both samples? It's easy, it's fast, it gives not only a point estimate but also a distribution an it gets rid of all ... | Mean difference for count data
A t-test has already been proposed, a Poisson-like generalized linear regression has been proposed. With > 1000 sample size, how about bootstrapping the difference between both samples? It's easy, it' |
48,755 | Mean difference for count data | Give your large sample sizes, you could probably use a t-test on the means. If your sample sizes are equal, you are in pretty good shape whether you want to use a pooled estimate of the variance or unpooled (Welch's test). Do a one sided test, if you are sure that the population of s1 has a mean at least as large as th... | Mean difference for count data | Give your large sample sizes, you could probably use a t-test on the means. If your sample sizes are equal, you are in pretty good shape whether you want to use a pooled estimate of the variance or un | Mean difference for count data
Give your large sample sizes, you could probably use a t-test on the means. If your sample sizes are equal, you are in pretty good shape whether you want to use a pooled estimate of the variance or unpooled (Welch's test). Do a one sided test, if you are sure that the population of s1 has... | Mean difference for count data
Give your large sample sizes, you could probably use a t-test on the means. If your sample sizes are equal, you are in pretty good shape whether you want to use a pooled estimate of the variance or un |
48,756 | Mean difference for count data | I would suggest you fit a Poisson or loglinear regression model with just one dummy variable created for the two groups and then test the slope parameter, say, $H_a: \beta_1 >0$. Any test method (LRT, Wald, or score) under the maximum likelihood framework can be used. As for over-dispersion problem, you may consider ot... | Mean difference for count data | I would suggest you fit a Poisson or loglinear regression model with just one dummy variable created for the two groups and then test the slope parameter, say, $H_a: \beta_1 >0$. Any test method (LRT, | Mean difference for count data
I would suggest you fit a Poisson or loglinear regression model with just one dummy variable created for the two groups and then test the slope parameter, say, $H_a: \beta_1 >0$. Any test method (LRT, Wald, or score) under the maximum likelihood framework can be used. As for over-dispersi... | Mean difference for count data
I would suggest you fit a Poisson or loglinear regression model with just one dummy variable created for the two groups and then test the slope parameter, say, $H_a: \beta_1 >0$. Any test method (LRT, |
48,757 | Whether to test items for normality (and transform) when performing confirmatory factor analysis on a set of scales? | Ordered categorical items and normality:
First, ordered categorical items are discrete and lumpy. In particular, 3-point response scales lack the granularity required to even provide a rudimentary approximation of normality. When you have more response options in your ordered categorical variable, the item has more pot... | Whether to test items for normality (and transform) when performing confirmatory factor analysis on | Ordered categorical items and normality:
First, ordered categorical items are discrete and lumpy. In particular, 3-point response scales lack the granularity required to even provide a rudimentary app | Whether to test items for normality (and transform) when performing confirmatory factor analysis on a set of scales?
Ordered categorical items and normality:
First, ordered categorical items are discrete and lumpy. In particular, 3-point response scales lack the granularity required to even provide a rudimentary approx... | Whether to test items for normality (and transform) when performing confirmatory factor analysis on
Ordered categorical items and normality:
First, ordered categorical items are discrete and lumpy. In particular, 3-point response scales lack the granularity required to even provide a rudimentary app |
48,758 | Can you use the chi-squared test when the expected values are not determined? | Testing for equality of ratio of females::males across groups is the same as testing for equality of proportion of females across all groups ($r_i = f_i/m_i$, $p_i = f_i/(f_i+m_i)$, so $p_i = r_i/(1+r_i)$ and $r_i = p_i/(1-p_i)$. If the $p_i$ differ so do the $r_i$.
If you check that the proportions, $p_i$ differ sign... | Can you use the chi-squared test when the expected values are not determined? | Testing for equality of ratio of females::males across groups is the same as testing for equality of proportion of females across all groups ($r_i = f_i/m_i$, $p_i = f_i/(f_i+m_i)$, so $p_i = r_i/(1+r | Can you use the chi-squared test when the expected values are not determined?
Testing for equality of ratio of females::males across groups is the same as testing for equality of proportion of females across all groups ($r_i = f_i/m_i$, $p_i = f_i/(f_i+m_i)$, so $p_i = r_i/(1+r_i)$ and $r_i = p_i/(1-p_i)$. If the $p_i... | Can you use the chi-squared test when the expected values are not determined?
Testing for equality of ratio of females::males across groups is the same as testing for equality of proportion of females across all groups ($r_i = f_i/m_i$, $p_i = f_i/(f_i+m_i)$, so $p_i = r_i/(1+r |
48,759 | Can you use the chi-squared test when the expected values are not determined? | It depends on your null hypothesis. If your hypothesis is that the ratio of males to females is equal then the expected value is 0.5.
EDIT:
So your data should look something like this:
1 2 3 4 5 6 TOTAL
MEN | a
WOMEN | b
---... | Can you use the chi-squared test when the expected values are not determined? | It depends on your null hypothesis. If your hypothesis is that the ratio of males to females is equal then the expected value is 0.5.
EDIT:
So your data should look something like this:
1 | Can you use the chi-squared test when the expected values are not determined?
It depends on your null hypothesis. If your hypothesis is that the ratio of males to females is equal then the expected value is 0.5.
EDIT:
So your data should look something like this:
1 2 3 4 5 6 TOTAL
MEN ... | Can you use the chi-squared test when the expected values are not determined?
It depends on your null hypothesis. If your hypothesis is that the ratio of males to females is equal then the expected value is 0.5.
EDIT:
So your data should look something like this:
1 |
48,760 | Can you use the chi-squared test when the expected values are not determined? | Is it mandatory to run a test based on the chi2 statistics ?
If not, I would suggest you use a likelihood ratio test which can properly account for the fact you do not know the expected fraction of females $p$.
If I write $p_i = p + \Delta p_i$ ($\Delta p_0 = 0$) the expected fraction of females in category i, the the ... | Can you use the chi-squared test when the expected values are not determined? | Is it mandatory to run a test based on the chi2 statistics ?
If not, I would suggest you use a likelihood ratio test which can properly account for the fact you do not know the expected fraction of fe | Can you use the chi-squared test when the expected values are not determined?
Is it mandatory to run a test based on the chi2 statistics ?
If not, I would suggest you use a likelihood ratio test which can properly account for the fact you do not know the expected fraction of females $p$.
If I write $p_i = p + \Delta p_... | Can you use the chi-squared test when the expected values are not determined?
Is it mandatory to run a test based on the chi2 statistics ?
If not, I would suggest you use a likelihood ratio test which can properly account for the fact you do not know the expected fraction of fe |
48,761 | How to draw ROC curve with three response variable? [duplicate] | You might want to have a look at the Volume Under the ROC Surface as defined in the following articles:
Ferri C, Hernández-orallo J, Salido MA. Volume Under the ROC Surface for Multi-class Problems. Exact Computation and Evaluation of Approximations. PROC OF 14TH EUROPEAN CONFERENCE ON MACHINE LEARNING. 2003;108‑120. ... | How to draw ROC curve with three response variable? [duplicate] | You might want to have a look at the Volume Under the ROC Surface as defined in the following articles:
Ferri C, Hernández-orallo J, Salido MA. Volume Under the ROC Surface for Multi-class Problems. | How to draw ROC curve with three response variable? [duplicate]
You might want to have a look at the Volume Under the ROC Surface as defined in the following articles:
Ferri C, Hernández-orallo J, Salido MA. Volume Under the ROC Surface for Multi-class Problems. Exact Computation and Evaluation of Approximations. PROC... | How to draw ROC curve with three response variable? [duplicate]
You might want to have a look at the Volume Under the ROC Surface as defined in the following articles:
Ferri C, Hernández-orallo J, Salido MA. Volume Under the ROC Surface for Multi-class Problems. |
48,762 | How to draw ROC curve with three response variable? [duplicate] | ROC Analysis was designed for dealing with only two variables: noise and no noise, so using it for 3 or more variables makes little sense.
However, you for any multi-classification problem it's possible to use a bunch of binary classifiers and do so-called One-Vs-All Classification
E.g. consider the IRIS data set: the... | How to draw ROC curve with three response variable? [duplicate] | ROC Analysis was designed for dealing with only two variables: noise and no noise, so using it for 3 or more variables makes little sense.
However, you for any multi-classification problem it's possi | How to draw ROC curve with three response variable? [duplicate]
ROC Analysis was designed for dealing with only two variables: noise and no noise, so using it for 3 or more variables makes little sense.
However, you for any multi-classification problem it's possible to use a bunch of binary classifiers and do so-calle... | How to draw ROC curve with three response variable? [duplicate]
ROC Analysis was designed for dealing with only two variables: noise and no noise, so using it for 3 or more variables makes little sense.
However, you for any multi-classification problem it's possi |
48,763 | How can a categorical variable where respondents can choose more than one response be used as a predictor in multiple regression? | Use dichotomous indicators (often referred to as dummy variables) to represent the items within this one question. For example, a variable called internet, and then a variable called newspaper, so on so forth. If a person picked both, they got a 1 in each. If a person only picked newspaper, then enter 0 for internet an... | How can a categorical variable where respondents can choose more than one response be used as a pred | Use dichotomous indicators (often referred to as dummy variables) to represent the items within this one question. For example, a variable called internet, and then a variable called newspaper, so on | How can a categorical variable where respondents can choose more than one response be used as a predictor in multiple regression?
Use dichotomous indicators (often referred to as dummy variables) to represent the items within this one question. For example, a variable called internet, and then a variable called newspap... | How can a categorical variable where respondents can choose more than one response be used as a pred
Use dichotomous indicators (often referred to as dummy variables) to represent the items within this one question. For example, a variable called internet, and then a variable called newspaper, so on |
48,764 | Bias correction of logarithmic transformations | Your variable is defined as
$$X_{t} = e^{\alpha t + \beta} e^{z_{t}} $$
Say you have a sample $S_n$ of $n$ observations of past values of the variable and you want to forecast period $n+1$.
Then
$$E\Big (X_{n+1}\mid S_n \Big ) = E\Big (e^{\alpha (n+1) + \beta} e^{z_{n+1}}\mid S_n\Big) = E\Big (e^{\alpha (n+1) + \beta}... | Bias correction of logarithmic transformations | Your variable is defined as
$$X_{t} = e^{\alpha t + \beta} e^{z_{t}} $$
Say you have a sample $S_n$ of $n$ observations of past values of the variable and you want to forecast period $n+1$.
Then
$$E\ | Bias correction of logarithmic transformations
Your variable is defined as
$$X_{t} = e^{\alpha t + \beta} e^{z_{t}} $$
Say you have a sample $S_n$ of $n$ observations of past values of the variable and you want to forecast period $n+1$.
Then
$$E\Big (X_{n+1}\mid S_n \Big ) = E\Big (e^{\alpha (n+1) + \beta} e^{z_{n+1}}... | Bias correction of logarithmic transformations
Your variable is defined as
$$X_{t} = e^{\alpha t + \beta} e^{z_{t}} $$
Say you have a sample $S_n$ of $n$ observations of past values of the variable and you want to forecast period $n+1$.
Then
$$E\ |
48,765 | Computing Out of Bag error in Random Forest: is it the average only over trees that didn't use each sample? | You second last paragraph is the correct answer. As you say, this is the estimate that uses the whole ensemble, but never uses any data that was used to construct the trees making the individual predictions. | Computing Out of Bag error in Random Forest: is it the average only over trees that didn't use each | You second last paragraph is the correct answer. As you say, this is the estimate that uses the whole ensemble, but never uses any data that was used to construct the trees making the individual predi | Computing Out of Bag error in Random Forest: is it the average only over trees that didn't use each sample?
You second last paragraph is the correct answer. As you say, this is the estimate that uses the whole ensemble, but never uses any data that was used to construct the trees making the individual predictions. | Computing Out of Bag error in Random Forest: is it the average only over trees that didn't use each
You second last paragraph is the correct answer. As you say, this is the estimate that uses the whole ensemble, but never uses any data that was used to construct the trees making the individual predi |
48,766 | Treatment of triple seasonal data | Possible yes, sensible no from most time series perspectives.
The main problem with your approach is an apparent assumption that removal of seasonality is, or should be, a trivial matter. But in practice most modern procedures require some kind of estimation of seasonal components based on some choice(s) on how to mod... | Treatment of triple seasonal data | Possible yes, sensible no from most time series perspectives.
The main problem with your approach is an apparent assumption that removal of seasonality is, or should be, a trivial matter. But in prac | Treatment of triple seasonal data
Possible yes, sensible no from most time series perspectives.
The main problem with your approach is an apparent assumption that removal of seasonality is, or should be, a trivial matter. But in practice most modern procedures require some kind of estimation of seasonal components bas... | Treatment of triple seasonal data
Possible yes, sensible no from most time series perspectives.
The main problem with your approach is an apparent assumption that removal of seasonality is, or should be, a trivial matter. But in prac |
48,767 | Treatment of triple seasonal data | You would find it easier to use the tbats() function in the forecast package. It will estimate the seasonality and produce the forecasts. | Treatment of triple seasonal data | You would find it easier to use the tbats() function in the forecast package. It will estimate the seasonality and produce the forecasts. | Treatment of triple seasonal data
You would find it easier to use the tbats() function in the forecast package. It will estimate the seasonality and produce the forecasts. | Treatment of triple seasonal data
You would find it easier to use the tbats() function in the forecast package. It will estimate the seasonality and produce the forecasts. |
48,768 | Gamma and exponential distributions | Usually, the support of a distribution is defined to always be a closed set, so in the case of the gamma distribution, $[0,\infty)$. Even if the density function defined by some formula, for some parameter values, then is undefined, that is not a problem. The reason is that density functions are not really functions! T... | Gamma and exponential distributions | Usually, the support of a distribution is defined to always be a closed set, so in the case of the gamma distribution, $[0,\infty)$. Even if the density function defined by some formula, for some para | Gamma and exponential distributions
Usually, the support of a distribution is defined to always be a closed set, so in the case of the gamma distribution, $[0,\infty)$. Even if the density function defined by some formula, for some parameter values, then is undefined, that is not a problem. The reason is that density f... | Gamma and exponential distributions
Usually, the support of a distribution is defined to always be a closed set, so in the case of the gamma distribution, $[0,\infty)$. Even if the density function defined by some formula, for some para |
48,769 | Visualising a linear model with 6 predictors in R | Here is some code that is hopefully self-explanatory:
set.seed(20987) # for reproducability
N = 200
# variables
days_since = rpois(N, lambda=60)
site = factor(sample(c("site1", "site2"), N, replace=T), c("site1", "site2"))
age = factor(sample(c("juv", "adult"), N, replace=T), c("juv", "ad... | Visualising a linear model with 6 predictors in R | Here is some code that is hopefully self-explanatory:
set.seed(20987) # for reproducability
N = 200
# variables
days_since = rpois(N, lambda=60)
site = factor(sample(c("site1", "si | Visualising a linear model with 6 predictors in R
Here is some code that is hopefully self-explanatory:
set.seed(20987) # for reproducability
N = 200
# variables
days_since = rpois(N, lambda=60)
site = factor(sample(c("site1", "site2"), N, replace=T), c("site1", "site2"))
age = factor(sampl... | Visualising a linear model with 6 predictors in R
Here is some code that is hopefully self-explanatory:
set.seed(20987) # for reproducability
N = 200
# variables
days_since = rpois(N, lambda=60)
site = factor(sample(c("site1", "si |
48,770 | Hausman test: Include or not year effects and/or interaction variables | 1) Are you using the hausman or the xtoverid command? You can try the hausman command with the sigmamore option which sometimes resolves the negative test statistic. A negative test statistic can be due to small sample size and the sigmamore option takes this into account. It is also useful with respect to the point ma... | Hausman test: Include or not year effects and/or interaction variables | 1) Are you using the hausman or the xtoverid command? You can try the hausman command with the sigmamore option which sometimes resolves the negative test statistic. A negative test statistic can be d | Hausman test: Include or not year effects and/or interaction variables
1) Are you using the hausman or the xtoverid command? You can try the hausman command with the sigmamore option which sometimes resolves the negative test statistic. A negative test statistic can be due to small sample size and the sigmamore option ... | Hausman test: Include or not year effects and/or interaction variables
1) Are you using the hausman or the xtoverid command? You can try the hausman command with the sigmamore option which sometimes resolves the negative test statistic. A negative test statistic can be d |
48,771 | How to assess multilevel model assumptions using residual plots | A multilevel model is defined as $y = Xβ + Zη + ǫ$
Thus there are 3 different kinds of residuals:
Marginal residuals: $y − Xβ\ (= Zη + ǫ)$
Conditional residuals: $y − Xβ − Zη\ (= ǫ)$
Random effects: $y − Xβ − ǫ\ (= Zη)$
Marginal residuals:
Should be mean 0, but may show grouping structure
May not be homoskedastic!
... | How to assess multilevel model assumptions using residual plots | A multilevel model is defined as $y = Xβ + Zη + ǫ$
Thus there are 3 different kinds of residuals:
Marginal residuals: $y − Xβ\ (= Zη + ǫ)$
Conditional residuals: $y − Xβ − Zη\ (= ǫ)$
Random effects: | How to assess multilevel model assumptions using residual plots
A multilevel model is defined as $y = Xβ + Zη + ǫ$
Thus there are 3 different kinds of residuals:
Marginal residuals: $y − Xβ\ (= Zη + ǫ)$
Conditional residuals: $y − Xβ − Zη\ (= ǫ)$
Random effects: $y − Xβ − ǫ\ (= Zη)$
Marginal residuals:
Should be mea... | How to assess multilevel model assumptions using residual plots
A multilevel model is defined as $y = Xβ + Zη + ǫ$
Thus there are 3 different kinds of residuals:
Marginal residuals: $y − Xβ\ (= Zη + ǫ)$
Conditional residuals: $y − Xβ − Zη\ (= ǫ)$
Random effects: |
48,772 | Relations between probabilities of "almost" independent random variables | Let $D_{\mathrm{KL}}(P\|Q)$ denote the Kullback–Leibler divergence between discrete probability distributions $P$ and $Q$. It is well-known that the following relation holds between the KL-divergence and mutual information:
$$I(X;Y)=D_{\mathrm{KL}}(P(X,Y)\|P(X)P(Y)) \enspace,$$
where $P(Z)$ denotes the probability dist... | Relations between probabilities of "almost" independent random variables | Let $D_{\mathrm{KL}}(P\|Q)$ denote the Kullback–Leibler divergence between discrete probability distributions $P$ and $Q$. It is well-known that the following relation holds between the KL-divergence | Relations between probabilities of "almost" independent random variables
Let $D_{\mathrm{KL}}(P\|Q)$ denote the Kullback–Leibler divergence between discrete probability distributions $P$ and $Q$. It is well-known that the following relation holds between the KL-divergence and mutual information:
$$I(X;Y)=D_{\mathrm{KL}... | Relations between probabilities of "almost" independent random variables
Let $D_{\mathrm{KL}}(P\|Q)$ denote the Kullback–Leibler divergence between discrete probability distributions $P$ and $Q$. It is well-known that the following relation holds between the KL-divergence |
48,773 | How to handle high dimensional feature vector in probability graph model? | A Hidden Markov Model is defined by two different probability distributions, namely
$$
\begin{align*}
p(s_t \mid s_{t-1}),&\;\;\;\text{the transition probabilities, and}\\
p(x_t \mid s_t),&\;\;\;\text{the emission probabilities.}
\end{align*}
$$
In typical presentations of HMMs the emission probabilities are taken to b... | How to handle high dimensional feature vector in probability graph model? | A Hidden Markov Model is defined by two different probability distributions, namely
$$
\begin{align*}
p(s_t \mid s_{t-1}),&\;\;\;\text{the transition probabilities, and}\\
p(x_t \mid s_t),&\;\;\;\text | How to handle high dimensional feature vector in probability graph model?
A Hidden Markov Model is defined by two different probability distributions, namely
$$
\begin{align*}
p(s_t \mid s_{t-1}),&\;\;\;\text{the transition probabilities, and}\\
p(x_t \mid s_t),&\;\;\;\text{the emission probabilities.}
\end{align*}
$$
... | How to handle high dimensional feature vector in probability graph model?
A Hidden Markov Model is defined by two different probability distributions, namely
$$
\begin{align*}
p(s_t \mid s_{t-1}),&\;\;\;\text{the transition probabilities, and}\\
p(x_t \mid s_t),&\;\;\;\text |
48,774 | How to handle high dimensional feature vector in probability graph model? | If you think the observations interact with the observations, there is a very elegant HMM with Features model proposed by Berkeley that might be useful for you.
ee Paper and Slides
Me and my collaborator recently implemented this algorithm. Although currently it is mostly written for educational applications, it is ge... | How to handle high dimensional feature vector in probability graph model? | If you think the observations interact with the observations, there is a very elegant HMM with Features model proposed by Berkeley that might be useful for you.
ee Paper and Slides
Me and my collabor | How to handle high dimensional feature vector in probability graph model?
If you think the observations interact with the observations, there is a very elegant HMM with Features model proposed by Berkeley that might be useful for you.
ee Paper and Slides
Me and my collaborator recently implemented this algorithm. Alth... | How to handle high dimensional feature vector in probability graph model?
If you think the observations interact with the observations, there is a very elegant HMM with Features model proposed by Berkeley that might be useful for you.
ee Paper and Slides
Me and my collabor |
48,775 | How to handle high dimensional feature vector in probability graph model? | You should check out the TrueSkill model proposed by Ralf Herbrich and Thore Graepel at Microsoft Research. (Some related papers are listed at the end of that page, where some implementation details are given.) Simply put, TrueSkill does very large scale learning with graphical models. It is able to handle very large d... | How to handle high dimensional feature vector in probability graph model? | You should check out the TrueSkill model proposed by Ralf Herbrich and Thore Graepel at Microsoft Research. (Some related papers are listed at the end of that page, where some implementation details a | How to handle high dimensional feature vector in probability graph model?
You should check out the TrueSkill model proposed by Ralf Herbrich and Thore Graepel at Microsoft Research. (Some related papers are listed at the end of that page, where some implementation details are given.) Simply put, TrueSkill does very lar... | How to handle high dimensional feature vector in probability graph model?
You should check out the TrueSkill model proposed by Ralf Herbrich and Thore Graepel at Microsoft Research. (Some related papers are listed at the end of that page, where some implementation details a |
48,776 | How to handle high dimensional feature vector in probability graph model? | See this answer: How to handle high dimensional feature vector in probability graph model? | How to handle high dimensional feature vector in probability graph model? | See this answer: How to handle high dimensional feature vector in probability graph model? | How to handle high dimensional feature vector in probability graph model?
See this answer: How to handle high dimensional feature vector in probability graph model? | How to handle high dimensional feature vector in probability graph model?
See this answer: How to handle high dimensional feature vector in probability graph model? |
48,777 | Understanding multinomial distribution | Suppose you roll a 6-sided die $N$ times.
The outcome of roll $i$, $i=1,\ldots,N$, is represented by the random variable $X_i$. The tuple $\mathbf{X}=\left(X_1,\ldots,X_N\right)$ contains the outcome of each roll.
We can obtain category-level count information from $\mathbf{X}$ by taking $N_j=\sum_{i=1}^{N}\delta\left(... | Understanding multinomial distribution | Suppose you roll a 6-sided die $N$ times.
The outcome of roll $i$, $i=1,\ldots,N$, is represented by the random variable $X_i$. The tuple $\mathbf{X}=\left(X_1,\ldots,X_N\right)$ contains the outcome | Understanding multinomial distribution
Suppose you roll a 6-sided die $N$ times.
The outcome of roll $i$, $i=1,\ldots,N$, is represented by the random variable $X_i$. The tuple $\mathbf{X}=\left(X_1,\ldots,X_N\right)$ contains the outcome of each roll.
We can obtain category-level count information from $\mathbf{X}$ by... | Understanding multinomial distribution
Suppose you roll a 6-sided die $N$ times.
The outcome of roll $i$, $i=1,\ldots,N$, is represented by the random variable $X_i$. The tuple $\mathbf{X}=\left(X_1,\ldots,X_N\right)$ contains the outcome |
48,778 | What exactly is the "proportion of variability explained"? | When you hear "more than 70% variability is explained by ...", the speaker is referring to the sums of squares (SS), not the mean squares (MS). I should note that exactly what they mean is not certain; they could be referring to either eta-squared or partial eta-squared:
\begin{align}
\eta^2&=\frac{SS~IV_j}{SS~Total} ... | What exactly is the "proportion of variability explained"? | When you hear "more than 70% variability is explained by ...", the speaker is referring to the sums of squares (SS), not the mean squares (MS). I should note that exactly what they mean is not certai | What exactly is the "proportion of variability explained"?
When you hear "more than 70% variability is explained by ...", the speaker is referring to the sums of squares (SS), not the mean squares (MS). I should note that exactly what they mean is not certain; they could be referring to either eta-squared or partial e... | What exactly is the "proportion of variability explained"?
When you hear "more than 70% variability is explained by ...", the speaker is referring to the sums of squares (SS), not the mean squares (MS). I should note that exactly what they mean is not certai |
48,779 | When does quantile regression produce biased coefficients (if ever)? | If you have a model
$$
Y_i = X_i B(\tau) + \epsilon_i(\tau)
$$
then a sufficient condition for $\tau$-quantile regression to give an unbiased estimate of $B(\tau)$ is that the $\tau$-th quantile of $\epsilon(\tau)$ conditional on $X$ is zero. This follows from the fact that (i) the sample quantile regression objectiv... | When does quantile regression produce biased coefficients (if ever)? | If you have a model
$$
Y_i = X_i B(\tau) + \epsilon_i(\tau)
$$
then a sufficient condition for $\tau$-quantile regression to give an unbiased estimate of $B(\tau)$ is that the $\tau$-th quantile of | When does quantile regression produce biased coefficients (if ever)?
If you have a model
$$
Y_i = X_i B(\tau) + \epsilon_i(\tau)
$$
then a sufficient condition for $\tau$-quantile regression to give an unbiased estimate of $B(\tau)$ is that the $\tau$-th quantile of $\epsilon(\tau)$ conditional on $X$ is zero. This f... | When does quantile regression produce biased coefficients (if ever)?
If you have a model
$$
Y_i = X_i B(\tau) + \epsilon_i(\tau)
$$
then a sufficient condition for $\tau$-quantile regression to give an unbiased estimate of $B(\tau)$ is that the $\tau$-th quantile of |
48,780 | Implementation of M-spline in R | Though I know it is not a new question, just want to mention one existing implementation of M-splines in R for reference.
Package splines2 provides function named mSpline for M-splines. If you had experience of using package splines, you have probably known how to use mSpline already since its user interface is exactly... | Implementation of M-spline in R | Though I know it is not a new question, just want to mention one existing implementation of M-splines in R for reference.
Package splines2 provides function named mSpline for M-splines. If you had exp | Implementation of M-spline in R
Though I know it is not a new question, just want to mention one existing implementation of M-splines in R for reference.
Package splines2 provides function named mSpline for M-splines. If you had experience of using package splines, you have probably known how to use mSpline already sin... | Implementation of M-spline in R
Though I know it is not a new question, just want to mention one existing implementation of M-splines in R for reference.
Package splines2 provides function named mSpline for M-splines. If you had exp |
48,781 | Implementation of M-spline in R | Well, after some tweaking with my code I tried to add this line to the definition of Mk :
if(ts[i+k]-ts[i]==0){0}
So that when it goes out of the list, the spline is simply zero. It worked and I could confirm that the basis was right. | Implementation of M-spline in R | Well, after some tweaking with my code I tried to add this line to the definition of Mk :
if(ts[i+k]-ts[i]==0){0}
So that when it goes out of the list, the spline is simply zero. It worked and I | Implementation of M-spline in R
Well, after some tweaking with my code I tried to add this line to the definition of Mk :
if(ts[i+k]-ts[i]==0){0}
So that when it goes out of the list, the spline is simply zero. It worked and I could confirm that the basis was right. | Implementation of M-spline in R
Well, after some tweaking with my code I tried to add this line to the definition of Mk :
if(ts[i+k]-ts[i]==0){0}
So that when it goes out of the list, the spline is simply zero. It worked and I |
48,782 | Is the Gaussian copula (for d=2) with normal margins identical to the bivariate normal? | Since the Gaussian copula results from taking a multivariate normal and transforming the margins to uniformity, a multivariate distribution with Gaussian copula and normal margins is multivariate normal.
Transforming the margins to normality merely undoes the original transform to uniform margins to obtain the copula.... | Is the Gaussian copula (for d=2) with normal margins identical to the bivariate normal? | Since the Gaussian copula results from taking a multivariate normal and transforming the margins to uniformity, a multivariate distribution with Gaussian copula and normal margins is multivariate norm | Is the Gaussian copula (for d=2) with normal margins identical to the bivariate normal?
Since the Gaussian copula results from taking a multivariate normal and transforming the margins to uniformity, a multivariate distribution with Gaussian copula and normal margins is multivariate normal.
Transforming the margins to... | Is the Gaussian copula (for d=2) with normal margins identical to the bivariate normal?
Since the Gaussian copula results from taking a multivariate normal and transforming the margins to uniformity, a multivariate distribution with Gaussian copula and normal margins is multivariate norm |
48,783 | Explanatory variables with many zeros | You are focusing on zeros as part of the distributions of several predictors, but the central questions for modelling include (a) what kind of response variable you have and (b) what kind of relationship you expect between the response and the predictors or explanatory variables.
Zeros in the predictors themselves rul... | Explanatory variables with many zeros | You are focusing on zeros as part of the distributions of several predictors, but the central questions for modelling include (a) what kind of response variable you have and (b) what kind of relations | Explanatory variables with many zeros
You are focusing on zeros as part of the distributions of several predictors, but the central questions for modelling include (a) what kind of response variable you have and (b) what kind of relationship you expect between the response and the predictors or explanatory variables.
... | Explanatory variables with many zeros
You are focusing on zeros as part of the distributions of several predictors, but the central questions for modelling include (a) what kind of response variable you have and (b) what kind of relations |
48,784 | Justifying the distribution for the maximum likelihood estimator in a linear regression example | Step 1: General: Recognize that $(x_i - \bar x)$, and its square, and $\frac{1}{\sum (x_i - \bar x)^2}$ are constants, not random variables. Further note that $\alpha$ and $\beta$ and $\sigma$ are also constants. First write $B$ as a constant times an expression containing a random variable. Focus carefully on the part... | Justifying the distribution for the maximum likelihood estimator in a linear regression example | Step 1: General: Recognize that $(x_i - \bar x)$, and its square, and $\frac{1}{\sum (x_i - \bar x)^2}$ are constants, not random variables. Further note that $\alpha$ and $\beta$ and $\sigma$ are als | Justifying the distribution for the maximum likelihood estimator in a linear regression example
Step 1: General: Recognize that $(x_i - \bar x)$, and its square, and $\frac{1}{\sum (x_i - \bar x)^2}$ are constants, not random variables. Further note that $\alpha$ and $\beta$ and $\sigma$ are also constants. First write... | Justifying the distribution for the maximum likelihood estimator in a linear regression example
Step 1: General: Recognize that $(x_i - \bar x)$, and its square, and $\frac{1}{\sum (x_i - \bar x)^2}$ are constants, not random variables. Further note that $\alpha$ and $\beta$ and $\sigma$ are als |
48,785 | Understanding the mean shift algorithm with Gaussian kernel | if I were you I would refer to one of the main mean shift papers: Mean Shift: A Robust Approach Toward Feature Space Analysis. The short answer to your questions: yes c is always positive and no the kernel (window) is not a circle.
Now the long version. The kernel density estimator is:
$\hat{f}_h(x) = \frac{1}{nh} ... | Understanding the mean shift algorithm with Gaussian kernel | if I were you I would refer to one of the main mean shift papers: Mean Shift: A Robust Approach Toward Feature Space Analysis. The short answer to your questions: yes c is always positive and no the k | Understanding the mean shift algorithm with Gaussian kernel
if I were you I would refer to one of the main mean shift papers: Mean Shift: A Robust Approach Toward Feature Space Analysis. The short answer to your questions: yes c is always positive and no the kernel (window) is not a circle.
Now the long version. The ke... | Understanding the mean shift algorithm with Gaussian kernel
if I were you I would refer to one of the main mean shift papers: Mean Shift: A Robust Approach Toward Feature Space Analysis. The short answer to your questions: yes c is always positive and no the k |
48,786 | Outliers in importance sampling | This is my first answer on stackexchange, so feel free to point out anything I'm doing wrong. Also, I am a student studying this subject so I may make mistakes.
Let's consider the importance weights which are often abbreviated in the literature as P(x)/Q(x). If the proposal density does not have heavy tails while the t... | Outliers in importance sampling | This is my first answer on stackexchange, so feel free to point out anything I'm doing wrong. Also, I am a student studying this subject so I may make mistakes.
Let's consider the importance weights w | Outliers in importance sampling
This is my first answer on stackexchange, so feel free to point out anything I'm doing wrong. Also, I am a student studying this subject so I may make mistakes.
Let's consider the importance weights which are often abbreviated in the literature as P(x)/Q(x). If the proposal density does ... | Outliers in importance sampling
This is my first answer on stackexchange, so feel free to point out anything I'm doing wrong. Also, I am a student studying this subject so I may make mistakes.
Let's consider the importance weights w |
48,787 | Wald test and F distribution | To emphasize that the distance between the point estimate $\hat{\mu}$ and the hypothesized value $\mu$ is being scaled by its standard error, I find it easier to write $W$ as
$$
W = \frac{(\hat{\mu} - \mu_0)^2}{\hat{\sigma}^2/n}.
$$
Recall the relationship between the $\hat{\sigma}^2$ and the unbiased sample variance $... | Wald test and F distribution | To emphasize that the distance between the point estimate $\hat{\mu}$ and the hypothesized value $\mu$ is being scaled by its standard error, I find it easier to write $W$ as
$$
W = \frac{(\hat{\mu} - | Wald test and F distribution
To emphasize that the distance between the point estimate $\hat{\mu}$ and the hypothesized value $\mu$ is being scaled by its standard error, I find it easier to write $W$ as
$$
W = \frac{(\hat{\mu} - \mu_0)^2}{\hat{\sigma}^2/n}.
$$
Recall the relationship between the $\hat{\sigma}^2$ and t... | Wald test and F distribution
To emphasize that the distance between the point estimate $\hat{\mu}$ and the hypothesized value $\mu$ is being scaled by its standard error, I find it easier to write $W$ as
$$
W = \frac{(\hat{\mu} - |
48,788 | Visualising relationship data | There is much of relevance at
Graph for relationship between two ordinal variables
The detail there of using ordinal variables does not bite with your problem where the workers are just different.
You might need to expand on "appealing": there is often tension here between clever and unusual but difficult to decode a... | Visualising relationship data | There is much of relevance at
Graph for relationship between two ordinal variables
The detail there of using ordinal variables does not bite with your problem where the workers are just different.
Y | Visualising relationship data
There is much of relevance at
Graph for relationship between two ordinal variables
The detail there of using ordinal variables does not bite with your problem where the workers are just different.
You might need to expand on "appealing": there is often tension here between clever and unu... | Visualising relationship data
There is much of relevance at
Graph for relationship between two ordinal variables
The detail there of using ordinal variables does not bite with your problem where the workers are just different.
Y |
48,789 | hyperspherical nature of K means (and other squared error clustering method) | Well, mathematically, k-means clusters are not spherical, but Voronoi cells.
However, the claim is not invalid, as the actual data usually does not fill the whole cell, but if you'd take the convex hull of the data it indeed is somewhat spherical in nature.
The reason probably is that when minimizing variance (and k-me... | hyperspherical nature of K means (and other squared error clustering method) | Well, mathematically, k-means clusters are not spherical, but Voronoi cells.
However, the claim is not invalid, as the actual data usually does not fill the whole cell, but if you'd take the convex hu | hyperspherical nature of K means (and other squared error clustering method)
Well, mathematically, k-means clusters are not spherical, but Voronoi cells.
However, the claim is not invalid, as the actual data usually does not fill the whole cell, but if you'd take the convex hull of the data it indeed is somewhat spheri... | hyperspherical nature of K means (and other squared error clustering method)
Well, mathematically, k-means clusters are not spherical, but Voronoi cells.
However, the claim is not invalid, as the actual data usually does not fill the whole cell, but if you'd take the convex hu |
48,790 | hyperspherical nature of K means (and other squared error clustering method) | Here is one way that one might think of k means in terms of hyperspheres. A point $x$ belongs to the cluster centered at $c \in CENTERS$ if there exists a radius $r$ such that $x$ belongs to the ball centered at $c$ of radius $r$ but does not belong to the ball radius $r$ centered at any $c' \neq c \in CENTERS$. What... | hyperspherical nature of K means (and other squared error clustering method) | Here is one way that one might think of k means in terms of hyperspheres. A point $x$ belongs to the cluster centered at $c \in CENTERS$ if there exists a radius $r$ such that $x$ belongs to the ball | hyperspherical nature of K means (and other squared error clustering method)
Here is one way that one might think of k means in terms of hyperspheres. A point $x$ belongs to the cluster centered at $c \in CENTERS$ if there exists a radius $r$ such that $x$ belongs to the ball centered at $c$ of radius $r$ but does not... | hyperspherical nature of K means (and other squared error clustering method)
Here is one way that one might think of k means in terms of hyperspheres. A point $x$ belongs to the cluster centered at $c \in CENTERS$ if there exists a radius $r$ such that $x$ belongs to the ball |
48,791 | Fit poisson regression | If the probability model for $Y$ is this:
$$P(Y_i=y) = \exp(\lambda_i) {\lambda_i}^y / y!$$
and $i$-th observations rate parameter is in fact given by:
$$ \log(\lambda_i) = \beta_0 + \beta_1 x_i$$
(with no model misspecification per others' comments here)
Then the answer is yes you can calculate the PMF for a new $Y$ ... | Fit poisson regression | If the probability model for $Y$ is this:
$$P(Y_i=y) = \exp(\lambda_i) {\lambda_i}^y / y!$$
and $i$-th observations rate parameter is in fact given by:
$$ \log(\lambda_i) = \beta_0 + \beta_1 x_i$$
(w | Fit poisson regression
If the probability model for $Y$ is this:
$$P(Y_i=y) = \exp(\lambda_i) {\lambda_i}^y / y!$$
and $i$-th observations rate parameter is in fact given by:
$$ \log(\lambda_i) = \beta_0 + \beta_1 x_i$$
(with no model misspecification per others' comments here)
Then the answer is yes you can calculate... | Fit poisson regression
If the probability model for $Y$ is this:
$$P(Y_i=y) = \exp(\lambda_i) {\lambda_i}^y / y!$$
and $i$-th observations rate parameter is in fact given by:
$$ \log(\lambda_i) = \beta_0 + \beta_1 x_i$$
(w |
48,792 | Fit poisson regression | Partially answered in comments:
Besides the fact that a conditional Poisson distribution (conditional on $x$) does not imply a marginal Poisson distribution, this would seem to be exactly the idea of Poisson regression, yes. – Nick Sabbe
For more information on Poisson regression, see Scaling vs Offsetting in Quasi-Po... | Fit poisson regression | Partially answered in comments:
Besides the fact that a conditional Poisson distribution (conditional on $x$) does not imply a marginal Poisson distribution, this would seem to be exactly the idea of | Fit poisson regression
Partially answered in comments:
Besides the fact that a conditional Poisson distribution (conditional on $x$) does not imply a marginal Poisson distribution, this would seem to be exactly the idea of Poisson regression, yes. – Nick Sabbe
For more information on Poisson regression, see Scaling vs... | Fit poisson regression
Partially answered in comments:
Besides the fact that a conditional Poisson distribution (conditional on $x$) does not imply a marginal Poisson distribution, this would seem to be exactly the idea of |
48,793 | Sufficient statistic and hypothesis testing | Not sure if this is an answer. But perhaps a few comments. If I am restating what you are probably already aware of, my apologies.
First, based on the Fisher–Neyman Factorization, if $T(\mathbf{x})$ is a sufficient statistic, then the likelihood function factorizes to the product of (1) a function that does not involve... | Sufficient statistic and hypothesis testing | Not sure if this is an answer. But perhaps a few comments. If I am restating what you are probably already aware of, my apologies.
First, based on the Fisher–Neyman Factorization, if $T(\mathbf{x})$ i | Sufficient statistic and hypothesis testing
Not sure if this is an answer. But perhaps a few comments. If I am restating what you are probably already aware of, my apologies.
First, based on the Fisher–Neyman Factorization, if $T(\mathbf{x})$ is a sufficient statistic, then the likelihood function factorizes to the pro... | Sufficient statistic and hypothesis testing
Not sure if this is an answer. But perhaps a few comments. If I am restating what you are probably already aware of, my apologies.
First, based on the Fisher–Neyman Factorization, if $T(\mathbf{x})$ i |
48,794 | How to determine the sample size of a Latin Hypercube sampling? | The total number of sample combinations you have is $2\times 3 \times 2 \times 3 \times 3 = 108$ (or what ever). Depending on your experiment (and the difficulty of taking samples), you should ideally just sample everything. If not, there a a few other options.
You can't technically do standard LHC sampling, or orthogo... | How to determine the sample size of a Latin Hypercube sampling? | The total number of sample combinations you have is $2\times 3 \times 2 \times 3 \times 3 = 108$ (or what ever). Depending on your experiment (and the difficulty of taking samples), you should ideally | How to determine the sample size of a Latin Hypercube sampling?
The total number of sample combinations you have is $2\times 3 \times 2 \times 3 \times 3 = 108$ (or what ever). Depending on your experiment (and the difficulty of taking samples), you should ideally just sample everything. If not, there a a few other opt... | How to determine the sample size of a Latin Hypercube sampling?
The total number of sample combinations you have is $2\times 3 \times 2 \times 3 \times 3 = 108$ (or what ever). Depending on your experiment (and the difficulty of taking samples), you should ideally |
48,795 | What regression analysis should I perform on my data and why? | Whether a variable is categorical depends only on the variable, not on any "sharing" of common values. In your case, LAW_FAM is categorical because it has four discrete categories: FRA, SCA, ENG, GER. In particular, LAW_FAM is nominal: the categories have no ordering. You could have several countries which happen to ha... | What regression analysis should I perform on my data and why? | Whether a variable is categorical depends only on the variable, not on any "sharing" of common values. In your case, LAW_FAM is categorical because it has four discrete categories: FRA, SCA, ENG, GER. | What regression analysis should I perform on my data and why?
Whether a variable is categorical depends only on the variable, not on any "sharing" of common values. In your case, LAW_FAM is categorical because it has four discrete categories: FRA, SCA, ENG, GER. In particular, LAW_FAM is nominal: the categories have no... | What regression analysis should I perform on my data and why?
Whether a variable is categorical depends only on the variable, not on any "sharing" of common values. In your case, LAW_FAM is categorical because it has four discrete categories: FRA, SCA, ENG, GER. |
48,796 | What regression analysis should I perform on my data and why? | Your situation is a bit complicated. We just need to take a step back.
In order for us to run this regression we need to know what your research question / hypothesis is?
You might not have to use the GLM, but could build a model from the linear regression and use the "test method" (which is not available in the drop m... | What regression analysis should I perform on my data and why? | Your situation is a bit complicated. We just need to take a step back.
In order for us to run this regression we need to know what your research question / hypothesis is?
You might not have to use the | What regression analysis should I perform on my data and why?
Your situation is a bit complicated. We just need to take a step back.
In order for us to run this regression we need to know what your research question / hypothesis is?
You might not have to use the GLM, but could build a model from the linear regression a... | What regression analysis should I perform on my data and why?
Your situation is a bit complicated. We just need to take a step back.
In order for us to run this regression we need to know what your research question / hypothesis is?
You might not have to use the |
48,797 | What regression analysis should I perform on my data and why? | OK, let me get this straight. In response to your older question here, you're trying to fit a more complicated mixed/multilevel/hierarchical model (yah for terminology). Not having any experience with SPSS, this is going to be more general, along with some guesses at what SPSS is looking for via the screenshots provide... | What regression analysis should I perform on my data and why? | OK, let me get this straight. In response to your older question here, you're trying to fit a more complicated mixed/multilevel/hierarchical model (yah for terminology). Not having any experience with | What regression analysis should I perform on my data and why?
OK, let me get this straight. In response to your older question here, you're trying to fit a more complicated mixed/multilevel/hierarchical model (yah for terminology). Not having any experience with SPSS, this is going to be more general, along with some g... | What regression analysis should I perform on my data and why?
OK, let me get this straight. In response to your older question here, you're trying to fit a more complicated mixed/multilevel/hierarchical model (yah for terminology). Not having any experience with |
48,798 | What regression analysis should I perform on my data and why? | I think that you are missing two critical factors. If you try to make a model of gravity but do not take into account mass or inter-mass distance, then no model will work well.
http://www.ted.com/talks/geoffrey_west_the_surprising_math_of_cities_and_corporations.html
I just love standing on the shoulders of giants. ... | What regression analysis should I perform on my data and why? | I think that you are missing two critical factors. If you try to make a model of gravity but do not take into account mass or inter-mass distance, then no model will work well.
http://www.ted.com/t | What regression analysis should I perform on my data and why?
I think that you are missing two critical factors. If you try to make a model of gravity but do not take into account mass or inter-mass distance, then no model will work well.
http://www.ted.com/talks/geoffrey_west_the_surprising_math_of_cities_and_corpo... | What regression analysis should I perform on my data and why?
I think that you are missing two critical factors. If you try to make a model of gravity but do not take into account mass or inter-mass distance, then no model will work well.
http://www.ted.com/t |
48,799 | Is ARIMA better in comparision with Neural Networks? | It looks like you are using both of these models for time-series forecasts. I would cross-validate both models and compare their out-of-sample error. | Is ARIMA better in comparision with Neural Networks? | It looks like you are using both of these models for time-series forecasts. I would cross-validate both models and compare their out-of-sample error. | Is ARIMA better in comparision with Neural Networks?
It looks like you are using both of these models for time-series forecasts. I would cross-validate both models and compare their out-of-sample error. | Is ARIMA better in comparision with Neural Networks?
It looks like you are using both of these models for time-series forecasts. I would cross-validate both models and compare their out-of-sample error. |
48,800 | Is ARIMA better in comparision with Neural Networks? | NN ignore outliers. If you ignore outliers, then you are in big trouble.
Your ARIMA model is also ignoring outliers so then you are also in big trouble.
As for cross-validating, that is for those that are fitting models to data instead of actually modeling. Only the 849 page text book "Principles of Forecasting" a... | Is ARIMA better in comparision with Neural Networks? | NN ignore outliers. If you ignore outliers, then you are in big trouble.
Your ARIMA model is also ignoring outliers so then you are also in big trouble.
As for cross-validating, that is for those | Is ARIMA better in comparision with Neural Networks?
NN ignore outliers. If you ignore outliers, then you are in big trouble.
Your ARIMA model is also ignoring outliers so then you are also in big trouble.
As for cross-validating, that is for those that are fitting models to data instead of actually modeling. Only... | Is ARIMA better in comparision with Neural Networks?
NN ignore outliers. If you ignore outliers, then you are in big trouble.
Your ARIMA model is also ignoring outliers so then you are also in big trouble.
As for cross-validating, that is for those |
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