In the discussion of mean square difference (MSD) and standard error of measurement (SEM), Barchard (2012) concluded that the MSD between 2 sets of test scores is greater than 2(SEM)[superscript 2] and SEM underestimates the score difference between 2 tests when the 2 tests are not parallel. This conclusion has limitations for 2 reasons. First,…

In multilevel modeling, group-level variables (L2) for assessing contextual effects are frequently generated by aggregating variables from a lower level (L1). A major problem of contextual analyses in the social sciences is that there is no error-free measurement of constructs. In the present article, 2 types of error occurring in multilevel data…

A simulation study compared the performance of robust normal theory maximum likelihood (ML) and robust categorical least squares (cat-LS) methodology for estimating confirmatory factor analysis models with ordinal variables. Data were generated from 2 models with 2-7 categories, 4 sample sizes, 2 latent distributions, and 5 patterns of category…

Recently, R. D. Stoel, F. G. Garre, C. Dolan, and G. van den Wittenboer (2006) reviewed approaches for obtaining reference mixture distributions for difference tests when a parameter is on the boundary. The authors of the present study argue that this methodology is incomplete without a discussion of when the mixtures are needed and show that they…

Across many areas of psychology, concordance is commonly used to measure the (intragroup) agreement in ranking a number of items by a group of judges. Sometimes, however, the judges come from multiple groups, and in those situations, the interest is to measure the concordance between groups, under the assumption that there is some within-group…

We evaluated the statistical power of single-indicator latent growth curve models (LGCMs) to detect correlated change between two variables (covariance of slopes) as a function of sample size, number of longitudinal measurement occasions, and reliability (measurement error variance). Power approximations following the method of Satorra and Saris…

Variants of adaptive Bayesian procedures for estimating the 5% point on a psychometric function were studied by simulation. Bias and standard error were the criteria to evaluate performance. The results indicated a superiority of (a) uniform priors, (b) model likelihood functions that are odd symmetric about threshold and that have parameter…

The correction for attenuation due to measurement error (CAME) has received many historical criticisms, most of which can be traced to the limited ability to use CAME inferentially. Past attempts to determine confidence intervals for CAME are summarized and their limitations discussed. The author suggests that inference requires confidence sets…

Often quantitative data in the social sciences have only ordinal justification. Problems of interpretation can arise when least squares multiple regression (LSMR) is used with ordinal data. Two ordinal alternatives are discussed, dominance-based ordinal multiple regression (DOMR) and proportional odds multiple regression. The Q[superscript 2]…