Hi everyone,
I am looking for the suitable method to perform a factor analysis of binary data. When going through the literature on factor analysis on binary response data, it appeared to me that both hierarchical item response theory (HIRT) and structural equation modelling (SEM) could be suitable methods. I was wondering therefore what the main differences are between both? Can HIRT be considered as a special case of SEM?
Any literature on that topic is welcome as well as advises on performing an HIRT (mainly, which software is recommanded?).
Thank you!
I am not an expert in SEM BUT it is based on ols regression. I have not seen a variant of SEM based on logistic regression which is presumably what you would need. I am wrong see the link:
https://www.google.com/search?q=SEM+based+on+logistic+regression&ie=utf-8&oe=utf-8&client=firefox-b
And
https://www.google.com/search?q=hierarchical+item+response+theory&ie=utf-8&oe=utf-8&client=firefox-b
These should help answer your questions.
Best wishes,David Booth
Hi Fanny!
In my experience I have used SEM to run multilevel models I know that it is possible to do with HIRT models. Psychometrics and Statistics are related in many ways, for example the item discrimination index is in fact an unstandarized factor loading and stuff like that.
To run a CFA with binary data (SEM o HIRT) you have to work with tetrachoric matrix covariance (polychoric with more than 2 categories), this can be done in AMOS, MPLUS, R, EQS, this kind of software is useful for your aim.
Moreover, if you want to explain, I highly recommend to use HIRT model, if you just want to describe your patterns CFA is the best option. It is up to you!
Best from Mexico City
Fernando A
Thanks very much both of you for your answer!
I thought about doing HIRT with R but did not find the right package yet. The mirt() package seems not to allow it except if you code it by yourself...
This should help
The Estimation of Item Response Models with the lmer Function from the lme4 Package in R
Article The Estimation of Item Response Models with the lmer Functio...
that is, the binary or ordinal outcomes are seen as nested within individuals etc with further levels of nesting.,That are not necessarily hierarchic - they could be crossed. Single diension models (the so-called Rasch model) can be estimated in standrad HLM software but the two dimesional IRP models involve latent variables and that is where SEM concepts come in.
I found these older papers a useful way into the data structures required in the simpler Rasch case
Kamata, A. (2001). Item analysis by the hierarchical generalized linear model. Journal of Educational Measurement, 38, 79-93.
and then more than one scale simultaneously (but still in Rasch context)
Article A Multivariate, Multilevel Rasch Model with Application to S...
and a longitudinal extension
Article A REPEATED MEASURES, MULTILEVEL RASCH MODEL WITH APPLICATION...
The Mplus implementation of IRT has a number of sophisticated features
https://www.statmodel.com/irtanalysis.shtml
Bartholomew et al. (Book Latent Variable Models and Factor Analysis: A Unified Approach
) show the relationship between latent variable models for metric and binary manifest variables. As noted above, the ones with binary variables are often called IRT or latent trait models. IRT is common in education and there are lots of commercial and free packages (e.g., mirt in R). The hierarchical in HIRT can mean a few things so I won't comment on that. SEM is also a latent variable approach, and different people include lots of different things within its boundaries. A really broad definition would be anything that includes direct relations between any latent variables. Some IRT models would include this, some wouldn't. So I'd say both are part of the latent variable family of models. (edit for clarification: So I'd say both are part of the latent variable family of models and they can overlap.)- Badges
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