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.

Correlation of the middle Eocene Kellogg Shale of northern California

The Kellogg Shale of northern California has traditionally been considered to be late Eocene in age on the basis of benthic foraminifer, radiolarian, and diatom correlations. The 30-m-thick Kellogg section exposed west of Byron, California, however, contains middle Eocene planktonic foraminifers (Zone P12), coccoliths (Subzones CP13c and CP14a), silicoflagellates (Dictyocha hexacantha Zone), and diatoms. Quantitative studies of the silicoflagellates and diatoms show a general cooling trend through the section which is consistent with paleoclimatic trends for this part of the middle Eocene (ca. 42-45 Ma) from elsewhere in the world. Seven new silicoflagellate taxa (Corbisema angularis. C, exilis, C, hastate miranda, C. inermis ballantina, C. regina, Dictyocha byronalis, Naviculopsis Americana) and one new coccolithophorid species (Helicosphaera neolophota) are described.