6.4. A Compromise between Fixed Effects and Random Effects

In the previous section, we obtained a fixed effects model by starting with a random effects model and then allowing for all possible correlations between the random effect α and the time-varying explanatory variables. But perhaps all those correlations aren't really needed. Output 6.4 shows estimated correlations and covariances between α and the time-varying variables produced by PROC CALIS. It appears that the correlations with the SELF variables are very small and not statistically significant, whereas the correlations with the POV variables are somewhat larger, and two of the three are statistically significant. This suggests that we could set the SELF correlations equal to 0 without appreciably worsening the fit of the model.

This is easily accomplished by modifying the COV statement to eliminate the SELF variables, i.e.,

COV
 falpha*pov90 pov92 pov94 =c:;

This produces the results shown in Output 6.5. The coefficient and t-statistic for POV is about the same as for the fixed effects model in Output 6.3. On the other hand, the coefficient and t-statistic for SELF is somewhat larger than in the pure fixed effects model. Taking the difference in the chi-squares for the two models, we get a chi-square of 3.00 with 3 degrees of freedom. This is definitely not statistically significant, indicating that we cannot reject the simpler model (which set three correlations equal to 0) in favor of the more complicated model.

Table 6.5. Output 6.5 Compromise Model Estimated with PROC CALIS