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In item response theory (IRT), the argument of the logit function can be expressed using a discrimination (a) and an intercept (b) as $a \theta + b$ or using a discrimination and location (c) as $a ( \theta - c )$

In the output from my estimating software, I was provided estimates and standard errors (SE) for the intercept parameters. I would like to report locations instead of intercepts. My question is this: Can the SE for the location be computed from the SE for the intercept and the discrimination as $SE(c)=\frac{SE(b)}{a}$ ? I am afraid this is not the case, since the discrimination is also estimated.

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I wrote a paper on this problem a while back in MBR. See here for the details.

Ultimately, if your software estimated the SEs from the slope-intercept form then some variant of the delta method likely was used to obtain the SE for the transformation. And often times, this approximation isn't great, so profile likelihood CI approaches may help solve the problem and avoid some paradoxical results.

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