Standard errors: grm versus gsem

[John Hansen]

Hi everyone,

I am trying to plot cut point coefficients from a graded response model along with standard errors. I understand that Stata fits the model using gsem, and I don't have any trouble switching from the slope-intercept parameterization (used by gsem) to the IRT parameterization for the coefficients, but I cannot figure out how to reproduce the irt-parameterized standard errors that Stata reports. I could not find the formula in the gsem or grm documentation. Can anyone point me in the right direction?

To give a concrete example, the discrimination, first two cut point coefficients, and standard errors for the first item are below:

	gsem-coef	gsem-se	grm-coef	grm-se
discrimination	2.431	0.071	2.431	0.071
cut point1	-7.555	0.201	-3.108	0.080
cut point2	-6.937	0.172	-2.853	0.067

Dividing the first cut point gsem-coefficient by the discrimination parameter (-7.555/2.431) produces the grm-coefficient, but 0.201/2.431=0.083, not 0.080. For other cut points, the results of dividing the gsem standard error by the discrimination parameter is much less close to the reported grm standard error, so I don't believe this is simply a matter of rounding. How does Stata re-parameterize the gsem standard errors for the irt parameterization?

[John Hansen]

Thank you!