Hi- I have 16 indicators that are measured on a 7-point Likert (hence, ordinal) scale that I would like to use in a LCA. I'm wondering whether it is appropriate to treat the indicators as either continuous or ordinal (using "CATEGORICAL ARE . . .")? My sense is that ordinal is more suitable. However, with this many items and 7 levels per item, interpretation can be more challenging (i.e., the means from output where items are not treated as ordinal are easier to interpret than the probabilities at each level).
1. Is it reasonable (albeit perhaps not ideal), from a statistical perspective, to treat the indicators as if they were continuous? I should mention that the distributions of the variables are not normal--if I treat the indicators as continuous, how problematic is it to violate the assumption of normality?
2. If I treat the indicators as ordinal, are there circumstances in which you would recommend collapsing the categories (from 7 into 5 or 3)?
3. As I mentioned above, I have 16 variables and am wondering if there are any rules of thumb for evaluating indicators in order to remove those that aren't contirbuting to the classifications. Does retaining indicators that are not contributing much harm the model?
CATEGORICAL = implies that a variable is dichotomous or, when polytomous, ordered categorical (ordinal).
You have answers to several of your questions in the two Muthen-Kaplan articles that are listed on our web site. The most important aspect is how strong floor and/or ceiling effects you have. If they are strong, you may want to use a categorical approach. If some categories have very low frequencies you may then want to collapse those. But if not, non-normality when treated as continuous is not problematic in that LCA works with within-class normality that implies non-normality for the mixture that you observe.
Retaining indicators that don't contribute to clear classification does not harm.