Evaluating Measurement Invariance with Censored Ordinal Data: A Monte Carlo Comparison of Alternative Model Estimators and Scales of Measurement

Evaluations of measurement invariance provide essential construct validity evidence. However, the quality of such evidence is partly dependent upon the validity of the resulting statistical conclusions. The presence of Type I or Type II errors can render measurement invariance conclusions meaningless. The purpose of this study was to determine the effects of categorization and censoring on the behavior of the chi-square/likelihood ratio test statistic and two alternative fit indices (CFI and RMSEA) under the context of evaluating measurement invariance. Monte Carlo simulation was used to examine Type I error and power rates for the (a) overall test statistic/fit indices, and (b) change in test statistic/fit indices. Data were generated according to a multiple-group single-factor CFA model across 40 conditions that varied by sample size, strength of item factor loadings, and categorization thresholds. Seven different combinations of model estimators (ML, Yuan-Bentler scaled ML, and WLSMV) and specified measurement scales (continuous, censored, and categorical) were used to analyze each of the simulation conditions. As hypothesized, non-normality increased Type I error rates for the continuous scale of measurement and did not affect error rates for the categorical scale of measurement. Maximum likelihood estimation combined with a categorical scale of measurement resulted in more correct statistical conclusions than the other analysis combinations. For the continuous and censored scales of measurement, the Yuan-Bentler scaled ML resulted in more correct conclusions than normal-theory ML. The censored measurement scale did not offer any advantages over the continuous measurement scale. Comparing across fit statistics and indices, the chi-square-based test statistics were preferred over the alternative fit indices, and ΔRMSEA was preferred over ΔCFI. Results from this study should be used to inform the modeling decisions of applied researchers. However, no single analysis combination can be recommended for all situations. Therefore, it is essential that researchers consider the context and purpose of their analyses.

Weekly Problems Scales: Instruments for Sexually Abused Youth and Their Nonoffending Parents in Treatment

This study’s purpose was to determine if efficient measures could be created to assess multiple problematic behaviors identified in youth who were sexually abused and in treatment. Because of the lack of easily administered brief instruments that assess multiple domains of interest in this population, complementary parent and child assessment measures were developed. The Weekly Problems Scale–Child Version (WPSC) and the Weekly Problems Scale–Parent Version (WPS-P) were created to monitor the weekly progress of the child and family in treatment and focus specifically on common areas of difficulties in this population. Exploratory factor analysis was conducted to assist in identifying the number of underlying dimensions in the scales. Results indicate that the WPS-C and WPS-P demonstrate adequate internal consistency, temporal stability, and construct validity. The WPS-C and WPSP display significant promise as research and clinical assessment tools for use with youth who are sexually abused and their nonoffending parents in treatment.