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Re: st: question with MLE and complex model
Jonathan,
3100 is not a particularly large sample in the context of a finite mixture
model. So, it does not surprise me entirely that your model has numerical
problems when you introduce covariates into the mixing probabilities. That
said, it's possible that the issue is somewhere else. If you send me your
dataset and code off list, I'll spend a bit of time investigating.
You ask "By the way, how does one obtain the estimated probability weight on
each component for an observation?"
For estimates of prior probabilities, after estimation -predict varname1,
eq(component1) prior- , etc. For posterior probabilities, -predict varname1,
eq(component1) posterior- , etc.
Jonathan Hanson wrote:
Partha,
On Jul 30, 2008, at 10:30 PM, Partha Deb wrote:
Jonathan,
There are a number of likely reasons why starting values are not
feasible.
1. If you have a small sample, it may be too ambitious to model the
probabilities as functions of covariates. You may simply be too close
to a boundary for some observations. What is your sample size?
My sample is about 3,100.
2. Although Stata is quite good about handling scaling issues, scaling
can matter. If your z's are scaled very differently, that could be a
source of the problem.
Thanks, they are not dramatically different, but I will try some rescaling.
What happens when you estimate 2 and 3 component mixtures without
covariates in the probabilities?
I can get results with no covariates in the probabilities when starting
with a 2 component mixture and then moving to 3 component mixture.
Usually, as soon as I add one covariate in the probabilities, Stata
cannot find initial values, whether there are 2 or three components.
By the way, how does one obtain the estimated probability weight on each
component for an observation? I've read the help file but can't figure
it out. I'd like to examine how the observations are being weighted.
Your generous help is greatly appreciated!
Jonathan
On your question about why your original effort fell short - obviously
I don't know for sure, but the likelihood you had written out was not
the likelihood for a mixture model - beyond that, I'm afraid I didn't
look particularly hard at the formulation.
Partha
Jonathan Hanson wrote:
Partha,
Thanks again for your help -- I really appreciate it. Your tip did
help me get up to a three-component model. I am not consistently
able to do so, however, especially when using variables to estimate
the component probabilities. When adding one of these variables,
even to a two-component model, Stata often reports that it cannot
find feasible values at the beginning of the estimation. Perhaps I
need to supply my own starting values?
Also, since I hope to learn how to use ml, I am still puzzling over
why my original effort is falling short. Are there some obvious
things that I should think about as I work on it?
Thanks!
Jonathan
On Jul 30, 2008, at 2:08 PM, Partha Deb wrote:
.
Correction, start here:
fmm y x1 x2 x3, components(2) mixtureof(normal) prob(z1 z2 z3)
fmm y x1 x2 x3, components(3) mixtureof(normal) prob(z1 z2 z3)
Partha Deb wrote:
Jonathan,
The easiest thing to do is try the following:
fmm y x1 x2 x3, components(2) mixtureof(normal) search(on) prob(z1
z2 z3)
fmm y x1 x2 x3, components(3) mixtureof(normal) search(on) prob(z1
z2 z3) from(?)
If a 3-component model follows a 2-component model, it gets "smart"
starting values based on the parameters in the 2-component model.
If you prefer to use -from()-, enter parameter values (separated by
spaces) in the other they would appear in the output. Obviously
this is hard to guess if you've never seen any output from -fmm- so
I recommend the "two-step" approach first.
Best.
Partha
Jonathan Hanson wrote:
Partha,
Thank you for your suggestion. I've downloaded the fmm procedure
and am experimenting with it. One question: I get a message
stating that I should provide starting values, which appears to be
done using the from() option. What is the form with which
starting values are provided?
For example, if I use:
fmm y x1 x2 x3, components(3) mixtureof(normal) search(on) prob(z1
z2 z3) from(?)
what replaces the question mark?
Many thanks!
Jonathan
On Jul 30, 2008, at 11:56 AM, Partha Deb wrote:
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
[email protected]
*
* For searches and help try:
* http://www.stata.com/help.cgi?search
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/
--
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
*
* For searches and help try:
* http://www.stata.com/help.cgi?search
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/
_______________________________________
Jonathan Hanson
Assistant Professor of Political Science
Maxwell School of Citizenship and Public Affairs
100 Eggers Hall
Syracuse University
Syracuse, NY 13244
[email protected]
*
* For searches and help try:
* http://www.stata.com/help.cgi?search
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/
--
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
*
* For searches and help try:
* http://www.stata.com/help.cgi?search
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/
_______________________________________
Jonathan Hanson
Assistant Professor of Political Science
Maxwell School of Citizenship and Public Affairs
100 Eggers Hall
Syracuse University
Syracuse, NY 13244
[email protected]
*
* For searches and help try:
* http://www.stata.com/help.cgi?search
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/
--
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
*
* For searches and help try:
* http://www.stata.com/help.cgi?search
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/
____________________________________
Jonathan Hanson
Assistant Professor of Political Science
Maxwell School of Citizenship and Public Affairs
100 Eggers Hall
Syracuse University
Syracuse, NY 13244
[email protected]
*
* For searches and help try:
* http://www.stata.com/help.cgi?search
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/
--
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
*
* For searches and help try:
* http://www.stata.com/help.cgi?search
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/