Janet Rosenbaum wrote:
Has anyone implemented a function in stata which estimates the standard
error of the tetrachoric correlation?
(e.g., Brown MB. Algorithm AS 116: the tetrachoric correlation and its
standard error. Applied Statistics, 1977, 26, 343-351.)
--------------------------------------------------------------------------------
Yes. Use -xtprobit- and examine rho's standard error.
Joseph Coveney
. clear
. set more off
. set seed `=date("2006-06-16", "ymd")'
. set obs 200
obs was 0, now 200
. forvalues i = 1/2 {
2. generate byte item`i' = uniform() > 0.5
3. }
. tetrachoric item*
Tetrachoric correlations (N=200)
----------------------------------
Variable | item1 item2
-------------+--------------------
item1 | 1
item2 | .1097 1
----------------------------------
. generate int row = _n
. reshape long item, i(row) j(column)
(note: j = 1 2)
Data wide -> long
-----------------------------------------------------------------------------
Number of obs. 200 -> 400
Number of variables 3 -> 3
j variable (2 values) -> column
xij variables:
item1 item2 -> item
-----------------------------------------------------------------------------
. xtprobit item column, i(row) intmethod(aghermite) intpoints(30) nolog
Random-effects probit regression Number of obs =
400
Group variable (i): row Number of groups =
200
Random effects u_i ~ Gaussian Obs per group: min =
2
avg =
2.0
max =
2
Wald chi2(1) =
0.01
Log likelihood = -276.75842 Prob > chi2 =
0.9174
------------------------------------------------------------------------------
item | Coef. Std. Err. z P>|z| [95% Conf.
Interval]
-------------+----------------------------------------------------------------
column | -.0132835 .1281024 -0.10 0.917 -.2643597
.2377926
_cons | .0265671 .2040708 0.13 0.896 -.3734043
.4265384
-------------+----------------------------------------------------------------
/lnsig2u | -2.09337 1.127269 -4.302775
.1160364
-------------+----------------------------------------------------------------
sigma_u | .3510998 .1978919 .1163226
1.059734
rho | .1097429 .1101335 .0133503
.5289766
------------------------------------------------------------------------------
Likelihood-ratio test of rho=0: chibar2(01) = 0.98 Prob >= chibar2 =
0.161
. xtprobit item column, i(row) intmethod(aghermite) intpoints(30)
vce(jackknife)
(running xtprobit on estimation sample)
Jackknife replications (200)
----+--- 1 ---+--- 2 ---+--- 3 ---+--- 4 ---+--- 5
.................................................. 50
.................................................. 100
.................................................. 150
.................................................. 200
Random-effects probit regression Number of obs =
400
Group variable (i): row Number of groups =
200
Random effects u_i ~ Gaussian Obs per group: min =
2
avg =
2.0
max =
2
F( 1, 199) =
0.01
Log likelihood = -276.75842 Prob > F =
0.9181
------------------------------------------------------------------------------
| Jackknife
item | Coef. Std. Err. t P>|t| [95% Conf.
Interval]
-------------+----------------------------------------------------------------
column | -.0132835 .1290378 -0.10 0.918 -.2677406
.2411735
_cons | .0265671 .2053563 0.13 0.897 -.3783866
.4315207
-------------+----------------------------------------------------------------
/lnsig2u | -2.09337 1.132609 -4.313243
.1265035
-------------+----------------------------------------------------------------
sigma_u | .3510998 .1988294 .1157154
1.065295
rho | .1097429 .1106553 .0132131
.5315838
------------------------------------------------------------------------------
Likelihood-ratio test of rho=0: chibar2(01) = 0.98 Prob >= chibar2 =
0.161
.
*
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