I am looking for the correct formula to convert IRT discrimination parameters obtained from a logit-link model to a correlation metric. Because of the logit scaling factor (1.702), I am a bit unsure as to the correct formula.

In the case of a probit model it is simply $\frac{\alpha}{\sqrt{1 + \alpha^2}}$, where $\alpha$ is the discrimination parameter. But how precisely does this formula change for the logit-link discrimination conversion?


1 Answer 1


I was able to track down the correct formula which is essentially the same as above except 1.00 in the denominator is replaced with 3.29, thus:

for a factor correlation metric (standardized) from a logit-link discrimination parameter

$\frac{\alpha}{\sqrt{3.29 + \alpha^2}}$, where $\alpha$ is the discrimination parameter.

  • $\begingroup$ Can you please provide a citation? $\endgroup$ Nov 7, 2018 at 0:33
  • $\begingroup$ See slide #6 in this link: lesahoffman.com/PSYC948/948_Lecture6_Binary_Responses.pdf $\endgroup$
    – Jhaltiga68
    Nov 8, 2018 at 11:47
  • $\begingroup$ I know both models are the same. I was asking about the loading to discrimination transformation. See page 144, table 2 of unc.edu/~dbauer/manuscripts/kamata-bauer-2008.pdf. I think the formula for probit always applies as the 1 is about the standardized latent factor variance, not the error variance. $\endgroup$ Nov 8, 2018 at 12:29
  • $\begingroup$ Not sure what your question is Jim. You asked for a citation re: my example of factor loading from discrimination. But you want discrimination from factor loading I see. Your point about the 1 makes intuitive sense, but I don't know for sure without doing due diligence. $\endgroup$
    – Jhaltiga68
    Nov 9, 2018 at 6:15
  • 1
    $\begingroup$ I ran some IRT models using Bayesian software, checked old class notes, looked at the linked paper a little closer (paper focused on probit since binary/ordinal CFA uses tetrachoric corr which is probit-based) and I'm now certain that your original answer was correct (+1 your answer). Only note is $\pi^2/3$ does not work well for the variance of logistic in practice. $1.7^2$ works better according to a number of papers in the psychometric literature researchgate.net/publication/… $\endgroup$ Nov 10, 2018 at 5:30

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