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On reading a number of prominent CFA studies on the structure of PTSD symptoms, I notice how every study appears to treat the variables as continuous. This puzzles me, as their data come from questionnaires with 4 or 5 response categories. None of the studies mention this issue. AFAIU, had they specified the variables as categorical in the analysis, they wouldn't be able to get χ2, CFI and absolute fit statistics, without carrying out two different analyses with different estimators (e.g. WLSMV for obtaining χ2, RMSEA, CFI and TLI, vs. ML/MLR for obtaining AIC and BIC). Also, AFAIU, they would not have been able to test for significant differences in χ2 (e.g. DIFFTEST in Mplus seems to only be available for continuous variables). So, am I missing out on an unspoken consensus, that Likert scale responses can be treated as continuous in CFA?

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    $\begingroup$ Can you give some references,and then describe one of those analyses more in detail? A likert scale variable is at least ordinal, so treating it as a numerical (that is, continuous) variable might be OK. It is categorical (that is, not ordered) variables which NEVER can be treated as numerical. $\endgroup$ Nov 17, 2014 at 13:16
  • $\begingroup$ If here by "categorical" you mean dichotomous variables, then, in most cases, it is equivalent to treat them as categorical and as continuous, as predictors. $\endgroup$
    – ttnphns
    Nov 17, 2014 at 14:10
  • $\begingroup$ @ttnphns: I don't see how you could specify a 4 or 5 response categories variable as dichotomous variables. $\endgroup$
    – Erik
    Feb 26, 2015 at 10:04
  • $\begingroup$ @kjetil: AFAIK a Likert scale cannot be considered categorical as its categories are arranged according to degree of agreement or perceived intensity of a phenomenon. As you say, it "might be OK" to treat it as continuous, and that seems to be the consensus. Yet I'm curious why I can't seem to find any references for this or some guidelines for how many data points would suffice (e.g. if 16 items with four categories is enough, how about 10 items with four categories?). $\endgroup$
    – Erik
    Feb 26, 2015 at 10:09

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