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51,601
Is it appropriate to examine an interaction effect that is almost statistically significant?
You might consider switching to mixed effects modelling, which in some cases provides superior power over ANOVA.
Is it appropriate to examine an interaction effect that is almost statistically significant?
You might consider switching to mixed effects modelling, which in some cases provides superior power over ANOVA.
Is it appropriate to examine an interaction effect that is almost statistically significant? You might consider switching to mixed effects modelling, which in some cases provides superior power over ANOVA.
Is it appropriate to examine an interaction effect that is almost statistically significant? You might consider switching to mixed effects modelling, which in some cases provides superior power over ANOVA.
51,602
Is it appropriate to examine an interaction effect that is almost statistically significant?
I agree with the others that you certainly can explore this interaction, but, if it's not significant, you might not have much power to aid your analysis.
Is it appropriate to examine an interaction effect that is almost statistically significant?
I agree with the others that you certainly can explore this interaction, but, if it's not significant, you might not have much power to aid your analysis.
Is it appropriate to examine an interaction effect that is almost statistically significant? I agree with the others that you certainly can explore this interaction, but, if it's not significant, you might not have much power to aid your analysis.
Is it appropriate to examine an interaction effect that is almost statistically significant? I agree with the others that you certainly can explore this interaction, but, if it's not significant, you might not have much power to aid your analysis.
51,603
Is it appropriate to examine an interaction effect that is almost statistically significant?
To say something similar to the other answers in slightly different words. I would do the following: Report that the (hopefully expected) interaction is almost or marginal significant or that there is a trend towards significance (these expressions are all common, at least in psychology). Then, state that therefore I i...
Is it appropriate to examine an interaction effect that is almost statistically significant?
To say something similar to the other answers in slightly different words. I would do the following: Report that the (hopefully expected) interaction is almost or marginal significant or that there is
Is it appropriate to examine an interaction effect that is almost statistically significant? To say something similar to the other answers in slightly different words. I would do the following: Report that the (hopefully expected) interaction is almost or marginal significant or that there is a trend towards significan...
Is it appropriate to examine an interaction effect that is almost statistically significant? To say something similar to the other answers in slightly different words. I would do the following: Report that the (hopefully expected) interaction is almost or marginal significant or that there is
51,604
Get the number of parameters of a linear model
Try something like: > x <- replicate(2, rnorm(100)) > y <- 1.2*x[,1]+rnorm(100) > summary(lm.fit <- lm(y~x)) > length(lm.fit$coefficients) [1] 3 > # or > length(coef(lm.fit)) [1] 3 You can have a better idea of what an R object includes with > str(lm.fit)
Get the number of parameters of a linear model
Try something like: > x <- replicate(2, rnorm(100)) > y <- 1.2*x[,1]+rnorm(100) > summary(lm.fit <- lm(y~x)) > length(lm.fit$coefficients) [1] 3 > # or > length(coef(lm.fit)) [1] 3 You can have a bet
Get the number of parameters of a linear model Try something like: > x <- replicate(2, rnorm(100)) > y <- 1.2*x[,1]+rnorm(100) > summary(lm.fit <- lm(y~x)) > length(lm.fit$coefficients) [1] 3 > # or > length(coef(lm.fit)) [1] 3 You can have a better idea of what an R object includes with > str(lm.fit)
Get the number of parameters of a linear model Try something like: > x <- replicate(2, rnorm(100)) > y <- 1.2*x[,1]+rnorm(100) > summary(lm.fit <- lm(y~x)) > length(lm.fit$coefficients) [1] 3 > # or > length(coef(lm.fit)) [1] 3 You can have a bet
51,605
Get the number of parameters of a linear model
A more general approach is to use the logLik() function. It returns an object with the attribute df that gives the fitted models degrees of freedom. The benefit of this approach is that it works with many other model classes (including glm). In the case of ordinary linear regression (lm) this corresponds to the numb...
Get the number of parameters of a linear model
A more general approach is to use the logLik() function. It returns an object with the attribute df that gives the fitted models degrees of freedom. The benefit of this approach is that it works wit
Get the number of parameters of a linear model A more general approach is to use the logLik() function. It returns an object with the attribute df that gives the fitted models degrees of freedom. The benefit of this approach is that it works with many other model classes (including glm). In the case of ordinary line...
Get the number of parameters of a linear model A more general approach is to use the logLik() function. It returns an object with the attribute df that gives the fitted models degrees of freedom. The benefit of this approach is that it works wit
51,606
Get the number of parameters of a linear model
May be it's a little bit hackish but you can do : n <- length(coefficients(model))
Get the number of parameters of a linear model
May be it's a little bit hackish but you can do : n <- length(coefficients(model))
Get the number of parameters of a linear model May be it's a little bit hackish but you can do : n <- length(coefficients(model))
Get the number of parameters of a linear model May be it's a little bit hackish but you can do : n <- length(coefficients(model))
51,607
Get the number of parameters of a linear model
I think you could use the component lm.fit$rank or else subtract lm.fit$df.residual from the sample size to get what you want. (I assume you want the number of free parameters.)
Get the number of parameters of a linear model
I think you could use the component lm.fit$rank or else subtract lm.fit$df.residual from the sample size to get what you want. (I assume you want the number of free parameters.)
Get the number of parameters of a linear model I think you could use the component lm.fit$rank or else subtract lm.fit$df.residual from the sample size to get what you want. (I assume you want the number of free parameters.)
Get the number of parameters of a linear model I think you could use the component lm.fit$rank or else subtract lm.fit$df.residual from the sample size to get what you want. (I assume you want the number of free parameters.)
51,608
Get the number of parameters of a linear model
The R function logLik seems to be an attractive solution to extract model degree of freedom in general, since it can be applied to many model objects including lm, glm, nls, Arima to name a few. But the df of attributes(logLik(obj)) seems to be 1 larger than the true value. So use it with caution.
Get the number of parameters of a linear model
The R function logLik seems to be an attractive solution to extract model degree of freedom in general, since it can be applied to many model objects including lm, glm, nls, Arima to name a few. But
Get the number of parameters of a linear model The R function logLik seems to be an attractive solution to extract model degree of freedom in general, since it can be applied to many model objects including lm, glm, nls, Arima to name a few. But the df of attributes(logLik(obj)) seems to be 1 larger than the true valu...
Get the number of parameters of a linear model The R function logLik seems to be an attractive solution to extract model degree of freedom in general, since it can be applied to many model objects including lm, glm, nls, Arima to name a few. But
51,609
Get the number of parameters of a linear model
Here is another solution if your model is nls, with an example dataset in r: # Fit a nls model (this is a light response curve of photosynthesis, in this case) mod<-nls(response~(alpha*x+Pm-sqrt(((alpha*x+Pm)^2)-4*alpha*x*Pm*theta))/(2*theta)+Rd, data = Data, start=list(alpha=0.05, theta=0.5, Rd=-1, Pm=30)) # There ar...
Get the number of parameters of a linear model
Here is another solution if your model is nls, with an example dataset in r: # Fit a nls model (this is a light response curve of photosynthesis, in this case) mod<-nls(response~(alpha*x+Pm-sqrt(((alp
Get the number of parameters of a linear model Here is another solution if your model is nls, with an example dataset in r: # Fit a nls model (this is a light response curve of photosynthesis, in this case) mod<-nls(response~(alpha*x+Pm-sqrt(((alpha*x+Pm)^2)-4*alpha*x*Pm*theta))/(2*theta)+Rd, data = Data, start=list(al...
Get the number of parameters of a linear model Here is another solution if your model is nls, with an example dataset in r: # Fit a nls model (this is a light response curve of photosynthesis, in this case) mod<-nls(response~(alpha*x+Pm-sqrt(((alp
51,610
Proportion data with number of trials known (and separation?): GLM or beta regression?
The data you have are really a classic binomial setting and you can use binomial GLMs to model the data, either using the standard maximum likelihood (ML) estimator or using a bias-reduced (BR) estimator (Firth's penalized estimator). I wouldn't use beta regression here. For treatment b you have 49 successes and 0 fail...
Proportion data with number of trials known (and separation?): GLM or beta regression?
The data you have are really a classic binomial setting and you can use binomial GLMs to model the data, either using the standard maximum likelihood (ML) estimator or using a bias-reduced (BR) estima
Proportion data with number of trials known (and separation?): GLM or beta regression? The data you have are really a classic binomial setting and you can use binomial GLMs to model the data, either using the standard maximum likelihood (ML) estimator or using a bias-reduced (BR) estimator (Firth's penalized estimator)...
Proportion data with number of trials known (and separation?): GLM or beta regression? The data you have are really a classic binomial setting and you can use binomial GLMs to model the data, either using the standard maximum likelihood (ML) estimator or using a bias-reduced (BR) estima
51,611
Proportion data with number of trials known (and separation?): GLM or beta regression?
It isn't that beta regression on its own solved the problem. It's that you adjusted the data with a line of code: y.doubleprime = ((y.prime*(length(y.prime)-1))+0.5)/length(y.prime)) so that the beta regression software didn't have to deal with the exact 0 or 1 proportions that it (like logistic regression) can't hand...
Proportion data with number of trials known (and separation?): GLM or beta regression?
It isn't that beta regression on its own solved the problem. It's that you adjusted the data with a line of code: y.doubleprime = ((y.prime*(length(y.prime)-1))+0.5)/length(y.prime)) so that the beta
Proportion data with number of trials known (and separation?): GLM or beta regression? It isn't that beta regression on its own solved the problem. It's that you adjusted the data with a line of code: y.doubleprime = ((y.prime*(length(y.prime)-1))+0.5)/length(y.prime)) so that the beta regression software didn't have ...
Proportion data with number of trials known (and separation?): GLM or beta regression? It isn't that beta regression on its own solved the problem. It's that you adjusted the data with a line of code: y.doubleprime = ((y.prime*(length(y.prime)-1))+0.5)/length(y.prime)) so that the beta
51,612
Proportion data with number of trials known (and separation?): GLM or beta regression?
There's already a good answer from Achim that points out that this is really not a good scenario for beta-regression, because you seem to be in a binomial sampling situation and beta-regression will simply be an approximation to that. If one uses a binomial likelihood, the only question is how to appropriately deal wit...
Proportion data with number of trials known (and separation?): GLM or beta regression?
There's already a good answer from Achim that points out that this is really not a good scenario for beta-regression, because you seem to be in a binomial sampling situation and beta-regression will s
Proportion data with number of trials known (and separation?): GLM or beta regression? There's already a good answer from Achim that points out that this is really not a good scenario for beta-regression, because you seem to be in a binomial sampling situation and beta-regression will simply be an approximation to that...
Proportion data with number of trials known (and separation?): GLM or beta regression? There's already a good answer from Achim that points out that this is really not a good scenario for beta-regression, because you seem to be in a binomial sampling situation and beta-regression will s
51,613
What core topics would all statisticians be required to know?
I agree with @Bayequentist but would go further. "Statistician" is a broader term than just people with a PhD in statistics. My PhD is in psychometrics, but I've worked as a statistician for more than 20 years. (When talking to statisticians, I call myself a data analyst). I know less theory than a lot of people (proba...
What core topics would all statisticians be required to know?
I agree with @Bayequentist but would go further. "Statistician" is a broader term than just people with a PhD in statistics. My PhD is in psychometrics, but I've worked as a statistician for more than
What core topics would all statisticians be required to know? I agree with @Bayequentist but would go further. "Statistician" is a broader term than just people with a PhD in statistics. My PhD is in psychometrics, but I've worked as a statistician for more than 20 years. (When talking to statisticians, I call myself a...
What core topics would all statisticians be required to know? I agree with @Bayequentist but would go further. "Statistician" is a broader term than just people with a PhD in statistics. My PhD is in psychometrics, but I've worked as a statistician for more than
51,614
What core topics would all statisticians be required to know?
Statisticians are an extremely diverse set of professionals/researchers, so the set of core topics that all of them should know is actually quite small. If you visit websites of statistics graduate programs in the US, you'll see that the common core topics are as follows: probability theory; theory of statistical infer...
What core topics would all statisticians be required to know?
Statisticians are an extremely diverse set of professionals/researchers, so the set of core topics that all of them should know is actually quite small. If you visit websites of statistics graduate pr
What core topics would all statisticians be required to know? Statisticians are an extremely diverse set of professionals/researchers, so the set of core topics that all of them should know is actually quite small. If you visit websites of statistics graduate programs in the US, you'll see that the common core topics a...
What core topics would all statisticians be required to know? Statisticians are an extremely diverse set of professionals/researchers, so the set of core topics that all of them should know is actually quite small. If you visit websites of statistics graduate pr
51,615
What core topics would all statisticians be required to know?
Applied statisticians should know conditional probability inside and out; this is the source of a great deal of misunderstandings about p-values and type I assertion probability $\alpha$ as well as holding back more usage of the Bayesian paradigm experimental design, sources of bias and variability measurement propert...
What core topics would all statisticians be required to know?
Applied statisticians should know conditional probability inside and out; this is the source of a great deal of misunderstandings about p-values and type I assertion probability $\alpha$ as well as h
What core topics would all statisticians be required to know? Applied statisticians should know conditional probability inside and out; this is the source of a great deal of misunderstandings about p-values and type I assertion probability $\alpha$ as well as holding back more usage of the Bayesian paradigm experiment...
What core topics would all statisticians be required to know? Applied statisticians should know conditional probability inside and out; this is the source of a great deal of misunderstandings about p-values and type I assertion probability $\alpha$ as well as h
51,616
What core topics would all statisticians be required to know?
A statistician, as in a Mathematical that is specialized in Statistics, as in my experience, has a basic set of theorical knowledge in: Probability Theory (most importat one) Mathematical Inference Mathematical optimization Regression Basic Programming Exploratory Data Research Stochastic methods Keep in mind that, ...
What core topics would all statisticians be required to know?
A statistician, as in a Mathematical that is specialized in Statistics, as in my experience, has a basic set of theorical knowledge in: Probability Theory (most importat one) Mathematical Inference M
What core topics would all statisticians be required to know? A statistician, as in a Mathematical that is specialized in Statistics, as in my experience, has a basic set of theorical knowledge in: Probability Theory (most importat one) Mathematical Inference Mathematical optimization Regression Basic Programming Expl...
What core topics would all statisticians be required to know? A statistician, as in a Mathematical that is specialized in Statistics, as in my experience, has a basic set of theorical knowledge in: Probability Theory (most importat one) Mathematical Inference M
51,617
What kind of t-test should I use for testing the significance of a Professor's IQ?
You don't need any significance tests. You already have the IQ of the professor in question, namely, 125, which is not equal to 100. The situation that you seem to have this situation confused with is when you have a sample of people from some population and you want to make an inference about the mean IQ of the popula...
What kind of t-test should I use for testing the significance of a Professor's IQ?
You don't need any significance tests. You already have the IQ of the professor in question, namely, 125, which is not equal to 100. The situation that you seem to have this situation confused with is
What kind of t-test should I use for testing the significance of a Professor's IQ? You don't need any significance tests. You already have the IQ of the professor in question, namely, 125, which is not equal to 100. The situation that you seem to have this situation confused with is when you have a sample of people fro...
What kind of t-test should I use for testing the significance of a Professor's IQ? You don't need any significance tests. You already have the IQ of the professor in question, namely, 125, which is not equal to 100. The situation that you seem to have this situation confused with is
51,618
What kind of t-test should I use for testing the significance of a Professor's IQ?
If the professor scored significantly below average, than that would be worth reporting. Therefore you are interested in both ends of the tails and need to perform a two tailed test. Usually you compare your p with some alpha. That alpha is agreed upon to be 0.05 just as testing is agreed to be two tailed. These are tw...
What kind of t-test should I use for testing the significance of a Professor's IQ?
If the professor scored significantly below average, than that would be worth reporting. Therefore you are interested in both ends of the tails and need to perform a two tailed test. Usually you compa
What kind of t-test should I use for testing the significance of a Professor's IQ? If the professor scored significantly below average, than that would be worth reporting. Therefore you are interested in both ends of the tails and need to perform a two tailed test. Usually you compare your p with some alpha. That alpha...
What kind of t-test should I use for testing the significance of a Professor's IQ? If the professor scored significantly below average, than that would be worth reporting. Therefore you are interested in both ends of the tails and need to perform a two tailed test. Usually you compa
51,619
Is it fine to slightly overfit, if its giving you good predictive power?
How do you know that your model is overfitted? If an "overfitted" model (let us call it model A) is giving you truly better predictive power (no cheating, honest out of sample assessment) than some benchmark model that you think is non-overfitted (call it model B), I would suspect that model B is actually underfitted w...
Is it fine to slightly overfit, if its giving you good predictive power?
How do you know that your model is overfitted? If an "overfitted" model (let us call it model A) is giving you truly better predictive power (no cheating, honest out of sample assessment) than some be
Is it fine to slightly overfit, if its giving you good predictive power? How do you know that your model is overfitted? If an "overfitted" model (let us call it model A) is giving you truly better predictive power (no cheating, honest out of sample assessment) than some benchmark model that you think is non-overfitted ...
Is it fine to slightly overfit, if its giving you good predictive power? How do you know that your model is overfitted? If an "overfitted" model (let us call it model A) is giving you truly better predictive power (no cheating, honest out of sample assessment) than some be
51,620
Is it fine to slightly overfit, if its giving you good predictive power?
Sounds like your issue is collinearity rather than overfitting, as user1320502 suggested in a comment. Do you know where these two variables came from? For example, if one is $x$ and one is $x^2$, centering the variables may help. If all you care about is predicting, collinearity is not a direct problem. But if you loo...
Is it fine to slightly overfit, if its giving you good predictive power?
Sounds like your issue is collinearity rather than overfitting, as user1320502 suggested in a comment. Do you know where these two variables came from? For example, if one is $x$ and one is $x^2$, cen
Is it fine to slightly overfit, if its giving you good predictive power? Sounds like your issue is collinearity rather than overfitting, as user1320502 suggested in a comment. Do you know where these two variables came from? For example, if one is $x$ and one is $x^2$, centering the variables may help. If all you care ...
Is it fine to slightly overfit, if its giving you good predictive power? Sounds like your issue is collinearity rather than overfitting, as user1320502 suggested in a comment. Do you know where these two variables came from? For example, if one is $x$ and one is $x^2$, cen
51,621
In Bayesian linear regression, why do we assume parameter prior has zero mean?
Encoding assumptions about the data isn't quite the role of the prior distribution in a Bayesian model. The prior does not reflect any assumptions about the data: It mathematically captures any assumptions the analyst makes about model parameters before observing the data. The posterior distribution reflects both the p...
In Bayesian linear regression, why do we assume parameter prior has zero mean?
Encoding assumptions about the data isn't quite the role of the prior distribution in a Bayesian model. The prior does not reflect any assumptions about the data: It mathematically captures any assump
In Bayesian linear regression, why do we assume parameter prior has zero mean? Encoding assumptions about the data isn't quite the role of the prior distribution in a Bayesian model. The prior does not reflect any assumptions about the data: It mathematically captures any assumptions the analyst makes about model param...
In Bayesian linear regression, why do we assume parameter prior has zero mean? Encoding assumptions about the data isn't quite the role of the prior distribution in a Bayesian model. The prior does not reflect any assumptions about the data: It mathematically captures any assump
51,622
In Bayesian linear regression, why do we assume parameter prior has zero mean?
You can use any prior that you want. It does not have to be normal, it can have different mean, or it can have no mean (Cauchy)... It is your subjective choice that you make before seeing the data. Recall that posterior is likelihood times prior $$ \underbrace{P(\theta|D)}_\text{posterior} \propto \underbrace{P(D|\thet...
In Bayesian linear regression, why do we assume parameter prior has zero mean?
You can use any prior that you want. It does not have to be normal, it can have different mean, or it can have no mean (Cauchy)... It is your subjective choice that you make before seeing the data. Re
In Bayesian linear regression, why do we assume parameter prior has zero mean? You can use any prior that you want. It does not have to be normal, it can have different mean, or it can have no mean (Cauchy)... It is your subjective choice that you make before seeing the data. Recall that posterior is likelihood times p...
In Bayesian linear regression, why do we assume parameter prior has zero mean? You can use any prior that you want. It does not have to be normal, it can have different mean, or it can have no mean (Cauchy)... It is your subjective choice that you make before seeing the data. Re
51,623
In Bayesian linear regression, why do we assume parameter prior has zero mean?
@user13985 IDK what you mean by no prediction. In your particular model you can derive the posterior distribution if you use a normal prior. If $\mathbf{y}\sim \text{N}(\mathbf{X}\beta,\mathbf{R})$ and $\beta \sim \text{N}(\mathbf{a},\mathbf{B})$ then the posterior is $\beta|\mathbf{y} \sim \text{N}(\mu, \Sigma)$ wher...
In Bayesian linear regression, why do we assume parameter prior has zero mean?
@user13985 IDK what you mean by no prediction. In your particular model you can derive the posterior distribution if you use a normal prior. If $\mathbf{y}\sim \text{N}(\mathbf{X}\beta,\mathbf{R})$ a
In Bayesian linear regression, why do we assume parameter prior has zero mean? @user13985 IDK what you mean by no prediction. In your particular model you can derive the posterior distribution if you use a normal prior. If $\mathbf{y}\sim \text{N}(\mathbf{X}\beta,\mathbf{R})$ and $\beta \sim \text{N}(\mathbf{a},\mathb...
In Bayesian linear regression, why do we assume parameter prior has zero mean? @user13985 IDK what you mean by no prediction. In your particular model you can derive the posterior distribution if you use a normal prior. If $\mathbf{y}\sim \text{N}(\mathbf{X}\beta,\mathbf{R})$ a
51,624
In Bayesian linear regression, why do we assume parameter prior has zero mean?
Perhaps one way to help motivate this is that selecting a normal prior with mean 0 is equivalent to ridge regression (i.e. adding an L2 penalty on your estimated coefficient). Ridge regression has been proven to be helpful in regression, therefore adding a normal prior with mean 0 should be helpful too.
In Bayesian linear regression, why do we assume parameter prior has zero mean?
Perhaps one way to help motivate this is that selecting a normal prior with mean 0 is equivalent to ridge regression (i.e. adding an L2 penalty on your estimated coefficient). Ridge regression has bee
In Bayesian linear regression, why do we assume parameter prior has zero mean? Perhaps one way to help motivate this is that selecting a normal prior with mean 0 is equivalent to ridge regression (i.e. adding an L2 penalty on your estimated coefficient). Ridge regression has been proven to be helpful in regression, the...
In Bayesian linear regression, why do we assume parameter prior has zero mean? Perhaps one way to help motivate this is that selecting a normal prior with mean 0 is equivalent to ridge regression (i.e. adding an L2 penalty on your estimated coefficient). Ridge regression has bee
51,625
Converting a Model from square feet to square meter
The intercept has exactly the same units as your response variable, here house price, and is thus unaffected by changing the units of area. Note incidentally that while the prediction of a negative price for a property with zero area (and with zero values for any other predictors) will be outside the range of the data...
Converting a Model from square feet to square meter
The intercept has exactly the same units as your response variable, here house price, and is thus unaffected by changing the units of area. Note incidentally that while the prediction of a negative p
Converting a Model from square feet to square meter The intercept has exactly the same units as your response variable, here house price, and is thus unaffected by changing the units of area. Note incidentally that while the prediction of a negative price for a property with zero area (and with zero values for any oth...
Converting a Model from square feet to square meter The intercept has exactly the same units as your response variable, here house price, and is thus unaffected by changing the units of area. Note incidentally that while the prediction of a negative p
51,626
Converting a Model from square feet to square meter
One way to figure this out (one that works with models more complex than linear regression and conversions more complex than square feet/meters, like Fahrenheit to Celsius) is to write your model and conversion as equations, and do the substitution. So you have a linear model $y = f(x) = mx + b$, where $x$ is in square...
Converting a Model from square feet to square meter
One way to figure this out (one that works with models more complex than linear regression and conversions more complex than square feet/meters, like Fahrenheit to Celsius) is to write your model and
Converting a Model from square feet to square meter One way to figure this out (one that works with models more complex than linear regression and conversions more complex than square feet/meters, like Fahrenheit to Celsius) is to write your model and conversion as equations, and do the substitution. So you have a line...
Converting a Model from square feet to square meter One way to figure this out (one that works with models more complex than linear regression and conversions more complex than square feet/meters, like Fahrenheit to Celsius) is to write your model and
51,627
Converting a Model from square feet to square meter
There are 0.092903 square meters in 1 square foot so slope should be (280.76)*(0.092903) and intercept remains same
Converting a Model from square feet to square meter
There are 0.092903 square meters in 1 square foot so slope should be (280.76)*(0.092903) and intercept remains same
Converting a Model from square feet to square meter There are 0.092903 square meters in 1 square foot so slope should be (280.76)*(0.092903) and intercept remains same
Converting a Model from square feet to square meter There are 0.092903 square meters in 1 square foot so slope should be (280.76)*(0.092903) and intercept remains same
51,628
Converting a Model from square feet to square meter
I can answer this. In this case, there will not be any change in the intercept.However,only the slope changes with the change in the magnitude. This house costs 280.76 per sqft. Hence it would cost 3022.08 per sq.metre assuming that there is no currency change and keeping in mind the scale of change from sqft to sq.met...
Converting a Model from square feet to square meter
I can answer this. In this case, there will not be any change in the intercept.However,only the slope changes with the change in the magnitude. This house costs 280.76 per sqft. Hence it would cost 30
Converting a Model from square feet to square meter I can answer this. In this case, there will not be any change in the intercept.However,only the slope changes with the change in the magnitude. This house costs 280.76 per sqft. Hence it would cost 3022.08 per sq.metre assuming that there is no currency change and kee...
Converting a Model from square feet to square meter I can answer this. In this case, there will not be any change in the intercept.However,only the slope changes with the change in the magnitude. This house costs 280.76 per sqft. Hence it would cost 30
51,629
How Can I Calculate Standard Deviation (step-by-step) in R? [closed]
> a <- c(179,160,136,227) > sd(a) [1] 38.57892 > sqrt(sum((a-mean(a))^2/(length(a)-1))) [1] 38.57892 ```
How Can I Calculate Standard Deviation (step-by-step) in R? [closed]
> a <- c(179,160,136,227) > sd(a) [1] 38.57892 > sqrt(sum((a-mean(a))^2/(length(a)-1))) [1] 38.57892 ```
How Can I Calculate Standard Deviation (step-by-step) in R? [closed] > a <- c(179,160,136,227) > sd(a) [1] 38.57892 > sqrt(sum((a-mean(a))^2/(length(a)-1))) [1] 38.57892 ```
How Can I Calculate Standard Deviation (step-by-step) in R? [closed] > a <- c(179,160,136,227) > sd(a) [1] 38.57892 > sqrt(sum((a-mean(a))^2/(length(a)-1))) [1] 38.57892 ```
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How Can I Calculate Standard Deviation (step-by-step) in R? [closed]
So, you want to calculate the standard deviation step-by-step. So, firstly, you should calculate the sum of the differences of all data points with the mean. Have a variable called count and set it to the value 0. For that, you loop through the data set with a variable, say i and subtract i every time with the mean. Me...
How Can I Calculate Standard Deviation (step-by-step) in R? [closed]
So, you want to calculate the standard deviation step-by-step. So, firstly, you should calculate the sum of the differences of all data points with the mean. Have a variable called count and set it to
How Can I Calculate Standard Deviation (step-by-step) in R? [closed] So, you want to calculate the standard deviation step-by-step. So, firstly, you should calculate the sum of the differences of all data points with the mean. Have a variable called count and set it to the value 0. For that, you loop through the data s...
How Can I Calculate Standard Deviation (step-by-step) in R? [closed] So, you want to calculate the standard deviation step-by-step. So, firstly, you should calculate the sum of the differences of all data points with the mean. Have a variable called count and set it to
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Can the coefficient of determination $R^2$ be more than one? What is its upper bound?
The best upper bound is $1$, no matter what the values of $R_1^2$ and $R_2^2$ may be. The following discussion explains why, in three increasingly detailed ways. The first explanation gives geometric intuition, leading to a simple example. The second one translates that into a procedure to generate specific datasets ...
Can the coefficient of determination $R^2$ be more than one? What is its upper bound?
The best upper bound is $1$, no matter what the values of $R_1^2$ and $R_2^2$ may be. The following discussion explains why, in three increasingly detailed ways. The first explanation gives geometric
Can the coefficient of determination $R^2$ be more than one? What is its upper bound? The best upper bound is $1$, no matter what the values of $R_1^2$ and $R_2^2$ may be. The following discussion explains why, in three increasingly detailed ways. The first explanation gives geometric intuition, leading to a simple ex...
Can the coefficient of determination $R^2$ be more than one? What is its upper bound? The best upper bound is $1$, no matter what the values of $R_1^2$ and $R_2^2$ may be. The following discussion explains why, in three increasingly detailed ways. The first explanation gives geometric
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Can the coefficient of determination $R^2$ be more than one? What is its upper bound?
@whuber: negative $R^2$ is possible in a regression model without an intercept. In a regression model with an intercept, the definition of $R^2$ is based on a decomposition of the total sum of squares, i.e. $\sum_i (Y_i - \bar{Y})^2$, $\bar{Y}$ is the average of $Y$, the dependent variable. (Note that $R^2$ it is not ...
Can the coefficient of determination $R^2$ be more than one? What is its upper bound?
@whuber: negative $R^2$ is possible in a regression model without an intercept. In a regression model with an intercept, the definition of $R^2$ is based on a decomposition of the total sum of square
Can the coefficient of determination $R^2$ be more than one? What is its upper bound? @whuber: negative $R^2$ is possible in a regression model without an intercept. In a regression model with an intercept, the definition of $R^2$ is based on a decomposition of the total sum of squares, i.e. $\sum_i (Y_i - \bar{Y})^2$...
Can the coefficient of determination $R^2$ be more than one? What is its upper bound? @whuber: negative $R^2$ is possible in a regression model without an intercept. In a regression model with an intercept, the definition of $R^2$ is based on a decomposition of the total sum of square
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Can the coefficient of determination $R^2$ be more than one? What is its upper bound?
Summing up the first two equations you find $2y_i=a_1+a_2+b_1x_i+b_2z_i+e_{i,1}+e_{i,2}$, if you subtract twice the third equation then you find $0=a_1+a_2+b_1x_i+b_2z_i+e_{i,1}+e_{i,2}-2a-2bx_i-2cz_i-2e_i$ or $(a_1+a_2-2a+e_{i,1}+e_{i,2}-2e_i)+(b_1-2b)x_i+(b_2-2c)z_i=0$. But from $(a_1+a_2-2a+e_{i,1}+e_{i,2}-2e_i)=0$...
Can the coefficient of determination $R^2$ be more than one? What is its upper bound?
Summing up the first two equations you find $2y_i=a_1+a_2+b_1x_i+b_2z_i+e_{i,1}+e_{i,2}$, if you subtract twice the third equation then you find $0=a_1+a_2+b_1x_i+b_2z_i+e_{i,1}+e_{i,2}-2a-2bx_i-2cz_i
Can the coefficient of determination $R^2$ be more than one? What is its upper bound? Summing up the first two equations you find $2y_i=a_1+a_2+b_1x_i+b_2z_i+e_{i,1}+e_{i,2}$, if you subtract twice the third equation then you find $0=a_1+a_2+b_1x_i+b_2z_i+e_{i,1}+e_{i,2}-2a-2bx_i-2cz_i-2e_i$ or $(a_1+a_2-2a+e_{i,1}+e_{...
Can the coefficient of determination $R^2$ be more than one? What is its upper bound? Summing up the first two equations you find $2y_i=a_1+a_2+b_1x_i+b_2z_i+e_{i,1}+e_{i,2}$, if you subtract twice the third equation then you find $0=a_1+a_2+b_1x_i+b_2z_i+e_{i,1}+e_{i,2}-2a-2bx_i-2cz_i
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Can the coefficient of determination $R^2$ be more than one? What is its upper bound?
I think I formalized the concern I had. Summing up 1 and 2 and transforming both sides you get: $y_i-(a_1+b_1*x_i) + y_i-(a_2+b_2*z_i)= e_{i,1}+e_{i,2} \sim N(0,\sigma_1^2+\sigma_2^2)$. Using the OLS estimates, you obtain, $\sum_{i} (e_{i,1}+e_{i,2})^2= \sum_{i} (y_i-(\hat{a_1}+\hat{b_1}*x_i) + y_i-(\hat{a_2}+\hat{b_2}...
Can the coefficient of determination $R^2$ be more than one? What is its upper bound?
I think I formalized the concern I had. Summing up 1 and 2 and transforming both sides you get: $y_i-(a_1+b_1*x_i) + y_i-(a_2+b_2*z_i)= e_{i,1}+e_{i,2} \sim N(0,\sigma_1^2+\sigma_2^2)$. Using the OLS
Can the coefficient of determination $R^2$ be more than one? What is its upper bound? I think I formalized the concern I had. Summing up 1 and 2 and transforming both sides you get: $y_i-(a_1+b_1*x_i) + y_i-(a_2+b_2*z_i)= e_{i,1}+e_{i,2} \sim N(0,\sigma_1^2+\sigma_2^2)$. Using the OLS estimates, you obtain, $\sum_{i} (...
Can the coefficient of determination $R^2$ be more than one? What is its upper bound? I think I formalized the concern I had. Summing up 1 and 2 and transforming both sides you get: $y_i-(a_1+b_1*x_i) + y_i-(a_2+b_2*z_i)= e_{i,1}+e_{i,2} \sim N(0,\sigma_1^2+\sigma_2^2)$. Using the OLS
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Is it always required to achieve stationarity before performing any time-series analysis?
ARIMA models are not stationary, ARMAs are. ARIMA includes the integration terms, e.g. a random walk model is ARIMA(0,1,0) and it's not stationary. There's a couple of different ways to exponentially smooth, here's EWMA and a different version. Neither of them requires stationarity. Here's an example in MATLAB with fit...
Is it always required to achieve stationarity before performing any time-series analysis?
ARIMA models are not stationary, ARMAs are. ARIMA includes the integration terms, e.g. a random walk model is ARIMA(0,1,0) and it's not stationary. There's a couple of different ways to exponentially
Is it always required to achieve stationarity before performing any time-series analysis? ARIMA models are not stationary, ARMAs are. ARIMA includes the integration terms, e.g. a random walk model is ARIMA(0,1,0) and it's not stationary. There's a couple of different ways to exponentially smooth, here's EWMA and a diff...
Is it always required to achieve stationarity before performing any time-series analysis? ARIMA models are not stationary, ARMAs are. ARIMA includes the integration terms, e.g. a random walk model is ARIMA(0,1,0) and it's not stationary. There's a couple of different ways to exponentially
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Is it always required to achieve stationarity before performing any time-series analysis?
exponential smoothing models do not assume stationary data. Citation: see Hyndman and Athana­sopou­los: "every ETS [exponential smoothing] model is non-stationary"
Is it always required to achieve stationarity before performing any time-series analysis?
exponential smoothing models do not assume stationary data. Citation: see Hyndman and Athana­sopou­los: "every ETS [exponential smoothing] model is non-stationary"
Is it always required to achieve stationarity before performing any time-series analysis? exponential smoothing models do not assume stationary data. Citation: see Hyndman and Athana­sopou­los: "every ETS [exponential smoothing] model is non-stationary"
Is it always required to achieve stationarity before performing any time-series analysis? exponential smoothing models do not assume stationary data. Citation: see Hyndman and Athana­sopou­los: "every ETS [exponential smoothing] model is non-stationary"
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Is it always required to achieve stationarity before performing any time-series analysis?
Exponential Smoothing model is a particular form of an ARIMA model. Instead of identifying the patterns, outliers and trends, you assume them.
Is it always required to achieve stationarity before performing any time-series analysis?
Exponential Smoothing model is a particular form of an ARIMA model. Instead of identifying the patterns, outliers and trends, you assume them.
Is it always required to achieve stationarity before performing any time-series analysis? Exponential Smoothing model is a particular form of an ARIMA model. Instead of identifying the patterns, outliers and trends, you assume them.
Is it always required to achieve stationarity before performing any time-series analysis? Exponential Smoothing model is a particular form of an ARIMA model. Instead of identifying the patterns, outliers and trends, you assume them.
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Is it always required to achieve stationarity before performing any time-series analysis?
Structural time series models do not assume stationarity either. These models a la Andrew Harvey are estimated via Kalman filter type of algorithms. http://www.stat.yale.edu/~lc436/papers/Harvey_Peters1990.pdf
Is it always required to achieve stationarity before performing any time-series analysis?
Structural time series models do not assume stationarity either. These models a la Andrew Harvey are estimated via Kalman filter type of algorithms. http://www.stat.yale.edu/~lc436/papers/Harvey_Pe
Is it always required to achieve stationarity before performing any time-series analysis? Structural time series models do not assume stationarity either. These models a la Andrew Harvey are estimated via Kalman filter type of algorithms. http://www.stat.yale.edu/~lc436/papers/Harvey_Peters1990.pdf
Is it always required to achieve stationarity before performing any time-series analysis? Structural time series models do not assume stationarity either. These models a la Andrew Harvey are estimated via Kalman filter type of algorithms. http://www.stat.yale.edu/~lc436/papers/Harvey_Pe
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Is it always required to achieve stationarity before performing any time-series analysis?
As it stands, I do not even agree that stationarity "needs to be achieved" before performing time-series analysis with an ARIMA process. It needs to be clarified what the goal of the analysis is. For example, there are tons of posts on this site relating to testing the null $\rho=1$ in the model $Y_t=\rho Y_{t-1}+\eps...
Is it always required to achieve stationarity before performing any time-series analysis?
As it stands, I do not even agree that stationarity "needs to be achieved" before performing time-series analysis with an ARIMA process. It needs to be clarified what the goal of the analysis is. For
Is it always required to achieve stationarity before performing any time-series analysis? As it stands, I do not even agree that stationarity "needs to be achieved" before performing time-series analysis with an ARIMA process. It needs to be clarified what the goal of the analysis is. For example, there are tons of po...
Is it always required to achieve stationarity before performing any time-series analysis? As it stands, I do not even agree that stationarity "needs to be achieved" before performing time-series analysis with an ARIMA process. It needs to be clarified what the goal of the analysis is. For
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What to do when your likelihood function has a double product with small values near zero - log transform doesn't work?
This is just a small addition to @whuber's answer (+1). To compute $$\log \sum \exp (x_i)$$ without overflowing or underflowing, a "log-sum-trick" is often used, see e.g. here for description. The trick is to compute $$\max(x_i) + \log \sum \exp (x_i - \max(x_i))$$ instead. This will prevent overflowing, and if some te...
What to do when your likelihood function has a double product with small values near zero - log tran
This is just a small addition to @whuber's answer (+1). To compute $$\log \sum \exp (x_i)$$ without overflowing or underflowing, a "log-sum-trick" is often used, see e.g. here for description. The tri
What to do when your likelihood function has a double product with small values near zero - log transform doesn't work? This is just a small addition to @whuber's answer (+1). To compute $$\log \sum \exp (x_i)$$ without overflowing or underflowing, a "log-sum-trick" is often used, see e.g. here for description. The tri...
What to do when your likelihood function has a double product with small values near zero - log tran This is just a small addition to @whuber's answer (+1). To compute $$\log \sum \exp (x_i)$$ without overflowing or underflowing, a "log-sum-trick" is often used, see e.g. here for description. The tri
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What to do when your likelihood function has a double product with small values near zero - log transform doesn't work?
I recently had to deal with the same issue when computing conditional probabilities involving numbers on the order of $10^{-10000}$ (because normalizing the probability distribution would have required a great deal of unnecessary calculations). The heart of this difficulty, which comes up repeatedly in statistical com...
What to do when your likelihood function has a double product with small values near zero - log tran
I recently had to deal with the same issue when computing conditional probabilities involving numbers on the order of $10^{-10000}$ (because normalizing the probability distribution would have require
What to do when your likelihood function has a double product with small values near zero - log transform doesn't work? I recently had to deal with the same issue when computing conditional probabilities involving numbers on the order of $10^{-10000}$ (because normalizing the probability distribution would have require...
What to do when your likelihood function has a double product with small values near zero - log tran I recently had to deal with the same issue when computing conditional probabilities involving numbers on the order of $10^{-10000}$ (because normalizing the probability distribution would have require
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How to deal with Z-score greater than 3?
Let me repeat (and correct) what I've said in my comment ad reply to your edit. You have to transfer from $X$ to $Z$ in order to use a z-score table. Since a z-score table contains a small finite subset of values, you often must settle for an approximation. So you could also settle for $P(Z<-3)\approx 0$ and $P(Z< 3)\a...
How to deal with Z-score greater than 3?
Let me repeat (and correct) what I've said in my comment ad reply to your edit. You have to transfer from $X$ to $Z$ in order to use a z-score table. Since a z-score table contains a small finite subs
How to deal with Z-score greater than 3? Let me repeat (and correct) what I've said in my comment ad reply to your edit. You have to transfer from $X$ to $Z$ in order to use a z-score table. Since a z-score table contains a small finite subset of values, you often must settle for an approximation. So you could also set...
How to deal with Z-score greater than 3? Let me repeat (and correct) what I've said in my comment ad reply to your edit. You have to transfer from $X$ to $Z$ in order to use a z-score table. Since a z-score table contains a small finite subs
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How to deal with Z-score greater than 3?
The standard normal ranges from $-\infty$ to $\infty$. Your problem appears to be that your table doesn't go further. Your question should therefore be modified to ask "*How do I deal with the fact that my table doesn't go as high as my $Z$ value?*" [Note that in your last paragraph, you have become confused. The regi...
How to deal with Z-score greater than 3?
The standard normal ranges from $-\infty$ to $\infty$. Your problem appears to be that your table doesn't go further. Your question should therefore be modified to ask "*How do I deal with the fact t
How to deal with Z-score greater than 3? The standard normal ranges from $-\infty$ to $\infty$. Your problem appears to be that your table doesn't go further. Your question should therefore be modified to ask "*How do I deal with the fact that my table doesn't go as high as my $Z$ value?*" [Note that in your last para...
How to deal with Z-score greater than 3? The standard normal ranges from $-\infty$ to $\infty$. Your problem appears to be that your table doesn't go further. Your question should therefore be modified to ask "*How do I deal with the fact t
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How to deal with Z-score greater than 3?
For $z >0$, the right tail of the standard normal distribution (that is, the area to the right of $z$) which is often denoted by $Q(z)$ is bounded as follows: $$\frac{\exp(-z^2/2)}{\sqrt{2\pi}}\left (\frac{1}{z} - \frac{1}{z^3}\right ) \ < \ Q(z) \ < \ \frac{\exp(-z^2/2)}{\sqrt{2\pi}}\left (\frac{1}{z}\right ).$$ See...
How to deal with Z-score greater than 3?
For $z >0$, the right tail of the standard normal distribution (that is, the area to the right of $z$) which is often denoted by $Q(z)$ is bounded as follows: $$\frac{\exp(-z^2/2)}{\sqrt{2\pi}}\left
How to deal with Z-score greater than 3? For $z >0$, the right tail of the standard normal distribution (that is, the area to the right of $z$) which is often denoted by $Q(z)$ is bounded as follows: $$\frac{\exp(-z^2/2)}{\sqrt{2\pi}}\left (\frac{1}{z} - \frac{1}{z^3}\right ) \ < \ Q(z) \ < \ \frac{\exp(-z^2/2)}{\sqr...
How to deal with Z-score greater than 3? For $z >0$, the right tail of the standard normal distribution (that is, the area to the right of $z$) which is often denoted by $Q(z)$ is bounded as follows: $$\frac{\exp(-z^2/2)}{\sqrt{2\pi}}\left
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How to deal with Z-score greater than 3?
The z (i.e., normal) distribution is not bounded. $\mathcal N(\mu=70,\sigma=4)$ is not standard normal either – that refers to $\mathcal N(0,1)$. If you're wondering what the p value is for z = 3.75, you can find it in r with pnorm(3.75). (You could also use pnorm(85,70,4).) The result is p = 0.9999116. If you want an...
How to deal with Z-score greater than 3?
The z (i.e., normal) distribution is not bounded. $\mathcal N(\mu=70,\sigma=4)$ is not standard normal either – that refers to $\mathcal N(0,1)$. If you're wondering what the p value is for z = 3.75,
How to deal with Z-score greater than 3? The z (i.e., normal) distribution is not bounded. $\mathcal N(\mu=70,\sigma=4)$ is not standard normal either – that refers to $\mathcal N(0,1)$. If you're wondering what the p value is for z = 3.75, you can find it in r with pnorm(3.75). (You could also use pnorm(85,70,4).) The...
How to deal with Z-score greater than 3? The z (i.e., normal) distribution is not bounded. $\mathcal N(\mu=70,\sigma=4)$ is not standard normal either – that refers to $\mathcal N(0,1)$. If you're wondering what the p value is for z = 3.75,
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transformation to normality of the dependent variable in multiple regression
I'd planned to link to an answer with a good list (with discussion) of the regression assumptions an answer with the multiple regression assumptions, but I can't find a completely suitable one for what I had in mind. There are plenty of discussions of the issues (especially in comments), but not quite everything I thin...
transformation to normality of the dependent variable in multiple regression
I'd planned to link to an answer with a good list (with discussion) of the regression assumptions an answer with the multiple regression assumptions, but I can't find a completely suitable one for wha
transformation to normality of the dependent variable in multiple regression I'd planned to link to an answer with a good list (with discussion) of the regression assumptions an answer with the multiple regression assumptions, but I can't find a completely suitable one for what I had in mind. There are plenty of discus...
transformation to normality of the dependent variable in multiple regression I'd planned to link to an answer with a good list (with discussion) of the regression assumptions an answer with the multiple regression assumptions, but I can't find a completely suitable one for wha
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Q: what book on Bayesian statistics, preferably with R? [duplicate]
Peter D. Huff. A First Course in Bayesian Statistical Methods. Springer (2010) Also Andrew Gelman et. al. Bayesian Data Analysis (3rd ed.). CRC (2013) The Gelman book isn't constrained to R but also uses Stan, a probabilistic programming language similar to BUGS or JAGS. I believe earlier editions of the book used B...
Q: what book on Bayesian statistics, preferably with R? [duplicate]
Peter D. Huff. A First Course in Bayesian Statistical Methods. Springer (2010) Also Andrew Gelman et. al. Bayesian Data Analysis (3rd ed.). CRC (2013) The Gelman book isn't constrained to R but als
Q: what book on Bayesian statistics, preferably with R? [duplicate] Peter D. Huff. A First Course in Bayesian Statistical Methods. Springer (2010) Also Andrew Gelman et. al. Bayesian Data Analysis (3rd ed.). CRC (2013) The Gelman book isn't constrained to R but also uses Stan, a probabilistic programming language si...
Q: what book on Bayesian statistics, preferably with R? [duplicate] Peter D. Huff. A First Course in Bayesian Statistical Methods. Springer (2010) Also Andrew Gelman et. al. Bayesian Data Analysis (3rd ed.). CRC (2013) The Gelman book isn't constrained to R but als
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Q: what book on Bayesian statistics, preferably with R? [duplicate]
Fortuitous timing, as Bayesian Data Analysis, 3rd ed was just released. It's a good general-purpose text, with an emphasis on hierarchical methods, a section on advanced computation (that is, Markov chain Monte Carlo), and an appendix on Gelman's Bayesian inference tool, rstan. The text focuses on statistics rather t...
Q: what book on Bayesian statistics, preferably with R? [duplicate]
Fortuitous timing, as Bayesian Data Analysis, 3rd ed was just released. It's a good general-purpose text, with an emphasis on hierarchical methods, a section on advanced computation (that is, Markov
Q: what book on Bayesian statistics, preferably with R? [duplicate] Fortuitous timing, as Bayesian Data Analysis, 3rd ed was just released. It's a good general-purpose text, with an emphasis on hierarchical methods, a section on advanced computation (that is, Markov chain Monte Carlo), and an appendix on Gelman's Baye...
Q: what book on Bayesian statistics, preferably with R? [duplicate] Fortuitous timing, as Bayesian Data Analysis, 3rd ed was just released. It's a good general-purpose text, with an emphasis on hierarchical methods, a section on advanced computation (that is, Markov
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Q: what book on Bayesian statistics, preferably with R? [duplicate]
Both are introductory, but useful imho: Bayesian Computation With R, by Jim Albert Applied Bayesian Statistics, With R and OpenBUGS Examples, by
Q: what book on Bayesian statistics, preferably with R? [duplicate]
Both are introductory, but useful imho: Bayesian Computation With R, by Jim Albert Applied Bayesian Statistics, With R and OpenBUGS Examples, by
Q: what book on Bayesian statistics, preferably with R? [duplicate] Both are introductory, but useful imho: Bayesian Computation With R, by Jim Albert Applied Bayesian Statistics, With R and OpenBUGS Examples, by
Q: what book on Bayesian statistics, preferably with R? [duplicate] Both are introductory, but useful imho: Bayesian Computation With R, by Jim Albert Applied Bayesian Statistics, With R and OpenBUGS Examples, by
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How to prepare variables with mild skew for multiple regression?
There's no requirement that this data be normal for regression, only the residuals of the model. So, do your regression and check the residuals and then see if you need to transform anything.
How to prepare variables with mild skew for multiple regression?
There's no requirement that this data be normal for regression, only the residuals of the model. So, do your regression and check the residuals and then see if you need to transform anything.
How to prepare variables with mild skew for multiple regression? There's no requirement that this data be normal for regression, only the residuals of the model. So, do your regression and check the residuals and then see if you need to transform anything.
How to prepare variables with mild skew for multiple regression? There's no requirement that this data be normal for regression, only the residuals of the model. So, do your regression and check the residuals and then see if you need to transform anything.
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How to prepare variables with mild skew for multiple regression?
Your original data looks fine. I've seen datasets where the skew was far more extreme than that. Do your regression and check the diagnostics (in particular, see if your estimated trend makes sense and there is no strong evidence of non-additivity) before making any transformations.
How to prepare variables with mild skew for multiple regression?
Your original data looks fine. I've seen datasets where the skew was far more extreme than that. Do your regression and check the diagnostics (in particular, see if your estimated trend makes sense an
How to prepare variables with mild skew for multiple regression? Your original data looks fine. I've seen datasets where the skew was far more extreme than that. Do your regression and check the diagnostics (in particular, see if your estimated trend makes sense and there is no strong evidence of non-additivity) before...
How to prepare variables with mild skew for multiple regression? Your original data looks fine. I've seen datasets where the skew was far more extreme than that. Do your regression and check the diagnostics (in particular, see if your estimated trend makes sense an
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How to prepare variables with mild skew for multiple regression?
If you're looking for a transformation of the data, you might want to consider the Box-Cox transformation which is reviewed in this article.
How to prepare variables with mild skew for multiple regression?
If you're looking for a transformation of the data, you might want to consider the Box-Cox transformation which is reviewed in this article.
How to prepare variables with mild skew for multiple regression? If you're looking for a transformation of the data, you might want to consider the Box-Cox transformation which is reviewed in this article.
How to prepare variables with mild skew for multiple regression? If you're looking for a transformation of the data, you might want to consider the Box-Cox transformation which is reviewed in this article.
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A multitrait-multimethod matrix and data set
I worked on this some the other day when you posted your same question to stack overflow. What I will provide won't be a finished solution, but hopefully it will give you enough ideas to finish the presentation on your own. This is what I could produce in SPSS, I have posted some code here using the same logic in R wi...
A multitrait-multimethod matrix and data set
I worked on this some the other day when you posted your same question to stack overflow. What I will provide won't be a finished solution, but hopefully it will give you enough ideas to finish the pr
A multitrait-multimethod matrix and data set I worked on this some the other day when you posted your same question to stack overflow. What I will provide won't be a finished solution, but hopefully it will give you enough ideas to finish the presentation on your own. This is what I could produce in SPSS, I have poste...
A multitrait-multimethod matrix and data set I worked on this some the other day when you posted your same question to stack overflow. What I will provide won't be a finished solution, but hopefully it will give you enough ideas to finish the pr
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A multitrait-multimethod matrix and data set
I built on @Andy W's R-code and hope my changes are useful to someone else. I mainly changed it, so that it obeys the new syntax (no more opts) in ggplot2, so no more warnings adds the correlations as text now correlation text size reflects its effect size colour scheme shows the type of correlation (hetero/mono-tra...
A multitrait-multimethod matrix and data set
I built on @Andy W's R-code and hope my changes are useful to someone else. I mainly changed it, so that it obeys the new syntax (no more opts) in ggplot2, so no more warnings adds the correlations
A multitrait-multimethod matrix and data set I built on @Andy W's R-code and hope my changes are useful to someone else. I mainly changed it, so that it obeys the new syntax (no more opts) in ggplot2, so no more warnings adds the correlations as text now correlation text size reflects its effect size colour scheme s...
A multitrait-multimethod matrix and data set I built on @Andy W's R-code and hope my changes are useful to someone else. I mainly changed it, so that it obeys the new syntax (no more opts) in ggplot2, so no more warnings adds the correlations
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A multitrait-multimethod matrix and data set
It looks like I forgot to link to the original resource I used to construct this picture, that was used as an illustration for an old course (I tend to prefer B&W pictures :-). I know nothing about the data, and that was not of primary interest at the time I used it (it was done with Omnigraffle for Mac). If the quest...
A multitrait-multimethod matrix and data set
It looks like I forgot to link to the original resource I used to construct this picture, that was used as an illustration for an old course (I tend to prefer B&W pictures :-). I know nothing about th
A multitrait-multimethod matrix and data set It looks like I forgot to link to the original resource I used to construct this picture, that was used as an illustration for an old course (I tend to prefer B&W pictures :-). I know nothing about the data, and that was not of primary interest at the time I used it (it was ...
A multitrait-multimethod matrix and data set It looks like I forgot to link to the original resource I used to construct this picture, that was used as an illustration for an old course (I tend to prefer B&W pictures :-). I know nothing about th
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Is it "rows by columns" or "columns by rows"?
"That depends." Rows are usually considered observations, and columns are variables. So I would say widgets by color level in your context. But it really depends on which are your dependent and independent variables (or how you're interpreting the data).
Is it "rows by columns" or "columns by rows"?
"That depends." Rows are usually considered observations, and columns are variables. So I would say widgets by color level in your context. But it really depends on which are your dependent and ind
Is it "rows by columns" or "columns by rows"? "That depends." Rows are usually considered observations, and columns are variables. So I would say widgets by color level in your context. But it really depends on which are your dependent and independent variables (or how you're interpreting the data).
Is it "rows by columns" or "columns by rows"? "That depends." Rows are usually considered observations, and columns are variables. So I would say widgets by color level in your context. But it really depends on which are your dependent and ind
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Is it "rows by columns" or "columns by rows"?
Of course you can view this table either way by transposing it. Conventionally, in a database rows represent objects and columns contain their attributes, whence this presentation would typically be viewed as a list of widgets, not a list of color levels.
Is it "rows by columns" or "columns by rows"?
Of course you can view this table either way by transposing it. Conventionally, in a database rows represent objects and columns contain their attributes, whence this presentation would typically be
Is it "rows by columns" or "columns by rows"? Of course you can view this table either way by transposing it. Conventionally, in a database rows represent objects and columns contain their attributes, whence this presentation would typically be viewed as a list of widgets, not a list of color levels.
Is it "rows by columns" or "columns by rows"? Of course you can view this table either way by transposing it. Conventionally, in a database rows represent objects and columns contain their attributes, whence this presentation would typically be
51,658
Is it "rows by columns" or "columns by rows"?
Typically, we talk about a r(ow) X (c)olumn matrix, from Linear Algebra. So, a matrix with 2 rows and 3 columns is a 2 X 3 matrix. By that logic, I'd call your data frame a "Widgets by Color" table.
Is it "rows by columns" or "columns by rows"?
Typically, we talk about a r(ow) X (c)olumn matrix, from Linear Algebra. So, a matrix with 2 rows and 3 columns is a 2 X 3 matrix. By that logic, I'd call your data frame a "Widgets by Color" table.
Is it "rows by columns" or "columns by rows"? Typically, we talk about a r(ow) X (c)olumn matrix, from Linear Algebra. So, a matrix with 2 rows and 3 columns is a 2 X 3 matrix. By that logic, I'd call your data frame a "Widgets by Color" table.
Is it "rows by columns" or "columns by rows"? Typically, we talk about a r(ow) X (c)olumn matrix, from Linear Algebra. So, a matrix with 2 rows and 3 columns is a 2 X 3 matrix. By that logic, I'd call your data frame a "Widgets by Color" table.
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Is it "rows by columns" or "columns by rows"?
for a table like that, I say it the same way I'd say "n by k" for a matrix with n rows and k columns (i.e. rows first).
Is it "rows by columns" or "columns by rows"?
for a table like that, I say it the same way I'd say "n by k" for a matrix with n rows and k columns (i.e. rows first).
Is it "rows by columns" or "columns by rows"? for a table like that, I say it the same way I'd say "n by k" for a matrix with n rows and k columns (i.e. rows first).
Is it "rows by columns" or "columns by rows"? for a table like that, I say it the same way I'd say "n by k" for a matrix with n rows and k columns (i.e. rows first).
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Convolution of Poisson with Binomial distribution?
Let's start by looking at a single pulse and figure out the distribution of the number of photons in that pulse that get through the filter. To do this, let $N$ denote the initial number of photons in the pulse and let $X$ denote the number of photons that make it through the filter. Then you have the model: $$\begin...
Convolution of Poisson with Binomial distribution?
Let's start by looking at a single pulse and figure out the distribution of the number of photons in that pulse that get through the filter. To do this, let $N$ denote the initial number of photons i
Convolution of Poisson with Binomial distribution? Let's start by looking at a single pulse and figure out the distribution of the number of photons in that pulse that get through the filter. To do this, let $N$ denote the initial number of photons in the pulse and let $X$ denote the number of photons that make it thr...
Convolution of Poisson with Binomial distribution? Let's start by looking at a single pulse and figure out the distribution of the number of photons in that pulse that get through the filter. To do this, let $N$ denote the initial number of photons i
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Convolution of Poisson with Binomial distribution?
Intuition You can view it intuitively as following. The Poisson distribution describes the number of counts for a Poisson process taking some time $T$ (like your pulse taking some time $T$ with photons being emitted randomly with a specific rate). You could randomly designate each event/case/photon as $X_i = 0$ or $X_i...
Convolution of Poisson with Binomial distribution?
Intuition You can view it intuitively as following. The Poisson distribution describes the number of counts for a Poisson process taking some time $T$ (like your pulse taking some time $T$ with photon
Convolution of Poisson with Binomial distribution? Intuition You can view it intuitively as following. The Poisson distribution describes the number of counts for a Poisson process taking some time $T$ (like your pulse taking some time $T$ with photons being emitted randomly with a specific rate). You could randomly de...
Convolution of Poisson with Binomial distribution? Intuition You can view it intuitively as following. The Poisson distribution describes the number of counts for a Poisson process taking some time $T$ (like your pulse taking some time $T$ with photon
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Convolution of Poisson with Binomial distribution?
This sounds like a compound Poisson distribution. You have a Poisson distributed number $N$ of binomial trials $X_i$, each trial coming from one incoming photon. Each photon either passes through or not - as long as the absorption probability is constant, each such choice is a Bernoulli trial, i.e., $P(X_i=1)=p$. So in...
Convolution of Poisson with Binomial distribution?
This sounds like a compound Poisson distribution. You have a Poisson distributed number $N$ of binomial trials $X_i$, each trial coming from one incoming photon. Each photon either passes through or n
Convolution of Poisson with Binomial distribution? This sounds like a compound Poisson distribution. You have a Poisson distributed number $N$ of binomial trials $X_i$, each trial coming from one incoming photon. Each photon either passes through or not - as long as the absorption probability is constant, each such cho...
Convolution of Poisson with Binomial distribution? This sounds like a compound Poisson distribution. You have a Poisson distributed number $N$ of binomial trials $X_i$, each trial coming from one incoming photon. Each photon either passes through or n
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What is the "grid" in Bayesian grid approximations?
Bayes theorem is $$ p(\theta|X) = \frac{p(X|\theta)\,p(\theta)}{p(X)} $$ where, by the law of total probability, for discrete distributions $p(X) = \sum_\theta \,p(X|\theta)\,p(\theta)$. So for the numerator, you multiply the likelihood by the prior, and for the denominator, you need to do the same for all the possible...
What is the "grid" in Bayesian grid approximations?
Bayes theorem is $$ p(\theta|X) = \frac{p(X|\theta)\,p(\theta)}{p(X)} $$ where, by the law of total probability, for discrete distributions $p(X) = \sum_\theta \,p(X|\theta)\,p(\theta)$. So for the nu
What is the "grid" in Bayesian grid approximations? Bayes theorem is $$ p(\theta|X) = \frac{p(X|\theta)\,p(\theta)}{p(X)} $$ where, by the law of total probability, for discrete distributions $p(X) = \sum_\theta \,p(X|\theta)\,p(\theta)$. So for the numerator, you multiply the likelihood by the prior, and for the denom...
What is the "grid" in Bayesian grid approximations? Bayes theorem is $$ p(\theta|X) = \frac{p(X|\theta)\,p(\theta)}{p(X)} $$ where, by the law of total probability, for discrete distributions $p(X) = \sum_\theta \,p(X|\theta)\,p(\theta)$. So for the nu
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What is the "grid" in Bayesian grid approximations?
Let me make up an example to make it easier to understand. It is not what the book says but it is the same idea and I think it will make it even easier. Suppose you have independent samples $x_1,...,x_{20}$ from a $\textbf{Nor}(\mu,\sigma^2)$ distribution. You would like to draw/find the posterior distribution of the ...
What is the "grid" in Bayesian grid approximations?
Let me make up an example to make it easier to understand. It is not what the book says but it is the same idea and I think it will make it even easier. Suppose you have independent samples $x_1,...,
What is the "grid" in Bayesian grid approximations? Let me make up an example to make it easier to understand. It is not what the book says but it is the same idea and I think it will make it even easier. Suppose you have independent samples $x_1,...,x_{20}$ from a $\textbf{Nor}(\mu,\sigma^2)$ distribution. You would ...
What is the "grid" in Bayesian grid approximations? Let me make up an example to make it easier to understand. It is not what the book says but it is the same idea and I think it will make it even easier. Suppose you have independent samples $x_1,...,
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What is the "grid" in Bayesian grid approximations?
Grid approximations let you compute a discrete posterior approximation The Cartesian grid used in this grid approximation is for one-dimensional parameter space so it consists of a set of vertices at evenly spaced points over the parameter range. If you were to use a Cartesian grid for a two-dimensional parameter spac...
What is the "grid" in Bayesian grid approximations?
Grid approximations let you compute a discrete posterior approximation The Cartesian grid used in this grid approximation is for one-dimensional parameter space so it consists of a set of vertices at
What is the "grid" in Bayesian grid approximations? Grid approximations let you compute a discrete posterior approximation The Cartesian grid used in this grid approximation is for one-dimensional parameter space so it consists of a set of vertices at evenly spaced points over the parameter range. If you were to use a...
What is the "grid" in Bayesian grid approximations? Grid approximations let you compute a discrete posterior approximation The Cartesian grid used in this grid approximation is for one-dimensional parameter space so it consists of a set of vertices at
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ML modelling where the output affects the DGP
is ML recommended in decision-making processes which inherently changes the nature of the environment? What is the alternative, given that we have to make decisions? Would HL (Human Learning) work better? Or NL (No Learning)? I work in retail forecasting, and our forecasts are used in automatic replenishment in superm...
ML modelling where the output affects the DGP
is ML recommended in decision-making processes which inherently changes the nature of the environment? What is the alternative, given that we have to make decisions? Would HL (Human Learning) work be
ML modelling where the output affects the DGP is ML recommended in decision-making processes which inherently changes the nature of the environment? What is the alternative, given that we have to make decisions? Would HL (Human Learning) work better? Or NL (No Learning)? I work in retail forecasting, and our forecasts...
ML modelling where the output affects the DGP is ML recommended in decision-making processes which inherently changes the nature of the environment? What is the alternative, given that we have to make decisions? Would HL (Human Learning) work be
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ML modelling where the output affects the DGP
That's a common problem with training ML models using data generated from a set-up where a ML model is already part of what happens. E.g. with search engine data, the results shown on the first page (and even better in first spot) are much more likely to be clicked than those shown further down. Additionally, there can...
ML modelling where the output affects the DGP
That's a common problem with training ML models using data generated from a set-up where a ML model is already part of what happens. E.g. with search engine data, the results shown on the first page (
ML modelling where the output affects the DGP That's a common problem with training ML models using data generated from a set-up where a ML model is already part of what happens. E.g. with search engine data, the results shown on the first page (and even better in first spot) are much more likely to be clicked than tho...
ML modelling where the output affects the DGP That's a common problem with training ML models using data generated from a set-up where a ML model is already part of what happens. E.g. with search engine data, the results shown on the first page (
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Is the use of cutoffs for dichotomisation of biomarkers really that bad?
It's really that bad, as detailed in many of Patrick and my writings. Think about it these ways, for starters: If you categorize a marker the loss of information is so great that you will need to go an collect more markers to make up for the loss. Why not instead get the most information out of a single marker? Then...
Is the use of cutoffs for dichotomisation of biomarkers really that bad?
It's really that bad, as detailed in many of Patrick and my writings. Think about it these ways, for starters: If you categorize a marker the loss of information is so great that you will need to go
Is the use of cutoffs for dichotomisation of biomarkers really that bad? It's really that bad, as detailed in many of Patrick and my writings. Think about it these ways, for starters: If you categorize a marker the loss of information is so great that you will need to go an collect more markers to make up for the loss...
Is the use of cutoffs for dichotomisation of biomarkers really that bad? It's really that bad, as detailed in many of Patrick and my writings. Think about it these ways, for starters: If you categorize a marker the loss of information is so great that you will need to go
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Is the use of cutoffs for dichotomisation of biomarkers really that bad?
Although cutoffs in biomarker values are admittedly not helpful for modeling within a single population (+1 to Frank Harrell's answer on that basis), they make sense when, together with extensive subject-matter knowledge, they can delineate fundamentally different populations that benefit from different therapy. In suc...
Is the use of cutoffs for dichotomisation of biomarkers really that bad?
Although cutoffs in biomarker values are admittedly not helpful for modeling within a single population (+1 to Frank Harrell's answer on that basis), they make sense when, together with extensive subj
Is the use of cutoffs for dichotomisation of biomarkers really that bad? Although cutoffs in biomarker values are admittedly not helpful for modeling within a single population (+1 to Frank Harrell's answer on that basis), they make sense when, together with extensive subject-matter knowledge, they can delineate fundam...
Is the use of cutoffs for dichotomisation of biomarkers really that bad? Although cutoffs in biomarker values are admittedly not helpful for modeling within a single population (+1 to Frank Harrell's answer on that basis), they make sense when, together with extensive subj
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Can duplicate examples create multi-collinearity?
As Christoph Hanck suggested, duplicate examples will not cause any problem of multi-collinearity. The multi-collinearity "problem" is caused by duplicate "columns" instead of "rows" in data matrix. Intuitively, rows are data samples, and columns are features/measures, multi-collinearity means we have redundant featur...
Can duplicate examples create multi-collinearity?
As Christoph Hanck suggested, duplicate examples will not cause any problem of multi-collinearity. The multi-collinearity "problem" is caused by duplicate "columns" instead of "rows" in data matrix.
Can duplicate examples create multi-collinearity? As Christoph Hanck suggested, duplicate examples will not cause any problem of multi-collinearity. The multi-collinearity "problem" is caused by duplicate "columns" instead of "rows" in data matrix. Intuitively, rows are data samples, and columns are features/measures,...
Can duplicate examples create multi-collinearity? As Christoph Hanck suggested, duplicate examples will not cause any problem of multi-collinearity. The multi-collinearity "problem" is caused by duplicate "columns" instead of "rows" in data matrix.
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Can duplicate examples create multi-collinearity?
There is no problem with duplicate rows. Consider some applied examples, such as "returns to education", i.e., how much do people earn given their education, gender, experience etc. There can, and often will, be people in the dataset with the same gender, years of education and years of labor market experience. So ther...
Can duplicate examples create multi-collinearity?
There is no problem with duplicate rows. Consider some applied examples, such as "returns to education", i.e., how much do people earn given their education, gender, experience etc. There can, and oft
Can duplicate examples create multi-collinearity? There is no problem with duplicate rows. Consider some applied examples, such as "returns to education", i.e., how much do people earn given their education, gender, experience etc. There can, and often will, be people in the dataset with the same gender, years of educa...
Can duplicate examples create multi-collinearity? There is no problem with duplicate rows. Consider some applied examples, such as "returns to education", i.e., how much do people earn given their education, gender, experience etc. There can, and oft
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Simulating a Coin toss [duplicate]
Somewhat related example: One way to generate 10 tosses of a coin with probability $0.4$ of heads is to use rbinom: set.seed(123); rbinom(10, 1, .4) [1] 0 1 0 1 1 0 0 1 0 0 Another way is to use the binomial inverse CDF (quantile) function) qbinom to transform uniform random numbers from runif get the desired Bernoull...
Simulating a Coin toss [duplicate]
Somewhat related example: One way to generate 10 tosses of a coin with probability $0.4$ of heads is to use rbinom: set.seed(123); rbinom(10, 1, .4) [1] 0 1 0 1 1 0 0 1 0 0 Another way is to use the
Simulating a Coin toss [duplicate] Somewhat related example: One way to generate 10 tosses of a coin with probability $0.4$ of heads is to use rbinom: set.seed(123); rbinom(10, 1, .4) [1] 0 1 0 1 1 0 0 1 0 0 Another way is to use the binomial inverse CDF (quantile) function) qbinom to transform uniform random numbers ...
Simulating a Coin toss [duplicate] Somewhat related example: One way to generate 10 tosses of a coin with probability $0.4$ of heads is to use rbinom: set.seed(123); rbinom(10, 1, .4) [1] 0 1 0 1 1 0 0 1 0 0 Another way is to use the
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Simulating a Coin toss [duplicate]
An historical note about sample is that it got recently modified for being biased in some extreme situations (as commented by Chris Haug). In earlier versions of R such as 3.4.4, still running on my ownlaptop, the outcome of the above would be the same as a cdf inversion (and as the complement of the standard Uniform d...
Simulating a Coin toss [duplicate]
An historical note about sample is that it got recently modified for being biased in some extreme situations (as commented by Chris Haug). In earlier versions of R such as 3.4.4, still running on my o
Simulating a Coin toss [duplicate] An historical note about sample is that it got recently modified for being biased in some extreme situations (as commented by Chris Haug). In earlier versions of R such as 3.4.4, still running on my ownlaptop, the outcome of the above would be the same as a cdf inversion (and as the c...
Simulating a Coin toss [duplicate] An historical note about sample is that it got recently modified for being biased in some extreme situations (as commented by Chris Haug). In earlier versions of R such as 3.4.4, still running on my o
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Simulating a Coin toss [duplicate]
I tried getting to the source code for both, but couldn't find it. I did, however, find the references for the building of the two algorithms. They do not use the same references, so it is reasonable that they do not generate them in a similar manner. Indeed, sample() function briefly says it uses an easier way to ha...
Simulating a Coin toss [duplicate]
I tried getting to the source code for both, but couldn't find it. I did, however, find the references for the building of the two algorithms. They do not use the same references, so it is reasonable
Simulating a Coin toss [duplicate] I tried getting to the source code for both, but couldn't find it. I did, however, find the references for the building of the two algorithms. They do not use the same references, so it is reasonable that they do not generate them in a similar manner. Indeed, sample() function brief...
Simulating a Coin toss [duplicate] I tried getting to the source code for both, but couldn't find it. I did, however, find the references for the building of the two algorithms. They do not use the same references, so it is reasonable
51,675
Coronavirus growth rate and its possibly spurious resemblance to vapor pressure model
"If all you have is a hammer, everything looks like a nail." The dataset you have is small, possibly underrepresented, and of unknown quality, since it is argued that many cases could have not been diagnosed. You observe an exponential growth, a common phenomena in many natural and artificial processes. The curve fits ...
Coronavirus growth rate and its possibly spurious resemblance to vapor pressure model
"If all you have is a hammer, everything looks like a nail." The dataset you have is small, possibly underrepresented, and of unknown quality, since it is argued that many cases could have not been di
Coronavirus growth rate and its possibly spurious resemblance to vapor pressure model "If all you have is a hammer, everything looks like a nail." The dataset you have is small, possibly underrepresented, and of unknown quality, since it is argued that many cases could have not been diagnosed. You observe an exponentia...
Coronavirus growth rate and its possibly spurious resemblance to vapor pressure model "If all you have is a hammer, everything looks like a nail." The dataset you have is small, possibly underrepresented, and of unknown quality, since it is argued that many cases could have not been di
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Coronavirus growth rate and its possibly spurious resemblance to vapor pressure model
The growth of infected cases $y$ is more or less exponential but the growth rate $c$ is not constant. $$ \frac{\partial y}{\partial t} \approx c y$$ For instance, note in the graph how the change in cases from day to day depends on the number of cases in a particular day and the increase in cases is larger when the cur...
Coronavirus growth rate and its possibly spurious resemblance to vapor pressure model
The growth of infected cases $y$ is more or less exponential but the growth rate $c$ is not constant. $$ \frac{\partial y}{\partial t} \approx c y$$ For instance, note in the graph how the change in c
Coronavirus growth rate and its possibly spurious resemblance to vapor pressure model The growth of infected cases $y$ is more or less exponential but the growth rate $c$ is not constant. $$ \frac{\partial y}{\partial t} \approx c y$$ For instance, note in the graph how the change in cases from day to day depends on th...
Coronavirus growth rate and its possibly spurious resemblance to vapor pressure model The growth of infected cases $y$ is more or less exponential but the growth rate $c$ is not constant. $$ \frac{\partial y}{\partial t} \approx c y$$ For instance, note in the graph how the change in c
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why there is no “error” term in survival analysis?
The distributional assumptions behind a relative risk model are hidden in the baseline hazard function $h_0(t)$. If you specify a form for this function, then you completely specify the distribution of your data. For example, $h_0(t) = \phi \psi t^{\phi - 1}$ corresponds to the Weibull distribution.
why there is no “error” term in survival analysis?
The distributional assumptions behind a relative risk model are hidden in the baseline hazard function $h_0(t)$. If you specify a form for this function, then you completely specify the distribution o
why there is no “error” term in survival analysis? The distributional assumptions behind a relative risk model are hidden in the baseline hazard function $h_0(t)$. If you specify a form for this function, then you completely specify the distribution of your data. For example, $h_0(t) = \phi \psi t^{\phi - 1}$ correspon...
why there is no “error” term in survival analysis? The distributional assumptions behind a relative risk model are hidden in the baseline hazard function $h_0(t)$. If you specify a form for this function, then you completely specify the distribution o
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why there is no “error” term in survival analysis?
There absolutely is an "error" in survival analysis. You can define the "time to event" according to a probability model with some $$g(T) = b (X, t) + \epsilon(X,t)$$ where $g$ would usually be something like a log transform. Of course requiring $\epsilon$ to be normal, identically distributed, or even stationary is ...
why there is no “error” term in survival analysis?
There absolutely is an "error" in survival analysis. You can define the "time to event" according to a probability model with some $$g(T) = b (X, t) + \epsilon(X,t)$$ where $g$ would usually be some
why there is no “error” term in survival analysis? There absolutely is an "error" in survival analysis. You can define the "time to event" according to a probability model with some $$g(T) = b (X, t) + \epsilon(X,t)$$ where $g$ would usually be something like a log transform. Of course requiring $\epsilon$ to be norm...
why there is no “error” term in survival analysis? There absolutely is an "error" in survival analysis. You can define the "time to event" according to a probability model with some $$g(T) = b (X, t) + \epsilon(X,t)$$ where $g$ would usually be some
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why there is no “error” term in survival analysis?
Simple Linear Regression Model \begin{equation} Y_i=B_0+B_1 X_i+ε_i \end{equation} Where $Y_i$ is the value of the response variable in the ith trial $ε_i $ is a random error term with mean $E[ε_i]=0$ and variance $σ^2 [ε_i ]=σ^2$ \begin{equation} E[Y_i ]=B_0+B_1 X_i \end{equation} Consider the simple linear regres...
why there is no “error” term in survival analysis?
Simple Linear Regression Model \begin{equation} Y_i=B_0+B_1 X_i+ε_i \end{equation} Where $Y_i$ is the value of the response variable in the ith trial $ε_i $ is a random error term with mean $E[ε_i]
why there is no “error” term in survival analysis? Simple Linear Regression Model \begin{equation} Y_i=B_0+B_1 X_i+ε_i \end{equation} Where $Y_i$ is the value of the response variable in the ith trial $ε_i $ is a random error term with mean $E[ε_i]=0$ and variance $σ^2 [ε_i ]=σ^2$ \begin{equation} E[Y_i ]=B_0+B_1 X...
why there is no “error” term in survival analysis? Simple Linear Regression Model \begin{equation} Y_i=B_0+B_1 X_i+ε_i \end{equation} Where $Y_i$ is the value of the response variable in the ith trial $ε_i $ is a random error term with mean $E[ε_i]
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why there is no “error” term in survival analysis?
This Answer is limited to frequentist statistics and statistical model without random effect. In fact, the statistical modeling is to find the conditional distribution of response variable conditional on fixed values of the covariates, i.e., distribution of $Y|X=x$. When writing the statistical model, abiding followin...
why there is no “error” term in survival analysis?
This Answer is limited to frequentist statistics and statistical model without random effect. In fact, the statistical modeling is to find the conditional distribution of response variable conditiona
why there is no “error” term in survival analysis? This Answer is limited to frequentist statistics and statistical model without random effect. In fact, the statistical modeling is to find the conditional distribution of response variable conditional on fixed values of the covariates, i.e., distribution of $Y|X=x$. W...
why there is no “error” term in survival analysis? This Answer is limited to frequentist statistics and statistical model without random effect. In fact, the statistical modeling is to find the conditional distribution of response variable conditiona
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How to determine the optimal threshold to achieve the highest accuracy
I suspect that the answer is "no", i.e., that there is no such way. Here is an illustration, where we plot the predicted probabilities against the true labels: Since the denominator $P+N$ in the formula for accuracy does not change, what you are trying to do is to shift the horizontal red line up or down (the height b...
How to determine the optimal threshold to achieve the highest accuracy
I suspect that the answer is "no", i.e., that there is no such way. Here is an illustration, where we plot the predicted probabilities against the true labels: Since the denominator $P+N$ in the form
How to determine the optimal threshold to achieve the highest accuracy I suspect that the answer is "no", i.e., that there is no such way. Here is an illustration, where we plot the predicted probabilities against the true labels: Since the denominator $P+N$ in the formula for accuracy does not change, what you are tr...
How to determine the optimal threshold to achieve the highest accuracy I suspect that the answer is "no", i.e., that there is no such way. Here is an illustration, where we plot the predicted probabilities against the true labels: Since the denominator $P+N$ in the form
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How to determine the optimal threshold to achieve the highest accuracy
Agreeing with @StephanKolassa, I'll just look from an algorithmic perspective. You'll need to sort your samples with respect to produced probabilities, which is $O(n\log n)$, if you've $n$ data samples. Then, your true class labels will order like $$0\ 0 \ 1\ 0\ 0\ 1 \ ...\ 1 \ 1\ 0\ 1 $$ Then, we'll put a separator $|...
How to determine the optimal threshold to achieve the highest accuracy
Agreeing with @StephanKolassa, I'll just look from an algorithmic perspective. You'll need to sort your samples with respect to produced probabilities, which is $O(n\log n)$, if you've $n$ data sample
How to determine the optimal threshold to achieve the highest accuracy Agreeing with @StephanKolassa, I'll just look from an algorithmic perspective. You'll need to sort your samples with respect to produced probabilities, which is $O(n\log n)$, if you've $n$ data samples. Then, your true class labels will order like $...
How to determine the optimal threshold to achieve the highest accuracy Agreeing with @StephanKolassa, I'll just look from an algorithmic perspective. You'll need to sort your samples with respect to produced probabilities, which is $O(n\log n)$, if you've $n$ data sample
51,683
How to determine the optimal threshold to achieve the highest accuracy
I implemented the solution proposed by Stephan Kolassa in python: def opt_threshold_acc(y_true, y_pred): A = list(zip(y_true, y_pred)) A = sorted(A, key=lambda x: x[1]) total = len(A) tp = len([1 for x in A if x[0]==1]) tn = 0 th_acc = [] for x in A: th = x[1] if x[0] == 1: ...
How to determine the optimal threshold to achieve the highest accuracy
I implemented the solution proposed by Stephan Kolassa in python: def opt_threshold_acc(y_true, y_pred): A = list(zip(y_true, y_pred)) A = sorted(A, key=lambda x: x[1]) total = len(A)
How to determine the optimal threshold to achieve the highest accuracy I implemented the solution proposed by Stephan Kolassa in python: def opt_threshold_acc(y_true, y_pred): A = list(zip(y_true, y_pred)) A = sorted(A, key=lambda x: x[1]) total = len(A) tp = len([1 for x in A if x[0]==1]) tn = 0 ...
How to determine the optimal threshold to achieve the highest accuracy I implemented the solution proposed by Stephan Kolassa in python: def opt_threshold_acc(y_true, y_pred): A = list(zip(y_true, y_pred)) A = sorted(A, key=lambda x: x[1]) total = len(A)
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How to understand confusion matrix for 3x3
Based on the 3x3 confusion matrix in your example (assuming I'm understanding the labels correctly) the columns are the predictions and the rows must therefore be the actual values. The main diagonal (64, 237, 165) gives the correct predictions. That is, the cases where the actual values and the model predictions are t...
How to understand confusion matrix for 3x3
Based on the 3x3 confusion matrix in your example (assuming I'm understanding the labels correctly) the columns are the predictions and the rows must therefore be the actual values. The main diagonal
How to understand confusion matrix for 3x3 Based on the 3x3 confusion matrix in your example (assuming I'm understanding the labels correctly) the columns are the predictions and the rows must therefore be the actual values. The main diagonal (64, 237, 165) gives the correct predictions. That is, the cases where the ac...
How to understand confusion matrix for 3x3 Based on the 3x3 confusion matrix in your example (assuming I'm understanding the labels correctly) the columns are the predictions and the rows must therefore be the actual values. The main diagonal
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How to understand confusion matrix for 3x3
True Positive, False Positive and similar counts and rates only make sense if there is a notion of "positive" and "negative" classes in your data. That is, only if you have exactly two classes. You have three classes, not two. In your case, you can more or less reasonably discuss analogues, like "True Male" numbers: ta...
How to understand confusion matrix for 3x3
True Positive, False Positive and similar counts and rates only make sense if there is a notion of "positive" and "negative" classes in your data. That is, only if you have exactly two classes. You ha
How to understand confusion matrix for 3x3 True Positive, False Positive and similar counts and rates only make sense if there is a notion of "positive" and "negative" classes in your data. That is, only if you have exactly two classes. You have three classes, not two. In your case, you can more or less reasonably disc...
How to understand confusion matrix for 3x3 True Positive, False Positive and similar counts and rates only make sense if there is a notion of "positive" and "negative" classes in your data. That is, only if you have exactly two classes. You ha
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How to understand confusion matrix for 3x3
TP, TN, FP, FN - in 3x3 matrix could be defined PER CLASS In the above example: For M class: TP - real M predicted as M (64) TN - real F predicted as F and real I predicted as I (237+165) FP - real F and I predicted as M (12+52) FN - real M predicted as F or I (46+139) Then you can calculate Precision and Recall metric...
How to understand confusion matrix for 3x3
TP, TN, FP, FN - in 3x3 matrix could be defined PER CLASS In the above example: For M class: TP - real M predicted as M (64) TN - real F predicted as F and real I predicted as I (237+165) FP - real F
How to understand confusion matrix for 3x3 TP, TN, FP, FN - in 3x3 matrix could be defined PER CLASS In the above example: For M class: TP - real M predicted as M (64) TN - real F predicted as F and real I predicted as I (237+165) FP - real F and I predicted as M (12+52) FN - real M predicted as F or I (46+139) Then yo...
How to understand confusion matrix for 3x3 TP, TN, FP, FN - in 3x3 matrix could be defined PER CLASS In the above example: For M class: TP - real M predicted as M (64) TN - real F predicted as F and real I predicted as I (237+165) FP - real F
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How does Bayesian analysis make accurate predictions using subjectively chosen probabilities?
You are talking about Bayesian analysis, not Bayes theorem, but we know what you mean. Let me hit you with an idea that is even more strange than the one you are thinking about. As long as you use your real prior density in constructing your model, then all Bayesian statistics are admissible, where admissibility is de...
How does Bayesian analysis make accurate predictions using subjectively chosen probabilities?
You are talking about Bayesian analysis, not Bayes theorem, but we know what you mean. Let me hit you with an idea that is even more strange than the one you are thinking about. As long as you use yo
How does Bayesian analysis make accurate predictions using subjectively chosen probabilities? You are talking about Bayesian analysis, not Bayes theorem, but we know what you mean. Let me hit you with an idea that is even more strange than the one you are thinking about. As long as you use your real prior density in c...
How does Bayesian analysis make accurate predictions using subjectively chosen probabilities? You are talking about Bayesian analysis, not Bayes theorem, but we know what you mean. Let me hit you with an idea that is even more strange than the one you are thinking about. As long as you use yo
51,688
How does Bayesian analysis make accurate predictions using subjectively chosen probabilities?
While a person might be wrong in a particular moment about the likelihood of a particular thing happening, the idea behind Bayes theorem (as applied to updating your understanding in the face of new information) is that the updated probability may not be entirely right, but that it will be more right than you were when...
How does Bayesian analysis make accurate predictions using subjectively chosen probabilities?
While a person might be wrong in a particular moment about the likelihood of a particular thing happening, the idea behind Bayes theorem (as applied to updating your understanding in the face of new i
How does Bayesian analysis make accurate predictions using subjectively chosen probabilities? While a person might be wrong in a particular moment about the likelihood of a particular thing happening, the idea behind Bayes theorem (as applied to updating your understanding in the face of new information) is that the up...
How does Bayesian analysis make accurate predictions using subjectively chosen probabilities? While a person might be wrong in a particular moment about the likelihood of a particular thing happening, the idea behind Bayes theorem (as applied to updating your understanding in the face of new i
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How does Bayesian analysis make accurate predictions using subjectively chosen probabilities?
When you consider specifying a prior vs using a raw frequentist method, sometimes the prediction will be much better even with an apparently wrong prior because you don't need the prior to be precise at all to improve things. A very rough prior helps to rule out what is unrealistic, and this helps even if specified ver...
How does Bayesian analysis make accurate predictions using subjectively chosen probabilities?
When you consider specifying a prior vs using a raw frequentist method, sometimes the prediction will be much better even with an apparently wrong prior because you don't need the prior to be precise
How does Bayesian analysis make accurate predictions using subjectively chosen probabilities? When you consider specifying a prior vs using a raw frequentist method, sometimes the prediction will be much better even with an apparently wrong prior because you don't need the prior to be precise at all to improve things. ...
How does Bayesian analysis make accurate predictions using subjectively chosen probabilities? When you consider specifying a prior vs using a raw frequentist method, sometimes the prediction will be much better even with an apparently wrong prior because you don't need the prior to be precise
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How does Bayesian analysis make accurate predictions using subjectively chosen probabilities?
First, Bayes theorem doesn't make predictions. It's a mathematical law. But you have to get the probabilities right for it to work. Second, you may be thinking of a Bayesian approach to data analysis. This does depend on priors but a) Sometimes (often) a uniform prior is chosen b) Other times, the prior is based on ...
How does Bayesian analysis make accurate predictions using subjectively chosen probabilities?
First, Bayes theorem doesn't make predictions. It's a mathematical law. But you have to get the probabilities right for it to work. Second, you may be thinking of a Bayesian approach to data analysis
How does Bayesian analysis make accurate predictions using subjectively chosen probabilities? First, Bayes theorem doesn't make predictions. It's a mathematical law. But you have to get the probabilities right for it to work. Second, you may be thinking of a Bayesian approach to data analysis. This does depend on pri...
How does Bayesian analysis make accurate predictions using subjectively chosen probabilities? First, Bayes theorem doesn't make predictions. It's a mathematical law. But you have to get the probabilities right for it to work. Second, you may be thinking of a Bayesian approach to data analysis
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How to do an ANOVA when your data are non-normal with possibly differing variances?
The data, as indicated by the variable names in the linked-to spreadsheet, pertains to number of organisms in 13 groups, so are some kind of count data. We could do better here if we knew some more about the data! But I do not agree with the answer by @gung that we should use some count data model, like Poisson regress...
How to do an ANOVA when your data are non-normal with possibly differing variances?
The data, as indicated by the variable names in the linked-to spreadsheet, pertains to number of organisms in 13 groups, so are some kind of count data. We could do better here if we knew some more ab
How to do an ANOVA when your data are non-normal with possibly differing variances? The data, as indicated by the variable names in the linked-to spreadsheet, pertains to number of organisms in 13 groups, so are some kind of count data. We could do better here if we knew some more about the data! But I do not agree wit...
How to do an ANOVA when your data are non-normal with possibly differing variances? The data, as indicated by the variable names in the linked-to spreadsheet, pertains to number of organisms in 13 groups, so are some kind of count data. We could do better here if we knew some more ab
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How to do an ANOVA when your data are non-normal with possibly differing variances?
I notice that your response is called "Number of Organisms", and that all the values are non-negative integers. I suspect these are count data. They should not be treated as normally distributed and analyzed with a traditional ANOVA. Instead, a count GLM is appropriate. We can try Poisson regression: anova(glm(N.Or...
How to do an ANOVA when your data are non-normal with possibly differing variances?
I notice that your response is called "Number of Organisms", and that all the values are non-negative integers. I suspect these are count data. They should not be treated as normally distributed and
How to do an ANOVA when your data are non-normal with possibly differing variances? I notice that your response is called "Number of Organisms", and that all the values are non-negative integers. I suspect these are count data. They should not be treated as normally distributed and analyzed with a traditional ANOVA. ...
How to do an ANOVA when your data are non-normal with possibly differing variances? I notice that your response is called "Number of Organisms", and that all the values are non-negative integers. I suspect these are count data. They should not be treated as normally distributed and
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How to do an ANOVA when your data are non-normal with possibly differing variances?
This is largely a footnote to @kjetil's answer, with which I tend to agree. But I have an extra graph that says a little more and that won't fit into a comment. This is a combination plot. For each group, there is a quantile plot showing the detail for each group, a superimposed box showing median and quartiles in stan...
How to do an ANOVA when your data are non-normal with possibly differing variances?
This is largely a footnote to @kjetil's answer, with which I tend to agree. But I have an extra graph that says a little more and that won't fit into a comment. This is a combination plot. For each gr
How to do an ANOVA when your data are non-normal with possibly differing variances? This is largely a footnote to @kjetil's answer, with which I tend to agree. But I have an extra graph that says a little more and that won't fit into a comment. This is a combination plot. For each group, there is a quantile plot showin...
How to do an ANOVA when your data are non-normal with possibly differing variances? This is largely a footnote to @kjetil's answer, with which I tend to agree. But I have an extra graph that says a little more and that won't fit into a comment. This is a combination plot. For each gr
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Extract BIC and AICc from arima() object
For the BIC and AIC, you can simply use AIC function as follow: > model <- arima(x=sunspots, order=c(2,0,2), method="ML") > AIC(model) [1] 23563.39 > bic=AIC(model,k = log(length(sunspots))) > bic [1] 23599.05 The function AIC can provide both AIC and BIC. Look at ?AIC.
Extract BIC and AICc from arima() object
For the BIC and AIC, you can simply use AIC function as follow: > model <- arima(x=sunspots, order=c(2,0,2), method="ML") > AIC(model) [1] 23563.39 > bic=AIC(model,k = log(length(sunspots))) > bic
Extract BIC and AICc from arima() object For the BIC and AIC, you can simply use AIC function as follow: > model <- arima(x=sunspots, order=c(2,0,2), method="ML") > AIC(model) [1] 23563.39 > bic=AIC(model,k = log(length(sunspots))) > bic [1] 23599.05 The function AIC can provide both AIC and BIC. Look at ?AIC.
Extract BIC and AICc from arima() object For the BIC and AIC, you can simply use AIC function as follow: > model <- arima(x=sunspots, order=c(2,0,2), method="ML") > AIC(model) [1] 23563.39 > bic=AIC(model,k = log(length(sunspots))) > bic
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Extract BIC and AICc from arima() object
Answer: One possible solution, although no claim to be the best, is as follows; it's a hack that I've come up with after looking at some source code. npar <- length(model$coef) + 1 nstar <- length(model$residuals) - model$arma[6] - model$arma[7] * model$arma[5] bic <- model$aic + npar * (log(nstar) - 2) aicc <- model$...
Extract BIC and AICc from arima() object
Answer: One possible solution, although no claim to be the best, is as follows; it's a hack that I've come up with after looking at some source code. npar <- length(model$coef) + 1 nstar <- length(mod
Extract BIC and AICc from arima() object Answer: One possible solution, although no claim to be the best, is as follows; it's a hack that I've come up with after looking at some source code. npar <- length(model$coef) + 1 nstar <- length(model$residuals) - model$arma[6] - model$arma[7] * model$arma[5] bic <- model$aic...
Extract BIC and AICc from arima() object Answer: One possible solution, although no claim to be the best, is as follows; it's a hack that I've come up with after looking at some source code. npar <- length(model$coef) + 1 nstar <- length(mod
51,696
Extract BIC and AICc from arima() object
Here is a function my TA in my time series analysis course at UC Davis wrote to extract the AICc Function aicc() computes the AICc of a given ARIMA model. INPUT: an ARIMA model object produced by arima() OUTPUT: AICc value for the given model object aicc = function(model){ n = model$nobs p = length(model$coef) aicc = m...
Extract BIC and AICc from arima() object
Here is a function my TA in my time series analysis course at UC Davis wrote to extract the AICc Function aicc() computes the AICc of a given ARIMA model. INPUT: an ARIMA model object produced by arim
Extract BIC and AICc from arima() object Here is a function my TA in my time series analysis course at UC Davis wrote to extract the AICc Function aicc() computes the AICc of a given ARIMA model. INPUT: an ARIMA model object produced by arima() OUTPUT: AICc value for the given model object aicc = function(model){ n = m...
Extract BIC and AICc from arima() object Here is a function my TA in my time series analysis course at UC Davis wrote to extract the AICc Function aicc() computes the AICc of a given ARIMA model. INPUT: an ARIMA model object produced by arim
51,697
Extract BIC and AICc from arima() object
Once you have loaded forecast package, you must use Arima() function for AIC, AICc and BIC. Notice upper "A" in Arima() function. If you use arima() function with lower "a", then R will use the function that comes with base R.
Extract BIC and AICc from arima() object
Once you have loaded forecast package, you must use Arima() function for AIC, AICc and BIC. Notice upper "A" in Arima() function. If you use arima() function with lower "a", then R will use the functi
Extract BIC and AICc from arima() object Once you have loaded forecast package, you must use Arima() function for AIC, AICc and BIC. Notice upper "A" in Arima() function. If you use arima() function with lower "a", then R will use the function that comes with base R.
Extract BIC and AICc from arima() object Once you have loaded forecast package, you must use Arima() function for AIC, AICc and BIC. Notice upper "A" in Arima() function. If you use arima() function with lower "a", then R will use the functi
51,698
Extract BIC and AICc from arima() object
what it seems like is you are using incorrect arima function to get the values. Note that, arima() is not part of forecast library, you will have to use Arima() instead. once the library(forecast) is imported use below function to extract the values: model=Arima(grow, order=c(2,0,0)) attributes(model) $names [1] "coef...
Extract BIC and AICc from arima() object
what it seems like is you are using incorrect arima function to get the values. Note that, arima() is not part of forecast library, you will have to use Arima() instead. once the library(forecast) is
Extract BIC and AICc from arima() object what it seems like is you are using incorrect arima function to get the values. Note that, arima() is not part of forecast library, you will have to use Arima() instead. once the library(forecast) is imported use below function to extract the values: model=Arima(grow, order=c(2...
Extract BIC and AICc from arima() object what it seems like is you are using incorrect arima function to get the values. Note that, arima() is not part of forecast library, you will have to use Arima() instead. once the library(forecast) is
51,699
Why is a deterministic trend process not stationary?
I think I nice way to get the intuition is to simulate 3 series for $t=0,...,500$ and plot them: Autoregressive Stationary Series: $A_{t}=0.05+0.95A_{t-1}+u_{t}$ Random Walk with Drift: $R_{t}=0.05+1R_{t-1}+u_{t}$ Explosive Series: $E_{t}=0.05+1.05E_{t-1}+u_{t}$ where $u_{t}$ is just some white noise, like iid $N(0,1...
Why is a deterministic trend process not stationary?
I think I nice way to get the intuition is to simulate 3 series for $t=0,...,500$ and plot them: Autoregressive Stationary Series: $A_{t}=0.05+0.95A_{t-1}+u_{t}$ Random Walk with Drift: $R_{t}=0.05+1
Why is a deterministic trend process not stationary? I think I nice way to get the intuition is to simulate 3 series for $t=0,...,500$ and plot them: Autoregressive Stationary Series: $A_{t}=0.05+0.95A_{t-1}+u_{t}$ Random Walk with Drift: $R_{t}=0.05+1R_{t-1}+u_{t}$ Explosive Series: $E_{t}=0.05+1.05E_{t-1}+u_{t}$ wh...
Why is a deterministic trend process not stationary? I think I nice way to get the intuition is to simulate 3 series for $t=0,...,500$ and plot them: Autoregressive Stationary Series: $A_{t}=0.05+0.95A_{t-1}+u_{t}$ Random Walk with Drift: $R_{t}=0.05+1
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Why is a deterministic trend process not stationary?
You answer your question yourself: Because stationarity implies both a constant variance, and a constant mean. If either term is dependent on time, the process is not stationary. In your first example, the mean is dependent on time, and in the second, variance is.
Why is a deterministic trend process not stationary?
You answer your question yourself: Because stationarity implies both a constant variance, and a constant mean. If either term is dependent on time, the process is not stationary. In your first example
Why is a deterministic trend process not stationary? You answer your question yourself: Because stationarity implies both a constant variance, and a constant mean. If either term is dependent on time, the process is not stationary. In your first example, the mean is dependent on time, and in the second, variance is.
Why is a deterministic trend process not stationary? You answer your question yourself: Because stationarity implies both a constant variance, and a constant mean. If either term is dependent on time, the process is not stationary. In your first example