Lois Downey posted on Monday, October 13, 2008 - 11:31 pm
Our factor indicators are 11-category ordinal measures with only the extreme values defined: 0 = terrible; 10 = almost perfect. Almost all have significant negative skew. In the past, we have modeled them as categorical indicators and have collapsed values of 0 and 1 into one category to accommodate Mplus's 10-category limit. However, I'm wondering whether it might make more sense to model these indicators as continuous and use a robust estimator to circumvent the problem of nonnormality. Would this technique be justifiable, given that respondents are given only the anchor definitions and allowed to impose their own quasi-continuous scale between these extremes? Or should one have more than 11 values before calling something "continuous"?
If you don't have a large floor or ceiling effect, I would treat the variable as continuous with that many categories. If you do have a large floor or ceiling effect, I would treat the variable as censored or do two-part modeling.
Lois Downey posted on Tuesday, October 14, 2008 - 5:39 pm
What percentage of responses at the minimum or maximum response option should one take as evidence of a "large" floor or ceiling effect?
Lois Downey posted on Thursday, October 16, 2008 - 5:37 pm
When one includes censored indicators, the tests of model fit no longer include those handy statistics like RMSEA that allow comparing the fit of models with different numbers of factors. If I run my 22-indicator model without defining any of the indicators as censored, I get inadequate fit with 5 factors, but adequate fit with 6 factors. (We expected 6 dimensions, based on our theoretical model, although not all of the 6 factors in the EFA look precisely like the dimensions we anticipated.) Can I use this information as a rough indication that when I redefine 10 of the indicators as censored from above, I should focus on a 6-factor model? (p.s. -- Thank you so much for your help to date, and in the future.)
I was thinking that you could use weighted least squares but I see that is not the case. I would not use fit statistics from treating the variables as continuous when some are censored. I would instead look at BIC. If you get six factors but they don't resemble what you expected, I might go back to the drawing board. It sounds like your items may have validity problems.