Joint test in PROC FMM?

[jl4443]

Since PROC FMM does not have an ESTIMATE or CONTRAST statement, the %NLEST macro can be used for hypothesis testing. However, the %NLEST macro does not support joint testing (according to this SAS note: https://support.sas.com/kb/24/094.html). 

Is there a procedure or alternative SAS macro that facilitates a joint hypothesis test of the PROBMODEL parameters in PROC FMM?

[SAS_Rob]

The problem is the FMM does not report a covariance matrix for the estimates of the PROBMODEL.  This would make performing a joint test impossible.

[jl4443]

Thank you for taking a look at this question. When I run PROC FMM with the COV option on the PROC FMM statement and use ODS OUTPUT COV = COV_OUTPUT,

The resulting COV_OUTPUT dataset includes a variable 'ModelNo' with a value of 1 and corresponding variable 'Label' = "Weibull" (since I have distribution=Weibull for my FMM outcome model) as well as data corresponding to a 'ModelNo' = 2 and 'Label' = "Probability Model". I interpreted this as the covariance matrix from the component membership model from the PROBMODEL statement, is that not the correct interpretation of that output?

[SAS_Rob]

No, you are interpreting it correctly.  I was wrong about what was contained in that data set.

In any regard, hypothesis testing in finite mixture models is not very well defined because it is difficult if not impossible to derive the asymptotic distribution for the mixture likelihood.  There is a paper that discusses the problem and makes a few suggestions related to goodness of fit tests that might work.  Anything that they propose would not be available in SAS, but you might be able to program it yourself.

Hypothesis testing for finite mixture models - ScienceDirect