I would like to get the R-squared within for a fixed effect regression with multiple fixed effects (let's say Country, Year, Trimester).
The least squared dummy variable (LSDV) model (lm in R/ reg in Stata) would only provide the overall R-squared.
The same is true if one uses areg (Stata).
Code/packages suggestions for R or Stata are both welcome.
R-squared within for a regression with multiple fixed effects
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1 Answers
Consider this dummy data but this time we know exactly the coefficient we want to estimate.
library(plm)
library(xtable)
library(texreg)
library(data.table)
set.seed(100)
Let's first generate some data with time and individual fixed effect
dt <- data.table(epsilon=rnorm(100),ind=rep(1:5,5),time=rep(1:5,each=5),x=rnorm(100,0,2))
dt[,mu:=6*mean(x)*rnorm(20),ind]
dt[,`:=`(delta=10*mean(x)+rnorm(20)),time]
dt[,y:=5*x+mu+delta+epsilon]
> ## head(dt)
## epsilon ind time x mu delta y x..bari. x..bar.t
## 1: -0.247885286 1 1 3.1530482 -34.563268 37.74058 18.69467015 3.686294 3.854510
## 2: 1.234916664 2 1 4.2520514 -30.682143 39.75175 31.56477572 3.508577 3.854510
## 3: 0.117692498 3 1 2.2582500 44.240719 37.24573 92.89539109 3.936578 3.854510
## 4: -0.002265777 4 1 1.9168626 -48.510759 38.83342 -0.09529645 3.455571 3.854510
## 5: -1.424864120 5 1 1.7842555 -11.278647 38.77298 34.99074471 4.282104 3.854510
## 6: -1.441965687 1 2 0.5658582 -2.075256 38.41338 37.72545392 3.686294 3.737549
estimate model pooled ols
pooled <- lm(y~x,data=dt)
estimate model individual effects
individual..effect <- lm(y~x+as.factor(ind),data=dt)
estimate model time and individual effects
individual..time..effect <- lm(y~x+as.factor(ind)+as.factor(time),data=dt)
create variable mean over time and mean over individuals
dt[,x..bari.:=mean(x),ind]
dt[,x..bar.t:=mean(x),time]
Estimate the within estimator
within..estimator <- lm(y~I(x-x..bari.-x..bar.t),data=dt)
Wrapping everything together
screenreg(list(pooled,individual..effect,individual..time..effect
,within..estimator))
## ==========================================================================
## Model 1 Model 2 Model 3 Model 4
## --------------------------------------------------------------------------
## (Intercept) 0.50 1.29 4.22 *** 0.73
## (0.33) (0.77) (0.80) (0.44)
## x 5.14 *** 5.18 *** 4.99 ***
## (0.21) (0.22) (0.18)
## as.factor(ind)2 -1.23 -1.08
## (1.09) (0.86)
## as.factor(ind)3 -0.97 -0.88
## (1.08) (0.85)
## as.factor(ind)4 -0.95 -0.82
## (1.08) (0.86)
## as.factor(ind)5 -0.80 -0.59
## (1.10) (0.87)
## as.factor(time)2 -3.88 ***
## (0.85)
## as.factor(time)3 -3.99 ***
## (0.85)
## as.factor(time)4 -1.39
## (0.85)
## as.factor(time)5 -5.94 ***
## (0.85)
## I(x - x..bari. - x..bar.t) 4.99 ***
## (0.29)
## --------------------------------------------------------------------------
## R^2 0.86 0.86 0.92 0.75
## Adj. R^2 0.86 0.85 0.91 0.75
## Num. obs. 100 100 100 100
## RMSE 3.34 3.38 2.68 4.44
## ==========================================================================
## *** p < 0.001, ** p < 0.01, * p < 0.05
I will let you explore with plm package if you wish to do so.
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