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…

This note is concerned with the benefits that can result from the use of the maximal reliability and optimal linear combination concepts in educational and psychological research. Within the widely used framework of unidimensional multi-component measuring instruments, it is demonstrated that the linear combination of their components that…

The recently proposed "continuous-time latent curve model with structured residuals" (CT-LCM-SR) addresses several challenges associated with longitudinal data analysis in the behavioral sciences. First, it provides information about process trends and dynamics. Second, using the continuous-time framework, the CT-LCM-SR can handle…

This paper aims to advocate for a balanced approach to model fit evaluation in structural equation modeling (SEM). The ongoing debate surrounding chi-square test statistics and fit indices has been characterized by ambiguity and controversy. Despite the acknowledged limitations of relying solely on the chi-square test, its careful application can…

The replication crisis in social and behavioral sciences has raised concerns about the reliability and validity of empirical studies. While research in the literature has explored contributing factors to this crisis, the issues related to analytical tools have received less attention. This study focuses on a widely used analytical tool -…

Data in social and behavioral sciences typically contain measurement errors and also do not have predefined metrics. Structural equation modeling (SEM) is commonly used to analyze such data. This article discuss issues in latent-variable modeling as compared to regression analysis with composite-scores. Via logical reasoning and analytical results…

Mediation analysis plays an important role in understanding causal processes in social and behavioral sciences. While path analysis with composite scores was criticized to yield biased parameter estimates when variables contain measurement errors, recent literature has pointed out that the population values of parameters of latent-variable models…

Exploratory factor analysis (EFA) is often conducted with ordinal data (e.g., items with 5-point responses) in the social and behavioral sciences. These ordinal variables are often treated as if they were continuous in practice. An alternative strategy is to assume that a normally distributed continuous variable underlies each ordinal variable.…

The focus on the individual that is possible in analyzing behavioral data provides the possibility of investigating sequencing effects. Autocorrelation--as illustrated with classroom data from a previous study--can cause standard procedures to underestimate the magnitude of measurement error. Recommendations are made to reduce the effects of…

The authors compare the operating characteristics of the bootstrap-F approach, a direct extension of the work of Berkovits, Hancock, and Nevitt, with Huynh's improved general approximation (IGA) and the Brown-Forsythe (BF) multivariate approach in a mixed repeated measures design when normality and multisample sphericity assumptions do not hold.…

Effects of response guided experimentation in applied behavior analysis on Type I error rates are explored. Data from T. A. Matyas and K. M. Greenwood (1990) suggest that, when visual inspection is combined with response guided experimentation, Type I error rates can be as high as 25%. (SLD)

This paper analyzes ways in which the methods used to measure psychological constructs contribute invalidity to measurements. The analysis distinguishes between inadequacies stemming from the behaviors selected for measurement and the harmful effects generated by the measurement operations themselves. (BS)

The importance of regression diagnostics in detecting influential data points is discussed, and five statistics are recommended for the applied researcher. The suggested diagnostics were used on a dataset of 24 subjects, and effects were analyzed. Colinearity-based diagnostics and diagnostics for a variety of procedures are discussed. (SLD)

In educational research, nonessential factors are commonly ignored and when accounted for, they are often treated statistically as fixed effects. Yet many researchers in these situations generalize their findings beyond the specific levels selected; however, the analyses may require treating the factor as a random effect. Such inappropriate…