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Re: st: Polychoric PCA error message


From   Stas Kolenikov <skolenik@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Polychoric PCA error message
Date   Tue, 29 Jan 2013 22:05:25 -0600

A zero cell means that the underlying two normal variables have a
correlation of 1 -- or at least that's the maximum likelihood
estimate. Visually, the normal distribution is degenerately
concentrated on a line that passes outside of zero. With a correlation
of 1, ML estimation breaks down: the maximizer runs out of the sample
space, and produces missing values for negative definite matrices that
have correlations > 1; and if a solution is claimed to exist, it can
not stable, as we work with poorly defined matrices that are unstable
to invert (in the sense of finite accuracy arithmetics). In your
example, not only you have zero cells that make estimation of the
correlations difficult; the small marginal proportions will not make
-polychoric- very happy, either.

Vika Savalei wrote about the existing tweaks
(http://www.mat.ulaval.ca/fileadmin/Cours/STT-7620/Savalei11.pdf), but
I don't have anything implemented in the code.

On Tue, Jan 29, 2013 at 9:34 PM, Yashin <yashin5@gmail.com> wrote:
> Dear Statalisters:
>
> I am trying to run polychoric PCA from Stas Kolenikov on a data subset
> (wealth index) that--pre-winnowing--has 32 dichotomous variables, four
> ordinal variables, and one continuous variable. I am getting the
> following error messages, repeated times:
>
> could not calculate numerical derivatives
> missing values encountered
> numerical derivatives are approximate
> nearby values are missing
>
> I found the following thread addressing this issue,
>
>                     http://www.stata.com/statalist/archive/2012-11/msg00826.html
>
> and similarly I also found that for those coefficients in the
> correlation matrix that are either zero or > 0.9, the 2x2 tables
> invariably have a cell with small numbers (usually 0, and in other
> cases 1, 2, 3 and in one case a 7). In this case, this would not be a
> structural zero but a sampling zero.
>
> I have related questions I am hoping someone might help shed light on:
>
> 1) When I examined the six 2x2 tables for variable pairs with
> correlation coefficients > 0.9, they did not appear to be highly
> correlated, and further, included one cell with 0
>
> I'm copying a couple of examples below:
>
> . /* tabulate high correlation pairs */
>
> . tab vacuum carpet
>
>            |        carpet
>     vacuum |         0          1 |     Total
> -----------+----------------------+----------
>          0 |        21        835 |       856
>          1 |         0        342 |       342
> -----------+----------------------+----------
>      Total |        21      1,177 |     1,198
>
>
> . tab computer stove
>
>            |         stove
>   computer |         0          1 |     Total
> -----------+----------------------+----------
>          0 |        12      1,033 |     1,045
>          1 |         0        146 |       146
> -----------+----------------------+----------
>      Total |        12      1,179 |     1,191
>
> 2) When I run the polychoric with only the dichotomous variables, and
> then with the same variables plus the additional 5 variables described
> above (ordinal and continuous), I get different correlation
> coefficients in the correlation matrix for the same variable pairs.
> How could this be? Sometimes the values are similar and yet different,
> and in other cases the values are quite different (some of the
> correlations > 0.9 when binary, ordinal and continuous variables are
> included in the matrix become zero when only binary variables are
> included in the matrix).
>
> 3) To address the issue of 2x2's with zeros, one colleague suggested
> flattening in the previous thread (
> http://www.stata.com/statalist/archive/2012-11/msg00829.html )--I
> wondered if there are other options.
>
> Many thanks for any thoughts!
>
> Yashin
>
> --
> ysl
> *
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-- 
-- Stas Kolenikov, PhD, PStat (SSC)  ::  http://stas.kolenikov.name
-- Senior Survey Statistician, Abt SRBI  ::  work email kolenikovs at
srbi dot com
-- Opinions stated in this email are mine only, and do not reflect the
position of my employer
*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
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*   http://www.ats.ucla.edu/stat/stata/


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