Dear all,
I am investigating the effects of several time-variant independent variables (X1, X2, X3) on a continuous outcome variable Y1 and I am further planing on implementing a time-constant variable Z1 which is why I am interested in using the Correlated RE/Mundlak approach, alternatively a model often referred to as Hybrid model. While both add the means of time-variing variables as explanatory variables, the former one uses the original time-variing variables and the latter one implements the demeaned variables. Independent of the specific model I am insecure about how to interpret the regression coefficients of the mean variables and even whether they can be interpreted at all.
(I am aware that there has been a similar topic on statalist (https://www.statalist.org/forums/for...ype-regression). I read the recommended passage and it helped me a lot understanding the general idea of both models, but I still don't know about the particular interpretation of coefficients.)
I have calculated both models using the -xthybrid- command.
CRE/Mundlak:
Hybrid:
So both models calculate the same within estimators for the time variing variables which are at the same time equivalent to the ones received by using FE estimation. I am also aware that the difference between the between effect B__X1 (mean estimator X1) and the within effect W__X1 in the Hybrid model is equal to the value of D__X1 in the CRE model.
But how exactly do I have to interpret the coefficients of the mean estimators in the respective models? What is their meaning relative to the within estimators and to what extent does (in)significancy of the estimators is important? I know that many authors do not interpret these coefficients at all, but it would be really helpful for my understanding of both models if you could help me with this.
Best regards
I am investigating the effects of several time-variant independent variables (X1, X2, X3) on a continuous outcome variable Y1 and I am further planing on implementing a time-constant variable Z1 which is why I am interested in using the Correlated RE/Mundlak approach, alternatively a model often referred to as Hybrid model. While both add the means of time-variing variables as explanatory variables, the former one uses the original time-variing variables and the latter one implements the demeaned variables. Independent of the specific model I am insecure about how to interpret the regression coefficients of the mean variables and even whether they can be interpreted at all.
(I am aware that there has been a similar topic on statalist (https://www.statalist.org/forums/for...ype-regression). I read the recommended passage and it helped me a lot understanding the general idea of both models, but I still don't know about the particular interpretation of coefficients.)
I have calculated both models using the -xthybrid- command.
CRE/Mundlak:
Code:
xthybrid Y1 X1 X2 X3 Z1, cre clusterid(ID) vce(cluster ID) se t p star full
Code:
Mixed-effects GLM Number of obs = 6,285
Family: Gaussian
Link: identity
Group variable: ID Number of groups = 419
Obs per group:
min = 15
avg = 15.0
max = 15
Integration method: mvaghermite Integration pts. = 7
Wald chi2(7) = 715.24
Log pseudolikelihood = -29039.214 Prob > chi2 = 0.0000
(Std. Err. adjusted for 419 clusters in ID)
------------------------------------------------------------------------------
| Robust
Y1 | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
R__Z1 | 67.84879 17.86932 3.80 0.000 32.82556 102.872
W__X1 | 98.76844 6.410146 15.41 0.000 86.20479 111.3321
W__X2 | 32.93256 4.261134 7.73 0.000 24.58089 41.28423
W__X3 | 34.70885 4.453705 7.79 0.000 25.97975 43.43795
D__X1 | -6.988898 14.21577 -0.49 0.623 -34.85129 20.87349
D__X2 | -37.11881 11.43237 -3.25 0.001 -59.52585 -14.71178
D__X3 | -36.48485 5.569395 -6.55 0.000 -47.40066 -25.56903
_cons | 65.07727 6.298562 10.33 0.000 52.73231 77.42222
-------------+----------------------------------------------------------------
ID |
var(_cons)| 361.4897 44.84565 283.4638 460.9928
-------------+----------------------------------------------------------------
var(e.Y1)| 512.6834 51.21356 421.5218 623.5603
------------------------------------------------------------------------------
Code:
xthybrid Y1 X1 X2 X3 Z1, clusterid(ID) vce(cluster ID) se t p star full
Code:
Mixed-effects GLM Number of obs = 6,285
Family: Gaussian
Link: identity
Group variable: ID Number of groups = 419
Obs per group:
min = 15
avg = 15.0
max = 15
Integration method: mvaghermite Integration pts. = 7
Wald chi2(7) = 715.24
Log pseudolikelihood = -29039.214 Prob > chi2 = 0.0000
(Std. Err. adjusted for 419 clusters in ID)
------------------------------------------------------------------------------
| Robust
Y1 | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
R__Z1 | 67.84879 17.86932 3.80 0.000 32.82556 102.872
W__X1 | 98.76844 6.410146 15.41 0.000 86.20479 111.3321
W__X2 | 32.93256 4.261134 7.73 0.000 24.58089 41.28423
W__X3 | 34.70885 4.453705 7.79 0.000 25.97975 43.43795
B__X1 | 91.77954 13.88398 6.61 0.000 64.56743 118.9917
B__X2 | -4.18625 11.12834 -0.38 0.707 -25.99739 17.62489
B__X3 | -1.776001 4.523073 -0.39 0.695 -10.64106 7.089059
_cons | 65.07727 6.298562 10.33 0.000 52.73231 77.42222
-------------+----------------------------------------------------------------
ID |
var(_cons)| 361.4897 44.84565 283.4638 460.9928
-------------+----------------------------------------------------------------
var(e.Y1)| 512.6834 51.21356 421.5218 623.5603
------------------------------------------------------------------------------
But how exactly do I have to interpret the coefficients of the mean estimators in the respective models? What is their meaning relative to the within estimators and to what extent does (in)significancy of the estimators is important? I know that many authors do not interpret these coefficients at all, but it would be really helpful for my understanding of both models if you could help me with this.
Best regards
