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I am looking for input with regard to the appropriate CFA estimation method when dealing with nonnormal Likert data. Items are on a 6point 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! 


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 followup 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? QX Category 1 0.034 Category 2 0.111 Category 3 0.057 Category 4 0.111 Category 5 0.594 Category 6 0.093 QY Category 1 0.023 Category 2 0.066 Category 3 0.032 Category 4 0.039 Category 5 0.737 Category 6 0.104 


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. 


Related to original post, if I have 5point 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! 


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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