Stata has added a maximum likelihood tetrachoric command to Stata 9.2. The matrix
of tetrachoric correlations is saved in r(Rho) for use pic pcamat or factormat.
If you need polychoric or polyserial correlations in addition to tetrachoric
then the polychoric command by Stas Kolenikov is meant for you. The correlation
matrix is displayed using the matrix list r(R) command.
You can download
polychoric over the internet by typing search
polychoric (see How can I used the search command to search for
programs and get additional
help? for more information about using search).
Now, let’s read in an example dataset,
tetra, which contains data several dichotomous variables
derived from the High School and Beyond study.
use https://stats.idre.ucla.edu/stat/stata/faq/tetra, clear
summarize female schtyp ses hon sci
Variable | Obs Mean Std. Dev. Min Max
-------------+--------------------------------------------------------
female | 200 .545 .4992205 0 1
schtyp | 200 .84 .367526 0 1
ses | 200 .765 .4250628 0 1
hon | 200 .265 .4424407 0 1
sci | 200 .335 .4731749 0 1
Let’s compute a standard correlation matrix followed by a tetrachoric
correlation matrix.
corr female schtyp ses hon sci
(obs=200)
| female schtyp ses hon sci
-------------+---------------------------------------------
female | 1.0000
schtyp | -0.0153 1.0000
ses | -0.1512 -0.1776 1.0000
hon | 0.1391 0.0148 0.0389 1.0000
sci | -0.1599 -0.0659 0.1435 0.3179 1.0000
tetrachoric female schtyp ses hon sci
(obs=200)
| female schtyp ses hon sci
-------------+---------------------------------------------
female | 1.0000
schtyp | -0.0291 1.0000
ses | -0.2636 -0.4475 1.0000
hon | 0.2362 0.0304 0.0735 1.0000
sci | -0.2562 -0.1253 0.2668 0.5037 1.0000
mat list r(Rho) /* note the upper-case R */
symmetric r(Rho)[5,5]
female schtyp ses hon sci
female 1
schtyp -.02907834 1
ses -.26359952 -.44745088 1
hon .23621208 .03040347 .07348643 1
sci -.25621193 -.12525624 .26676862 .50370596 1
And now for the polychoric version.
polychoric female schtyp ses hon sci
matrix list r(R)
symmetric r(R)[5,5]
female schtyp ses hon sci
female 1
schtyp -.02893308 1
ses -.26297321 -.44527627 1
hon .23643947 .03044205 .07352325 1
sci -.25634248 -.12494757 .2666472 .504248 1