How can i manual calculating R-squared for random effects?

[Oksana Uhr]

Hallo,

i´m sorry for this simple question in a forum like this. But I don’t know what to do next.
I run random effects regression and obtain the overall R-squared. Then I would like to calculate the r-squared manual.

I know the formula for r-squared and this work for usual regress command.

reg y x
predict y_hat

Then i obtain the standard deviation for y and y_hat.

r-squared = SSE / SST = (standard deviation_ y_hat)^2/(standard deviation_y)^2

I get exactly reported r-squared.

But this approach doesn’t work after xtreg / xtregar command. The manual calculated r-squared is always approx.0,01 or 0,02 smaller or higher like reported r2. I know the formula for overall r-squared is corr(xitβ^,yit)2 . But I think xitβ = y_it_hat and I can use the usual r-squared formula r2= SSE/ SST.

I am very grateful for your help.

[Aspen Chen]

I am afraid this is pretty confusing. Which of the reported R² are you referring to? Both -xtreg- and -xtregar- produce three R² measures--within, between, and overall. Also none is likely the same as from the OLS because these regression methods account for the effects of panels/grouping. Part of the variation are modeled at the panel level (thus the subscript t).

[Carlo Lazzaro]

Oksana:
as Aspen notices, your question is quite vague.
I would advice you to take a look at -help xtreg - and related entry in Stata 13.1 .pdf manual and/or any advanced econometric textbook covering panel data analysis. For Stata users, the following one is very interesting and widely covers panel data analysis: http://www.stata.com/bookstore/micro...ata/index.html.

Kind regards,
Carlo

[Oksana Uhr]

i´m sorry for my vague question.

i try manuall to calculate overall R^2.

- help xtreg - report only the formula corr(xitβ^,yit)2 for overall R^2. i would like to understand how stata calculate the value of OVERALL R^2.

i found a solution of my question. insteatd of r-squared = SSE / SST = (standard deviation_ y_hat)^2/(standard deviation_y)^2 i use corr(y_hat_it, y_it)^2.
to i get the reported overall R^2 value.

[Gosia Aslan]

suppose you have the following regression:

xtreg y x1 x2 , re
predict yh , xb
corr yh y
* Overall R2
scalar r2 = r(rho)^2
di r2

[Aspen Chen]

Oksana, glad you figured it out.
I need to correct myself--the "overall" R² from random effect models in -xtreg- should be the same as from the OLS estimates. For example,

webuse nlswork,clear
reg ln_wage grade
xtset idcode
xtreg ln_wage grade,re

The manual does offer information to the original question. See page 368 (for Stata 13). I typed "yhat" to represent the notation with a hat on top.

...the R-squares reported do not have all the properties of the OLS R². The ordinary properties of R² include being equal to the squared correlation between yhat and y and being equal to the fraction of the variation in y explained by yhat, formally defined as Var(yhat)/Var(y). The identity of the definitions is from a special property of the OLS estimates...

Then the next paragraph goes on to explain that the overall R² from -xtreg- can be understood as the product of a weighted prediction.

Interestingly, the respective predicted values from the -reg- and -xtreg- estimates have a perfect correlation of one. I was not aware of this property.