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.

METHODS OF CONTROLLING COYOTES, BOBCATS, AND FOXES

In reviewing methods of predator control, it would first seem appropriate to define what is meant "by "methods" and what is meant by "control." Taking the last term first, control, as applied to the predatory coyotes, bobcats, and foxes, may be defined as regulating the numbers of these animals to the point where the economic losses for which they are responsible will be reduced to a practicable minimum. In some situations, area control, i.e., limiting the numbers of the offending predator over wide areas, may be necessary for satisfactory reduction of economic losses; in other situations, spot control or localized reduction of numbers of a certain predator may be called for; in still other situations, elimination of an individual animal may be all the control that is needed. In no sense is control, as applied to coyotes, bobcats, and foxes, intended to mean extermi¬nation of a species. The term "methods" is interpreted as meaning the procedures employed against coyotes, bobcats, and foxes, and not the broader systems of predator control such as the paid hunter system, the extension system, or the much-discredited bounty system. For an excellent review of the systems of predator control, see Latham (l).

METHODS OF CONTROLLING STARLINGS AND BLACKBIRDS

Most people have accepted the fact that all living things can be beneficial to mankind in some way or other. This is especially true of our wild birds, since they provide enjoyment and wholesome recreation for most of us, regardless of whether we live on farms or in the city. But despite the fact that wild birds are for the most part beneficial, at times individuals or populations of certain species can seriously affect man's interests. When such situations occur, some measures of relief are desirable and usually eagerly sought. This report is not intended to answer all the questions that may arise concerning problems with blackbirds and starlings; instead, it is merely a summary of measures used to protect agricultural crops from these birds.