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.

Movements of satellite-monitored humpback whales from New Caledonia

Knowledge of the local and migratory movements of humpback whales (Megaptera novaeangliae) from New Caledonia is very limited. To investigate this topic, we attached satellite-monitored tags to 12 whales off southern New Caledonia. Tag longevity ranged from 1 to 52 days (X = 22.5 days). Tagged whales generally moved to the south or southeast, with several spending time in a previously unknown seamount habitat named Antigonia before resuming movement, generally toward Norfolk Island or New Zealand. However, 1 female with a calf traveled the entire length of the western coast of New Caledonia (~450 km) and then west in the direction of the Chesterfield Reefs, a 19th century American (“Yankee”) whaling ground. None of the New Caledonia whales traveled to or toward eastern Australia, which is broadly consistent with the low rate of interchange observed from photo-identification comparisons between these 2 areas. The connections between New Caledonia and New Zealand, together with the relatively low numbers of whales seen in these places generally, support the idea that whales from these 2 areas constitute a single population that remains small and unrecovered.