The iterative optimization steps for maximum likelihood estimation of mixture models might not always find estimates that achieve a global maximum or even a best local maximum in likelihood. One way to alleviate this problem is to generate multiple sets of starting values for the optimization and find the best solution over those sets. PROC FMM supports this approach by automating a two-stage method that generates multiple sets of random starting values in maximum likelihood estimation. You can use this two-stage method by specifying the RANDSTART statement.
In the first stage, the procedure uses its default starting values as the first set of starting values. If you specify starting values by using the PARAMETERS option in either the MODEL statement or the PROBMODEL statement, PROC FMM uses those values as the first set of starting values instead. Then, the procedure randomly draws multiple sets of starting values around the values of the first random set; the variability is controlled by a standard deviation parameter, which you can adjust by using the STD= option. You can use the NFIRST= option to control the number of sets that the procedure generates in the first stage. The procedure repeatedly optimizes the model, using each set of random starting values in turn to start the optimization. It uses the convergence criterion that you specify in the RANDGCONV= option to terminate each fit in the first stage.
In the second stage, PROC FMM identifies the sets that have the best log likelihood at the end of the first stage and continues the fit for each of those sets. You can use the NSECOND= option to control the number of sets to carry forward from the first stage. If not enough of the first-stage sets converge to supply the second stage, the procedure generates additional sets and optimizes by using those sets. The procedure will not generate more than the maximum number of sets that you specify in the MAXFIRST= option. At the end of the second stage, the procedure identifies the model that has the best fit, and it uses the corresponding converged estimates as the maximum likelihood estimates for the model.
The "Random Start Information" table displays the values that control the two-stage fitting process.
The "Random Start Convergence" table displays the random starting sets, the final objective function from optimization, and an indicator of convergence. This table contains identifiers for the starting sets and the stages of fitting. These identifiers are also displayed in the "Iteration History" table.
The "Parameter Mapping" table provides a mapping between the parameters in the "Random Start Convergence" table and their roles in the associated mixture component.