Symmetry considerations are important in science, and Group Theory is a theory of symmetry. Classical Measurement Theory is the most used measurement theory in the social and behavioral sciences. In this article, the author uses Matrix Lie (Lee) group theory to formulate a measurement model. Symmetry is defined and illustrated using symmetries of…

The frequent practice of overall fit evaluation for latent variable models in educational and behavioral research is reconsidered. It is argued that since overall plausibility does not imply local plausibility and is only necessary for the latter, local misfit should be considered a sufficient condition for model rejection, even in the case of…

The detection of differential item functioning (DIF) is important in psychological and behavioral sciences. Standard DIF detection methods perform an item-by-item test iteratively, often assuming that all items except the one under investigation are DIF-free. This article proposes a Bayesian adaptive Lasso method to detect DIF in graded response…

This note is concerned with evaluation of location parameters for polytomous items in multiple-component measuring instruments. A point and interval estimation procedure for these parameters is outlined that is developed within the framework of latent variable modeling. The method permits educational, behavioral, biomedical, and marketing…

It is demonstrated that the popular three-parameter logistic model can lead to markedly inaccurate individual ability level estimates for mixture populations. A theoretically and empirically important setting is initially considered where (a) in one of two subpopulations (latent classes) the two-parameter logistic model holds for each item in a…

A common problem in exploratory factor analysis is how many factors need to be extracted from a particular data set. We propose a new method for selecting the number of major common factors: the Hull method, which aims to find a model with an optimal balance between model fit and number of parameters. We examine the performance of the method in an…

The logistic person response function (PRF) models the probability of a correct response as a function of the item locations. Reise (2000) proposed to use the slope parameter of the logistic PRF as a person-fit measure. He reformulated the logistic PRF model as a multilevel logistic regression model and estimated the PRF parameters from this…

Following G. T. Fechner (1966), thresholds have been conceptualized as the amount of intensity needed to transition between mental states, such as between a states of unconsciousness and consciousness. With the advent of the theory of signal detection, however, discrete-state theory and the corresponding notion of threshold have been discounted.…

Two experiments examined how pigeons differentiate response patterns along the dimension of number. In Experiment 1, 5 pigeons received food after pecking the left key at least N times and then switching to the right key (Mechner's Fixed Consecutive Number schedule). Parameter N varied across conditions from 4 to 32. Results showed that run length…

Correlational analyses are one of the most popular quantitative methods, yet also one of the mostly frequently misused methods in social and behavioral research, especially when analyzing ordinal data from Likert or other rating scales. Although several correlational analysis options have been developed for ordinal data, there seems to be a lack…

We studied the choice behavior of 2 monkeys in a discrete-trial task with reinforcement contingencies similar to those Herrnstein (1961) used when he described the matching law. In each session, the monkeys experienced blocks of discrete trials at different relative-reinforcer frequencies or magnitudes with unsignalled transitions between the…

Fuzzy trace theory posits that during development the use of verbatim information for solving transitive relationships shifts to the use of gist information. In cognitive developmental research that uses a cross-sectional design, the binomial mixture model is often used to identify such shifts. Because the binomial mixture model assumes equal task…