CFA + nonnormal Likert data PreviousNext
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 Amy Briesch posted on Tuesday, May 01, 2012 - 7:34 am
I am looking for input with regard to the appropriate CFA estimation method when dealing with non-normal Likert data. Items are on a 6-point scale (which typically I would treat as continuous); however, there is a high degree of both univariate skewness and kurtosis in the data. First inclination is to treat as ordinal and use WLSMV, but am hoping for an external opinion. Thanks!
 Linda K. Muthen posted on Tuesday, May 01, 2012 - 1:53 pm
If you have Likert items with piling up at one or both ends, you should treat them as ordinal. WLSMV is a good choice unless you have a lot of missing data in which case I would recommend ML and the CATEGORICAL option unless you have a large number of factors. If you have a lot of missing data, you can also impute using DATA IMPUTATION and then use WLSMV.
 Amy Briesch posted on Wednesday, May 02, 2012 - 6:45 am
Thank you for your quick response. Missing data is not a big issue (less than 1% of total item responses). I do have a quick follow-up question:

Looking at the categorical data proportions, would these more skewed items demonstrate a significant degree of "piling up" at the ends that you referenced?

Category 1 0.034
Category 2 0.111
Category 3 0.057
Category 4 0.111
Category 5 0.594
Category 6 0.093

Category 1 0.023
Category 2 0.066
Category 3 0.032
Category 4 0.039
Category 5 0.737
Category 6 0.104
 Linda K. Muthen posted on Wednesday, May 02, 2012 - 9:38 am
The piling up I refer to would be large proportions in the first or last category. I would say this should be treated as categorical because one category seems to dominate. You don't show the numbers in each cell. If some are very small, you might want to consider collapsing categories. You don't want a lot of zero cells in the bivariate tables for these variables.
 J.D. Haltigan posted on Monday, February 09, 2015 - 9:31 pm
Related to original post, if I have 5-point Likert scale data that is not suffering from severe skew or kurtosis (e.g., skew > 2; kurtosis > 7; West, Finch, & Curran, 1995), is it acceptable to treat the indicators as continuous in a CFA and model using the MLR estimator?

Thank you!
 Linda K. Muthen posted on Monday, February 09, 2015 - 9:42 pm
If you do not have floor or ceiling effects, piling up at either end, you can probably treat it as continuous. If you have piling up at either end, you should treat it as categorical. Skew and kurtosis are concepts relevant to continuous variables.
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