

Assumptions of analyses using dichoto... 

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Hello, I would like to conduct an exploratory factor analysis and a confirmatory factor analysis (comparing alternative measurement models) using 28 dichotomous indicators of depression in a very large sample. I hear Mplus is the way to go. I am concerned because most of the methods for accomodating dichotomous data in these analyses I have found (not just in Mplus) involve computing tetrachoric correlations. I am also under the impression that tetrachoric correlations contain the "strict" assumptions that the underlying variables that are being measured by the dichotomous indicators are continuous and multivariate normal. While I am comfortable with the former condition (underlying variables are continuous), I am certain that at least some of my indicators (which include suicidal ideation and behavior) are not representing underlying normally distributed variables (I believe this would violate the assumptions of fullinformationfactoranalysis in IRT as well). I know that WLS estimation in Mplus involves more than "just" factor analyzing a matrix of tetrachorics, but I am not certain if this estimation procedure "eliminates" the assumption of multivariate normal underlying variables. I also understand that there are other estimation methods available in Mplus for dichotomous indicators. I'm wondering which of these would be appropriate for my analyses (please indicate what additional information would be needed to reach that decision). Any guidance with undertaking these analyses (especially containing references) would be greatly appreciated. Thanks in advance, Jim 

bmuthen posted on Friday, March 04, 2005  6:39 pm



Fullinformation factor analysis in IRT assumes normal factors and either a probit or a logit relationship between the factors and the items. Taken together, with a probit link this produces exactly the same model as assuming underlying normal variables for the items  with the logit link, the models are close. One just hears more about the underlying normality assumption with tetrachorics than in the IRT context, but it is there in both traditions. So the essential assumption is the normality of the factors. Mplus can do the FIML factor analysis in the IRT tradition  i.e. using logistic links. Mplus cannot yet do EFA with rotations in this way, only CFA. I think, however, that a simple EFA using unweighted least squares on tetrachoric correlations is a very practical way to get the information you need. There was a 1986 JEBS article by Mislevy comparing this to FIMLIRT and no real differences emerged. I get the impression that you are not prepared to make a normality assumption for the factors. Note then that Mplus can also allow nonnormality for the factors using "nonparametric" estimation of the factor distributions  this is available through the Mplus mixture track. This is straightforward with one factor. 

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