Does 'mirt' calculate categorical item factor analysis (CIFA)?

[Danilo Assis Pereira]

Dear Phil,

I saw a paper about the differences between FIML (Full information maximum likelihood) and CIFA (Categorical Item Factor Analysis) using MPlus. Does 'mirt' package calculate CIFA? If so, how can I found these functions?
http://www.statmodel.com/download/limited%20vs%20full%20info%20IRT%20estimation%20pm09.pdf

Thanks a lot,


Danilo A Pereira
IBNeuro

[Phil Chalmers]

Categorical factor analysis is the limited information version of FIML. While FIML uses all the moments in the data to estimate the parameters, CIFA uses only the first 2 (the mean and covariance). It requires a special matrix of correlations to be computed via polychoric correlations, and special weighting matrices must be employed. The lavaan package will do this by specifying an ordered = NAMES argument to sem(...). If you use the graded response model in mirt the packages will give very similar estimates, mirt using all the moments in the data while lavaan using only the first two. There are pros and cons to both approaches, so picking which one is better is debatable (I prefer the former if it's possible since you can estimate more interesting models than just 'ordinal', and the latter only when FIML is not numerically feasible in high dimensional cases). Hope that helps.

Phil

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[Phil Chalmers]

Oh, and how missing data is handled in FIML is much more elegant than CIFA since the missing data are handled directly (I've estimated models with as much as 70% missing data and still got meaningful results). There are articles about this problem as well, notably by Victoria Savalei at UBC are worth checking out. 

Phil

[Danilo Assis Pereira]

Thank you very much!

Actually, I wanted to use it in a Likert scale inventory... maybe "gpcm" or "nominal" are more adequate...