Applied Psychological Measurement

In this article the authors focus on the issue of the nonuniqueness of the maximum likelihood (ML) estimator of proficiency level in item response theory (with special attention to logistic models). The usual maximum a posteriori (MAP) method offers a good alternative within that framework; however, this article highlights some drawbacks of its use. The authors then propose an iteratively based MAP estimator (IMAP), which can be useful in detecting multiple local likelihood maxima. The efficiency of the IMAP estimator is studied and is compared to the ML and MAP methods by means of a simulation study.

Peer nominations are used widely in psychological and sociological research to examine intergroup dynamics, even though this assessment tool suffers from thorny methodological problems: Gender, ethnic, age, and trait compositions vary across subsamples, subjects differ in the number of nominations they make, and the issue of sampling without replacement is often ignored. To overcome these problems, the authors have developed a differential index for the peer nominations procedure, with the number of individuals chosen above or below chance as the unit of measure. The index is specifically designed for use with individuals (as opposed to subgroups like classrooms), so that group means, confidence intervals, and standard deviations are readily determined, opening the door to research designs that go beyond null hypothesis testing. Here, we introduce the index and illustrate its unique capabilities in a study examining preference and bias reciprocity among fourth-grade students.

The severity of bias in respondents’ self-reports due to acquiescence response style (ARS) and extreme response style (ERS) depends strongly on how consistent these response styles are over the course of a questionnaire. In the literature, different alternative hypotheses on response style (in)consistency circulate. Therefore, nine alternative models are derived and fitted to secondary and primary data. It is found that response styles are best modeled as a tau-equivalent factor complemented with a time-invariant autoregressive effect. This means that ARS and ERS are largely but not completely consistent over the course of a questionnaire, a finding that has important implications for response style measurement and correction.

Lengthy scales or testlets pose certain challenges for structural equation modeling (SEM) if all the items are included as indicators of a latent construct. Three general approaches to modeling lengthy scales in SEM (parceling, latent scoring, and shortening) have been reviewed and evaluated. A hypothetical population model is simulated containing two exogenous constructs with 14 indicators each and an endogenous construct with four indicators. The simulation generates data sets with varying numbers of response options, two types of distributions, factor loadings ranging from low to high, and sample sizes ranging from small to moderate. The population model is varied to incorporate one of the following: (a) single parcels, (b) various parcels as indicators of two exogenous constructs, (c) latent scores as observed exogenous variables, and (d) four and six individual items as indicators of two exogenous constructs. The dependent variables evaluated are biases in the covariance and partial covariance population parameters. Biases in these parameters are found to be minimal under the following conditions: (a) when parcels of indicators of five response options are used as indicators of two latent exogenous constructs, (b) when latent scores are used as observed variables at sample sizes above 100 and with indicators that are relatively less skewed in the case of dichotomous indicators, and (c) when four or six individual items with high or diverse factor loadings are used as indicators of two exogenous constructs. These findings provide guidelines for resolving the inconsistency of findings from applying various approaches to empirical data.