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Example 35
Label Switching
If you attempt to replicate the analysis in this example, it is possible that you will get
the results that are reported here but with the group names permuted. The results
reported here for Group number 1 might correspond to the results you get for Group
number 2 or Group number 3. This is sometimes called label switching (Chung,
Loken, and Schafer, 2004). Label switching is not really a problem unless it occurs
during the course of a single analysis. Unfortunately, label switching can in fact occur
in the middle of an analysis. When label switching occurs, it is usually revealed by
trace plots for individual parameters. To display a trace plot during Bayesian
estimation:
E Right-click a parameter in the Bayesian SEM window and choose Show Posterior from
the pop-up menu.
E In the Posterior window, select Trace.
Label switching did not occur in the analysis of the present example. The following
figure, from another analysis, shows a trace plot that is typical of label switching. This
trace plot came from an analysis of data with two clusters of cases. In one cluster, the
mean of a variable called X was about 4. In the other cluster, the mean of the X variable
was about 17. The trace plot shows that, in the group called Group number 1, the
sampled values of the mean of X stayed close to 4 most of the time until about the
5,000-th iteration of the MCMC algorithm. At about the 5,000-th iteration, sampled
values started fluctuating around 17. This abrupt shift in the trace plot is evidence that
the group labels (Group number 1 and Group number 2) were switched at about the
5,000-th iteration. The trace plot shows that this label switching occurred several times
during the first 20,000 iterations of the MCMC algorithm.