Re: st: Concavity issues using -gmm- estimating parameters from a normal distribution

[Keith Kapetan <keith.kapetan@gmail.com>]

Hi,

Thank you for the response.  I believe I understand the issue now.

Keith

On Sun, Aug 22, 2010 at 10:47 PM, Stas Kolenikov <skolenik@gmail.com> wrote:
> This is an identification issue, that is, your fault, not -gmm-'s one.
> The parameters {mean} and {SD} are not identified: if you change the
> scale of the normal variate to the standard normal, and redefine your
> thresholds {NO}, {MAYBE}, {YES} accordingly, you will get exactly the
> same observed data. As in any model with a latent index/latent
> variables, you need to set the location and scale of those latents,
> and your call to -gmm- does not specify these.
>
> On Fri, Aug 20, 2010 at 11:05 AM, Keith Kapetan <keith.kapetan@gmail.com> wrote:
>> Hi all,
>>
>> I am using stata 11.1 to estimate some parameters and the mean and
>> standard deviation of a normal distribution using the -gmm- command.
>>
>> I have data in the form of 1's and 0's with 1's occurring if it falls
>> left of a cutoff from some normal distribution.  I am trying to
>> determine the mean and standard deviation of this distribution and
>> also estimate the parameters that determine the cutoffs.
>>
>> Here is some sample code illustrating what I am trying to do:
>>
>> set obs 10000
>> gen random=20+10*rnormal()
>>
>> gen X_1_NO=0
>> gen X_2_NO=0
>> gen X_1_MAYBE=0
>> gen X_2_MAYBE=0
>> gen X_1_YES=0
>> gen X_2_YES=0
>>
>> replace X_1_NO = 1 if random<25
>> replace X_2_NO = 1 if random<35
>> replace X_1_MAYBE = 1 if random<15
>> replace X_2_MAYBE = 1 if random<20
>> replace X_1_YES = 1 if random<5
>> replace X_2_YES = 1 if random<10
>>
>> gmm (X_1_NO-normal((25-{mean})/{
>> SD}))(X_2_NO-normal((35-{mean})/{SD}))(X_1_MAYBE-normal((15-{mean})/{SD}))(X_2_MAYBE-normal((20-{mean})/{SD}))(X_1_YES-normal((5-{mean})/{SD}))(X_2_YES-normal((10-{mean})/{SD})),
>> from(mean 5 SD 5) winitial(identity) onestep
>>
>>
>> gmm (X_1_NO-normal((1*{P}-{NO}-20)/10))(X_2_NO-normal((2*{P}-{NO}-20)/10))(X_1_MAYBE-normal((1*{P}-{MAYBE}-20)/10))(X_2_MAYBE-normal((2*{P}-{MAYBE}-20)/10))(X_1_YES-normal((1*{P}-{YES}-20)/10))(X_2_YES-normal((2*{P}-{YES}-20)/10)),
>> from(NO -20 MAYBE -5 YES 0 P .5) winitial(identity) onestep
>>
>> gmm (X_1_NO-normal((1*{P}-{NO}-{mean})/{SD}))(X_2_NO-normal((2*{P}-{NO}-{mean})/{SD}))(X_1_MAYBE-normal((1*{P}-{MAYBE}-{mean})/{SD}))(X_2_MAYBE-normal((2*{P}-{MAYBE}-{mean})/{SD}))(X_1_YES-normal((1*{P}-{YES}-{mean})/{SD}))(X_2_YES-normal((2*{P}-{YES}-{mean})/{SD})),
>> from(NO -10 MAYBE -5 YES 0 P .5 mean 5 SD 5) winitial(identity)
>> onestep
>>
>>
>> The first gmm output correctly returns the mean and standard deviation
>> of 20 and 10 respectively.
>>
>> The second gmm output correctly estimates the parameters P, NO, MAYBE, and YES.
>>
>> The last gmm output is what I am trying to do, which combines the
>> first and second commands.  It does not converge and returns the error
>> "(not concave)" on every iteration.  Is there a way to estimate P, NO,
>> MAYBE, YES, mean, and SD using -gmm-?
>>
>> Keith
>>
>> *
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>>
>
>
>
> --
> Stas Kolenikov, also found at http://stas.kolenikov.name
> Small print: I use this email account for mailing lists only.
>
> *
> *   For searches and help try:
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>

*
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