st: Class membership probabiliy and mlogit

[Jonathan Sterne <Jonathan.Sterne@bristol.ac.uk>]

Dear statalisters

We have been fitting latent class models, the output of which is a set of 
posterior probabilities that each subject falls into one of six latent 
classes. We now want to use multinomial logistic regression (mlogit) to 
examine predictors of class membership.

One option is to assign each subject to her/his modal class (the class for 
which there is the highest probability of membership. However loses 
information (some subjects will have a high probability that they belong to 
a particular class, others will have relatively similar probabilities of 
membership of two or more classes.

As an alternative, we wish to fit multinomial logistic regression models 
using the class variable as the multinomial outcome and weighting the 
analysis using class membership probabilities.

We have stacked the data so we have multiple rows for each subject in the 
following form

	ID     Exposure     Class     Prob
       1      1            1         0.1
       1      1            2         0.1
       1      1            3         0.4
       1      1            4         0.3
       1      1            5         0.05
       1      1            6         0.05

'Prob' sums to one within subject and class repeats 1,2,3,4,5,6 through the 
whole dataset.

We weight using pweights [pw = prob]

Consequently, our model of choice has been:

xi: mlogit class xvars [pw = prob], rrr
(identical to xi: mlogit class xvars [iw = prob], rrr robust)

and we have also experimented with

xi: mlogit class xvars [pw = prob], rrr robust cluster(id)

which gives lower SE's, and

xi: mlogit class exposure [iweight = prob], rrr

which gives *higher* SE's than the pweight model without 'robust'

We would be grateful for advice on the following questions:

1. Is it appropriate to weight according to class membership probability 
(we are pretty convinced that it is)?

2. Does anyone have a recommendation as to which of the above model 
formulations gives theoretically appropriate standard errors?

Many thanks

Jonathan Sterne




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