Re: st: question with MLE and complex model

[Partha Deb <partha.deb@hunter.cuny.edu>]

Jonathan,

It appears that the model you are trying to estimate (in principle) is a 
finite mixture of 3 normal densities - your code is not quite that, however. 
Unless you are sure yours is the model you want, I suggest you estimate a 
standard finite mixture model for the problem you describe.  You can code that 
up yourself or use -fmm- .  -findit fmm- will get you to the link to install it.

Best.

Partha


Jonathan Hanson wrote:

> 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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--
Partha Deb
Department of Economics
Hunter College
ph:  (212) 772-5435
fax: (212) 772-5398
http://urban.hunter.cuny.edu/~deb/

Emancipate yourselves from mental slavery
None but ourselves can free our minds.
	- Bob Marley

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