Chongming Yang, Joseph A Olsen, Sarah Coyne and Jing Yu
Ordinal scales can be used in latent growth curve modeling in three ways: mean, weighted mean scores, and factors measured by scale items. Sum and mean scores are commonly used in growth curve modeling in spite of certain discouragement. It was unclear how much bias these practices could produce in terms of the change rates and patterns. This study compared three methods with Monte Carlo Simulations under different number of response categories of the items, in terms of five key parameters of growth curve modeling. The hypothetical population models were derived from real empirical data to generate datasets of binary, trichotomous, five- and seven-point scales with sample size of 300. Latent growth curve modeling of mean, weighted mean, and factors measured by the ordinal scales were respectively fit to these datasets. Results indicated that modeling the factors that are measured with ordinal scales yield the fewest biases. Biases of modeling the means and weighted of the scales were under one decimal point in the change rates, whereas biases in the variances and covariance of the intercept and slope factors were large. In conclusion, it is inadvisable to use means or weighted means of ordinal scales for latent growth curve modeling. It produces the best results modeling the factors that are measured with the ordinal scales.
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