1. Re-estimate the 3-class model estimated earlier in Tutorial #1. Now, change the technical parameter setting for the ‘Bayes Constants for both Categorical Variables and as well as for Latent Variables’ from ‘1’ to ‘0’ and estimate new model. (You will find the ‘Bayes Constants’ settings labeled in the upper right portion of the Technical Tab.)
Notice that the L-squared statistic is now slightly better than the original model (L² = 21.8920 vs. the original value of 22.0872). An Estimation Warning message is produced along with an Iteration Output file. At the bottom of the Iteration Output is a message saying that 2 boundary solutions were encountered. Go to the Profile output. Where are the 2 boundary solutions that were encountered? How do these estimates compare to the corresponding estimates obtained in the original model?
Next, change the Bayes constant from ‘0’ to ‘2’ and estimate the model. Compare the profile output in these two models. Notice that as the Bayes constant is increased, the extreme parameter estimates become less extreme. The greater the value of the Bayes constant, the greater the weight that is placed on a conservative null model (‘prior distribution’) which specifies that all variables are mutually independent. Use of the default Bayes constant of 1 provides a fairly small weight for this ‘prior’ distribution.
2. Return to the 3-class model estimated in Exercise B1 above when the Bayes constant was set to 0. Open the Variables Tab, remove the variable COOPERATE from the model and estimate it. Again, you will get an Estimation Warning Message. Estimate the model once again. Do you get the same L-squared value? If not, re-estimate it again until you get the same L-squared value at least twice. Examine the ‘Parameters’ Output for models having the same L-square value. Notice that some of the parameter estimates are different! This is an indication that these parameter estimates are not identified.
For this exercise, you may obtain an L-squared value of .0705 (which is actually an unidentified ‘local’ solution), or .0220 which is the unidentified ‘global solution’ (At least I believe that it is the global solution. When local solutions exist, it is never 100% certain that the solution you obtain is a global solution.) You may also encounter other L-squared values associated with other local solutions when estimating this model. See the section on ‘Local solutions’ above.)
Now, repeat the exercise after restoring the Bayes Constant to its default value of ‘1’. Notice that for models having the same L-squared value, the parameters estimates no longer are different. That is because the information provided by non-zero Bayes constant is sufficient to uniquely identify the model.
How many degrees of freedom are associated with this model? When Bayes Constants = 0, negative degrees of freedom indicate that the model is not identified.
3. If you estimate and re-estimate a model several times and always get the same L- squared value and always the same parameter estimates, and the output is very interpretable from a substantive perspective, can you be comfortable with your interpretation? What if you notice that the degrees of freedom are negative?