Hi there,
Maybe people who know both R and econometrics will be able to answer my questions. I want to run panel regressions in R with fixed-effect. I know two ways to do it. First, I can include factor(grouping_variable) in my regression equation. Second, I plan to subtract group mean from my variables and run OLS panel regression with function lm(). I plan to do it with the second way because the number of groups is large, which incur computational problems inverting large model-matrix. I am interested in the R-squared and adjusted R-squared out of these regressions. Do I need to adjust my R-squared after I run OLS regressions with demeaned variables? Are there any functions that specifically deal with fixed-effects? Thanks. Best, Jia ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. |
There is the plm package for linear panel models. Further, since estimation of fixed effects models rests on the within-subject or -object variance, the R-squared of interest is typically the within R-squared, not the overall or between R-squared. Read up about it before you use it though.
Daniel |
In reply to this post by chen jia-3
On 5/11/10, chen jia <[hidden email]> wrote:
> Are there any functions that specifically deal with fixed-effects? > Other than plm and its vignette, you may want to check this document [1]. Liviu [1] http://cran.r-project.org/doc/contrib/Farnsworth-EconometricsInR.pdf ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. |
In reply to this post by Daniel Malter
Dear Daniel
On 5/11/10, Daniel Malter <[hidden email]> wrote: > R-squared of interest is typically the within R-squared, not the overall or > Could you point to an example on how to compute the within R-squared in R, either via lm() or plm()? Thank you Liviu ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. |
In reply to this post by Liviu Andronic
Thanks. I have the PDF document that you suggest. It is very brief on
fixed-effect in panel regressions. I will look into plm package. Best, Jia On Tue, May 11, 2010 at 8:19 AM, Liviu Andronic <[hidden email]> wrote: > On 5/11/10, chen jia <[hidden email]> wrote: >> Are there any functions that specifically deal with fixed-effects? >> > Other than plm and its vignette, you may want to check this document [1]. > Liviu > > [1] http://cran.r-project.org/doc/contrib/Farnsworth-EconometricsInR.pdf > -- Ohio State University - Finance 248 Fisher Hall 2100 Neil Ave. Columbus, Ohio 43210 Telephone: 614-292-2830 http://www.fisher.osu.edu/~chen_1002/ ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. |
In reply to this post by Liviu Andronic
if the plm function only puts out one r-squared, it should be the within r-squared, but I could be wrong. Stata, for example, gives you a within, a between, and an overall r-squared. Here is what they do.
set.seed(1) x=rnorm(100) fe=rep(rnorm(10),each=10) id=rep(1:10,each=10) ti=rep(1:10,10) e=rnorm(100) y=x+fe+e data=data.frame(y,x,id,ti) library(plm) reg=plm(y~x,model="within",index=c("id","ti"),data=data) summary(reg) cat("R-squared: ", 1-83.908/178.5) #Let's compute the squared residuals of this regression SSR=sum(residuals(reg)^2) #let's compute the total squares of the ys SS0=sum((y-mean(y))^2) SS0 #Note that this is not the TSS given by plm #Now, let's demean y and x for each individual separately y.dem=y-tapply(y,id,mean)[id] x.dem=x-tapply(x,id,mean)[id] #and regress them #note that we do not estimate the intercept because we have demeaned the data reg.fe=lm(y.dem~-1+x.dem) summary(reg.fe) #The coefficient is correct, i.e., the same as in plm #Note that the standard error is wrong, however. We would need to account for #that we are losing degrees of freedom by taking out the fixed effects. #now let's look at the sum of squares after demeaning y SSR.y.dem=sum((y.dem-mean(y.dem))^2) SSR.y.dem #Note, this is the Total sum of squares given by plm #Now, we know that the total sum of squares #not accounting for fixed effects is # TSS=SS0=331.7986 #However, we know that after taking out the fixed effects (demeaning y) # the total sum of squares is # SSR.y.dem=178.5050 #The within R-squared is then the variance explained by x AFTER having taken out the fixed effects # So the R-squared computable from the plm output is in fact the within R-squared cat("Within R-squared: ", 1-SSR/SSR.y.dem) #which is identical to the r-squared in our hand-computed FE regression summary(reg.fe)$r.squared #The two other R-squareds Stata would give you are: #The overall r-squared #which is the r-squared of a pooled OLS of y on x WITHOUT accounting for the fixed effects #Pooled OLS reg1=lm(y~x) summary(reg1) #This is what Stata shows as overall R-squared summary(reg1)$r.squared #The second R-squared Stata shows is the between R-squared # which is the R-squared of regressing the mean of the individual y(i) # on the mean(s) of the individual X(i) #Get the means of y and x for each individual y.means=tapply(y,id,mean)[id] x.means=tapply(x,id,mean)[id] #Regress them on each other reg2=lm(y.means~x.means) #This is what Stata shows as between R-squared summary(reg2)$r.squared So you see that the R-squared computable from the plm output is indeed the within R-squared. For comparison, look at the Stata output: Fixed-effects (within) regression Number of obs = 100 Group variable: id Number of groups = 10 R-sq: within = 0.5299 Obs per group: min = 10 between = 0.1744 avg = 10.0 overall = 0.3367 max = 10 F(1,89) = 100.34 corr(u_i, Xb) = 0.0547 Prob > F = 0.0000 ------------------------------------------------------------------------------ y | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- x | 1.111187 .1109319 10.02 0.000 .8907682 1.331607 _cons | .3155321 .0978457 3.22 0.002 .1211147 .5099495 -------------+---------------------------------------------------------------- sigma_u | 1.2318621 sigma_e | .97097297 rho | .61679513 (fraction of variance due to u_i) ------------------------------------------------------------------------------ F test that all u_i=0: F(9, 89) = 16.05 Prob > F = 0.0000 HTH, Daniel |
In reply to this post by chen jia-3
Dear Liviu,
we're still working on measures of fit for panels. If I get you right, what you mean is the R^2 of the demeaned, or "within", regression. A quick and dirty function to do this is: pmodel.response<-plm:::pmodel.response.plm # needs this to make the method accessible r2<-function(x, adj=TRUE) { ## fetch response and residuals y <- pmodel.response(x, model="within") myres <- resid(x) n <- length(myres) if(adj) { adjssr <- x$df.residual adjtss <- n-1 } else { adjssr <- 1 adjtss <- 1 } ssr <- sum(myres^2)/adjssr tss <- sum(y^2)/adjtss return(1-ssr/tss) } and then > r2(yourmodel) Hope this helps Giovanni ------------------------------ Message: 13 Date: Tue, 11 May 2010 13:21:02 +0100 From: Liviu Andronic <[hidden email]> To: Daniel Malter <[hidden email]> Cc: [hidden email] Subject: Re: [R] Regressions with fixed-effect in R Message-ID: <[hidden email]> Content-Type: text/plain; charset=UTF-8 Dear Daniel On 5/11/10, Daniel Malter <[hidden email]> wrote: > R-squared of interest is typically the within R-squared, not the overall or > Could you point to an example on how to compute the within R-squared in R, either via lm() or plm()? Thank you Liviu -------------------------------- Giovanni Millo Research Dept., Assicurazioni Generali SpA Via Machiavelli 4, 34132 Trieste (Italy) tel. +39 040 671184 fax +39 040 671160 ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. |
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