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.

Linkage & Selective Mapping and QTL Analysis in a Harosoy x Clark population of 300 RILs

Four of the 12 major Glycine max ancestors of all modern elite U.S.A. soybean cultivars were the grandparents of Harosoy and Clark, so a Harosoy x Clark population would include some of that genetic diversity. A mating of eight Harosoy and eight Clark plants generated eight F1 plants. The eight F1:2 families were advanced via a plant-to-row selfing method to produce 300 F6-derived RILs that were genotyped with 266 SSR, 481 SNP, and 4 classical markers. SNPs were genotyped with the Illumina 1536-SNP assay. Three linkage maps, SSR, SNP, and SSR-SNP, were constructed with a genotyping error of < 1 %. Each map was compared with the published soybean consensus map. The best subset of 94 RILs for a high-resolution framework (joint) map was selected based on the expected bin length statistic computed with MapPop. The QTLs of seven traits measured in a 2-year replicated performance trial of the 300 RILs were identified using composite interval mapping (CIM) and multiple-interval mapping (MIM). QTL x Year effects in multiple trait analysis were compared with results of multiple-interval mapping. QTL x QTL effects were identified in MIM.