st: question with MLE and complex model

[Jonathan Hanson <johanson@maxwell.syr.edu>]

Greetings,

I am working on an MLE procedure to use in situations where there may  
be distinct, or at least mostly distinct, causal processes at work for  
different parts of the sample.  For example, suppose there are three  
different states of the world, and the coefficients on key explanatory  
variables vary across these states.  Additionally, suppose that there  
is a set of variables that determines (probabilistically) the extent  
to which to a particular case falls into each state.

In other words, I have three linear models: mod1, mod2, and mod3.   
Also, I have a weighting function, similar to that used in multinomial  
logit, that estimates a set of weights that sum to 1:  p1 + p2 + p3.

I am fairly new to ML programming, so I started with the ML version of  
a standard linear regression (with adjustments to s_e suggested by  
Gould and Sribney) and incorporated the three linear models with their  
corresponding weighting functions.  The trouble is, when I try to  
estimate the model, Stata goes through thousands of iterations, nearly  
all of which report "not concave".  Convergence is achieved only  
rarely, and it depends very much upon specification.

program define stage3ml
 args lnf mod1 st1 mod2 st2 mod3 ctrls s_e
 tempvar den p1 p2 p3
 quietly gen double `den' = 1 + exp(`st1') + exp(`st2')
 quietly gen double `p1' = exp(`st1')/`den'
 quietly gen double `p2' = exp(`st2')/`den'
 quietly gen double `p3' = 1/`den'
 quietly replace `lnf'=ln(normalden(($ML_y1 - `p1'*`mod1' -  
`p2'*`mod2' - `p3'*`mod3' - `ctrls')/exp(`s_e'))) - `s_e'
end

ml model lf stage3ml (mod1: y = x1 x2 x3) (p1: z1 z2 z3) (mod2: x1 x2  
x3) (p2: z1 z2 z3) (mod3: x1 x2 x3) (ctrs: ) ()

Any advice on what steps I should next take would be greatly  
appreciated!

Many thanks,

Jonathan Hanson
Assistant Professor of Political Science
Maxwell School of Citizenship and Public Affairs
100 Eggers Hall
Syracuse University
Syracuse, NY 13244
johanson@maxwell.syr.edu




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