2PLM IRT modeling of rare event behavioral data: Why changing discrimination and difficulty values? I am using the 2PLM (2-parameter logistic model) IRT model to examine how sets of very rare (negative/aversive) maternal behaviors (towards their children) are associated with a priori conceptualizations of various unitary dimensions of maternal behavior. In short, the maternal behaviors are coded as present/absent and are zero-inflated. For some behaviors, the cuts are very extreme with less than 1% of the sample showing the behavior. My sample size is 343.
I have run the models both in Mplus and in R using the LTM package. In general, the discrimination and 'difficulty' estimates are plausible and consistent across platforms, leading me to believe they are being reliably estimated in my sample. However, for two particular dimensions, the items change their direction from + to - for both discrimination and difficulty parameters. In addition, the absolute magnitude of the discrimination parameters seem more plausible using the LTM package in R. For example, for one very rare behavior, the discrimination parameter in Mplus is 36.26 and using LTM it is -7.07. The corresponding difficulty parameters are 2.08 and -2.18, respectively.
I am hoping for some thoughts on what might account for the behavior of these particular models across platforms and if anyone has performed binary factor analyses with similar rare event data.
*Just to update this post, what caused the 'switch' of the signs of the discrimination parameters can be accounted for by the following in the LTM package: "In the case of the one-factor model, the optimization algorithm works under the constraint that the discrimination parameter of the first item is always positive...". Given that the Mplus optimization algorithm must not work under the same constraint, I am curious as to whether that estimation routine might more reliably approximate the true direction of the sample parameter estimates (discrimination and difficulty parameters) for these items.
 A: For anyone reading this thread and interested, the issue had to do with the numerical integration setting in the MPlus environment. As the LTM package uses Gauss-Hermite integration it was necessary to change the Mplus setting for this from standard to INTEGRATION=GAUSSHERMITE(35). Note that 35 simply was the value I chose for the number of integration points and is used across both platforms (default for both platforms is 15). After doing this, the results are virtually identical across platforms which leaves me a bit more confident in the reliability of the results for these IRT models.
One further note I wanted to add is that I made sure that the number of EM and quasi-Newton iterations were identical between the two platforms. This was accomplished by changing the Mplus defaults to match what I was using in the LTM package with the following commands:
ITERATIONS=150;
MITERATIONS=100;
Finally, for one dimension, all of the signs remained reversed in the Mplus run. This is not an issue as it is a simple rotation of the same (unidimensional) factor structure (something that took a minute for me to realize). What was important is that the absolute values of the parameter estimates were approximately the same in each platform.
