Random Effects   Fixed Effects Example:
Summary
Least Squares Dummy Variables Models 

Model 
Specification 
RSS 
Log Likelihood 
1 
5465 
188.3 

2 
4827 
185.2 

3 
3380 
176.3 

4 
2663 
170.3 
Ftest Between LSDV Models 


2 
3 
4 
1 
1.45 
2.67 
2.83 
2 


3.16 
3 


2.35 
Random Effects Models: Chisquare Tests 

Model 
Specification 
Estimates of Variance Components 
LM for Model j versus Model 1 
Hausman for Model j versus Model j3 
5 
.063 
1.19 

6 
4.43 
1.24 

7 
4.49 
2.91 
On the basis of the LM Test:
We prefer model 1 to model 5: The random individual effect is zero.
We prefer model 6 to model 1: The random time effect is not zero.
We prefer model 1 to model 7: We cannot reject the null hypothesis that both the random individual and time effects are zero.
The only REM preferred to OLS is model 6. OLS is better than either of the remaining two specifications.
On the basis of the Hausman Test:
We prefer model 5 to model 2: The random individual effect model is better than the individual fixed effect model.
We prefer model 6 to model 3: The random time effects model is better than fixed time effects model.
We prefer model 7 to model 4: The random effects model is better.
When given a choice, we never pick the fixed effects model.
CONCLUSION
From the three groups of tests we have the following intransitivity involving model 7:
so we'll eliminate 7 from the competition. From the different sets of tests we can establish the following ordering;
So we'll choose model 6 as the best model.
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