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  • Standard errors: grm versus gsem

    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?

  • #2
    Thank you!

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