Testing bivariate normal assumption PreviousNext
Mplus Discussion > Confirmatory Factor Analysis >
 Jessica Schumacher posted on Wednesday, October 24, 2007 - 1:34 pm
I am running a CFA on ordered categorical variables. I know that the underlying variable approach used in M-Plus is based on the fit of the standard linear factor model using the matrix of polychoric correlation coefficients. Does this approach assume univariate and bivariate normality of the underlying variables? Is there a way to confirm in M-Plus whether this assumption holds? Are there statistical methods to handle cases where this assumption might not hold? In my particular case, I am looking at a 5-point scale and each of the variables is fairly skewed. Would an item response function approach be a better choice in this case? Thank you for your help.
 Bengt O. Muthen posted on Wednesday, October 24, 2007 - 3:10 pm
This testing is not currently available in Mplus. For a discussion of this topic see paper #45 at


It is unclear how important it is to have a nominally good fit in the bivariate tables. See also

Flora, D.B. & Curran P.J. (2004). An empirical evaluation of alternative methods of estimation for confirmatory factor analysis with ordinal data. Psychological Methods, 9, 466-491.

which you find on our web site under Papers, Categorical Factor Analysis.
 Salma Ayis posted on Friday, October 26, 2007 - 2:08 am
I am using IRT models and wondering if Mplus provide me with an INFIT stattistics or an alternative!. From the literature, few articles seems to judge the fit of each item within a model (Rasch for example) only from the INFIT statistics, range 0.6-1.4 (suggested by Wright,. et. al: 1994). What else can I use to judge the fit of an individual item within the model, using MPlus? in my situation the model as a whole has a good fit, but one item has estimated difficulty farther away from the rest. Any advice is very much appreciated!.
 Linda K. Muthen posted on Friday, October 26, 2007 - 8:50 am
Mplus does not provide INFIT statistics for each item. We do provide residuals for each item. Use the RESIDUAL option of the OUTPUT command.
 Rob Dvorak posted on Tuesday, March 29, 2011 - 12:04 pm
Hi Drs. Muthen,

I'm currently trying to fit a Rasch model to categorical survey data with 50 items. I need to parse this down to just a few items. However, without INFIT & OUTFIT statistics I'm having a difficult time doing this. Is there a reference you could recommend that talks about item selection in IRT based on residuals? Thanks in advance.
 Bengt O. Muthen posted on Tuesday, March 29, 2011 - 5:55 pm
You are right that Mplus does not have those Rasch statistics yet. I am not up to date on the Rasch fitting literature I'm afraid - but it should be possible to Google that.
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