In a mixture model the ith ETA has a different distribution for each subpopulation. Accordingly, different instances of the above output will appear, one for each of the different subpopulations. Using a standard Bayesian-type computation, each individual is classified into one of the subpopulations, and the conditional estimate of the ith eta under the model for this subpopulation is used in the sample average for that subpopulation. If under the mth submodel, the ith eta does not influence the data from any individual, but it does influence the data from some individual under some other submodel, then the sample average for the ith eta for the mth submodel will be 0. If the ith eta does not influence the data from any individual under any model, then the sample average for the ith eta for the mth submodel will usually be 0, but it will not be if

1. the ith eta is correlated with an eta that influences some individual's data under the mth submodel, and
2. that individual is classified to be in the mth subpopulation.

The population average of the conditional estimates is only approximately zero because a conditional estimate is a (Bayesian) posterior mode, and not a posterior expectation. However with a mixture model, with the estimate for a given individual, the posterior distribution is that for the subpopulation into which the individual is classified, and due to possible missclassification the expectation of the estimate may be even "further from" zero than with a nonmixture model. For this reason too, the centered FOCE method may not work well with a mixture model.

With a mixture model, or with a nonmixture model, one may implement a second Estimation Step (in a subsequent problem), and then a second ETABAR estimate (EB2) can be obtained, with which the first ETABAR estimate (EB1) can be compared. If the data-analytic model is wellspecified, the two estimates should represent nearly the same quantity. Using an option on the $ESTIMATION record, the second P-value assesses the magnitude of the difference between EB1 and EB2, and a P-value under 0.05 would suggest that the data-analytic model is not well-specifed. To obtain EB2, a data set is simulated under the fitted model, and EB2 is obtained using this data set. Both EB1 and EB2 are (univariate) measures of central tendency of the distribution of interindividual "residuals", i.e. the distribution of the conditional estimates of the ETAs. In both cases the residuals are defined in terms of the data-analytic model. But for EB1, the distribution is governed by the true (unknown) model, and for EB2, the distribution is governed by the fitted model. If the two models are "close", EB1 and EB2 will be close. The conditional estimates of the ETAs from the simulated data should be based on the population parameter estimates from these data. It may cost considerable CPU time to obtain this second set of parameter estimates, and so it may not always be feasi- ble to compute EB2.

One proceeds by constructing a problem that

1. includes the same $INPUT record as was used with a previous problem wherein EB1 was obtained.
2. includes an $MSFI record specifying a model specification file from that previous problem, so that in particular, EB1 is available.
3. includes a $SIMULATION TRUE=FINAL, so that a data set will be simulated using the final parameter estimate from that previous problem.
4. includes a $ESTIMATION ETABARCHECK option (and either the option METHOD=COND or METHOD=HYBRID).

This will result in a simulated data set and calculted EB2, additionally

• with ETABARCHECK, the P-value for EB2-EB1;

• with NOETABARCHECK,

  • for a nonmixture model, the P-value for EB2, and EB1 is ignored;
  • for a mixture model, no P-value will be output (only the standard error for EB2 will be output).