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 Anonymous posted on Sunday, October 17, 2004 - 7:58 am
Hi; Simple question. In a CFA w/all continuous indicators, how can I be assured the relationship between the indicators and the latent variables is linear, as I would check in a regression proceedure? The reason I ask is I have some heavily skewed indicators. Thanks in advance for your help.
 bmuthen posted on Sunday, October 17, 2004 - 9:01 am
That's a good question. Seems like there are many possibilities, but that we know little about how they compare. One way is to use the Mplus Version 3 facility of non-linear factor relationship using ML - check if the quadratic term is significant. You can also try to plot residuals after estimating the factor scores and doing a regular regression of the outcomes on the factors (although that is distorted by the possible nonlinearity when estimating the scores). You can try a censored-normal (inflated) model instead. Etc. Perhaps this is a topic for a paper, motivated by actually being able to fit nonlinear models?
 Anonymous posted on Sunday, October 17, 2004 - 11:49 am
Thanks for the quick response. I'll try the non-linear specification (I'm new to MPLUS-could you point to an example in the manual?). The residuals sound problematic, but worth looking at. I am curious about the censored-normal model, with which I am completely unfamiliar. Can you point me to a reference on how this works? I would appreciate it.
 bmuthen posted on Sunday, October 17, 2004 - 12:28 pm
A non-linear example is given as Ex5.7 in the Version 3 User's Guide and 5.4 gives a censored example. For censored factor analysis, see also my 1989 Tobit factor analysis paper in BJMSP given on the Mplus web site under References (or my UCLA site).
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