st: how to compute pseudo-r2 at cluster level using xtreg?

[Clara Barata <maria_barata@mail.harvard.edu>]

Hi!
I was trying to figure out how to recreate the pseudo r2 values that
are outputed with xtreg with random effects . I basically computed
sigma_e squared and estimated the proportional decline in sigma_e
squared comparing each model with the unconditional model to get r2_w
(individual level) . I did the same for sigma_u to get r2_b (cluster
level). However, this formula only seems to work for r2_w but not for
the cluster level r2.

                  M1        M2           M3
N	          933	       933	      933
Sigma_u	1.242     1.015	      0.696
Sigma_e	5.048     3.335	      3.339
Rho	        0.057     0.085	      0.042
R2-b	        0.000     0.466	      0.725
R2_w	0.000     0.564	      0.564
Chi2		            1196.634    1224.520
df	          0	      2         	11

My computations indicate that r2_b for model 2 should be 0.33 and
should be 0.68 for model 3:
	          M1	         M2	         M3	     Sigma2 M1	Sigma2 M2  Sigma2
M3	Pseudo-R2, M1 M2	Pseudo-R2, M1 M3
Sigma_u   1.242 	1.015	0.696    1.542564	1.030225	
0.484416	0.33213468	          0.685967
Sigma_2	5.048	3.335	3.339   25.482304	11.122225	
11.148921	0.563531422	          0.562483793


Alternatively I also used xtmixed with random effects for the same
level of clustering and I get different variance estimates and a
different pseudo r2 at the cluster level from what I get using my
computations and xtreg.

                  M1         M2           M3
N	         933	        933	        933
var_u1	1.578	0.671	0.203
var_e 	25.467	11.144	11.127
rho1  	0.058	0.057	0.018
-2LL	  -2849.348	-2463.522	-2454.328
df	         0.0    	2.0	        11.0
AIC	  5704.696	   4937.044	4936.656
BIC	  5719.212	   4961.236	5004.393
Pseudo-R^2, L1		0.57	          0.87

I appreciate any comments or suggestions,
Clara

ps- code for xtreg and xtmixed is below.

XTREG CODE:
xtset  idcoleg1
xtreg w2p1, re
eststo model1
xtreg w2p1 interv1 w1p1, re
eststo model2
xtreg w2p1 interv1 w1p1 masculino rdmage  mteacher_age mteachingless5
mteaching5to14 mPrivado mpostgrad com2 com3, re
eststo model3
esttab using withinschool1.rtf, cells(b(fmt(3) star) se(par fmt(3)))
noconstant ///
stats(N  sigma_u sigma_e rho r2_b r2_w chi2 df_m pr2, ///
fmt(0 3 3 3 3 3 3 0) label(N  SD-Cluster SD-Individual ICC R2-Between
R2-Within Chi-Squared df pr2)) ///
star(~ 0.10 * 0.05 ** 0.01 *** 0.001) replace


XTMIXED code:
xtmixed w2p1 || idcoleg1: , cov(un) mle var
xtmrho
eststo model1
xtmixed w2p1 interv1 w1p1  || idcoleg1: , cov(un) mle var
xtmrho
eststo model2
xtmixed w2p1 interv1 w1p1 masculino rdmage  mteacher_age
mteachingless5 mteaching5to14 mPrivado mpostgrad com2 com3|| idcoleg1:
, cov(un) mle var
xtmrho
eststo model3
esttab using WJ__impacts.rtf, cells(b(fmt(3) star) se(par fmt(3)) ci)
noconstant ///
stats(N  var_u1 var_u2 var_e  rho1 rho2 ll df_m aic bic pr2, ///
fmt(0 3 3 3 3 3 3 1 3 3 3) label(N  Var-L1 Var-L2 Var-R ICC-L1 ICC-L2
-2LL df AIC BIC pr2)) ///
star(~ 0.10 * 0.05 ** 0.01 *** 0.001) replace
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