- ML has been recommended for use with ordered categorical data when item-level characteristics are approximately normal (Skewness/Kurtosis ranging from -1 to +1)(Muthen&Kaplan,1985); if not, then we shoule use weighted Least Squares (WLS; with polychoric correlation input), not Maximum Likelihood (ML; with Pearson Product–Moment input).
- Categorization increases the kurtosis of the variables.
- that reliability increases as a function of the number of response categories,
untilvthe number of categories reaches five or seven, at which point reliability increases
- When categorical data show small skewness and kurtosis values (in the range from -1.5 to +1.5), normal theory can be used (Randall et al., 2004).
- if both variables are continuous--Pearson correlation
- if both variables are ordinal--polychoric correlation
- if both variables are dichotomous--tetrachoric correlation
- if one variable is ordinal and the other is continuous--a polyserial correlation
- use polychoric/polyserial correlations matrix as input, use weighted least squares (WLS) estimation method
- first use PRELIS to analyze a matrix of polychoric correlations, and from this analysis, produce an estimate of the asymptotic (large sample) covariance matrix of the estimated sample variances and covariances. The estimated covariance matrix from PRELIS was analyzed in LISREL, using generally-weighted-least-squares method of estimation
- When multivariare normality is not met, the appropriate estimation technique is weighted least square (WLS), not ML. Calculaitons of WLS are based on polychoric correlation matrix, rather than covariance matrix