Treatments of Ordinal Scales in Latent Profile Analyses: A Comparison with Monte Carlo Simulations

Person-centered approaches to analysis/modeling provide certain advantages and methodological possibilities. Ordinal psychological scales have been used differently in latent profile analysis (LPA), including sums, means, standardized scores, and factor/latent scores, meanwhile it was uncertain to what extent these treatments would yield equivalent class proportions and univariate differences. This study simulated LPA of different treatments of ordinal scales (unweighted and weighted means, sums, standardized sums, and latent factor scores) with different response options (2, 3, 5, and 7) at different sample sizes (N = 240/300 or 600) under maximum likelihood (ML) and Bayesian estimations. Compared to other treatments of ordinal scales, LPA of factor scores showed slight advantages in recovering the population class proportions and univariate differences, especially under small samples and two/three response options. It was concluded that LPA of means and sums of ordinal scales, either weighted or unweighted, may be better replaced with FMA with Bayesian estimation when sample size is sufficient. Alternatively, LPA of factor scores in two-steps is preferred when samples are less than desirable sizes.