W. Holmes Finch

Confirmatory Factor Analytic Procedures for the Determination of Measurement Invariance.

Confirmatory factor analytic (CFA) procedures can be used to provide evidence of measurement invariance. However, empirical evaluation has not focused on the accuracy of common CFA steps used to detect a lack of invariance across groups. This investigation examined procedures for detection of test structure differences across groups under several conditions through simulation. Specifically, sample size, number of factors, number of indicators per factor, and the distribution of the observed variables were manipulated, and 3 criteria for assessing measurement invariance were evaluated. Power and Type I error were examined to evaluate the accuracy of detecting a lack of invariance. Results suggest that the chi-square difference test adequately controls the Type I error rate in nearly all conditions, and provides relatively high power when used with maximum likelihood (ML) estimation and normally distributed observed variables. In addition, the power of the test to detect group differences for dichotomous observed variables with robust weighted least squares estimation was generally very low.

Conducting Confirmatory Latent Class Analysis Using M"plus".

Latent class analysis (LCA) is an increasingly popular tool that researchers can use to identify latent groups in the population underlying a sample of responses to categorical observed variables. LCA is most commonly used in an exploratory fashion whereby no parameters are specified a priori. Although this exploratory approach is reasonable when very little prior research has been conducted in the area under study, it can be very limiting when much is already known about the variables and population. Confirmatory latent class analysis (CLCA) provides researchers with a tool for modeling and testing specific hypotheses about response patterns in the observed variables. CLCA is based on placing specific constraints on the parameters to reflect these hypotheses. The popular and easy-to-use latent variable modeling software package Mplus can be used to conduct a variety of CLCA types using these parameter constraints. This article focuses on the basic principles underlying the use of CLCA, and the Mplus programming code necessary for carrying it out.

Multigroup Confirmatory Factor Analysis: Locating the Invariant Referent Sets.

Multigroup confirmatory factor analysis (MCFA) is a popular method for the examination of measurement invariance and specifically, factor invariance. Recent research has begun to focus on using MCFA to detect invariance for test items. MCFA requires certain parameters (e.g., factor loadings) to be constrained for model identification, which are assumed to be invariant across groups, and act as referent variables. When this invariance assumption is violated, location of the parameters that actually differ across groups becomes difficult. The factor ratio test and the stepwise partitioning procedure in combination have been suggested as methods to locate invariant referents, and appear to perform favorably with real data examples. However, the procedures have not been evaluated through simulations where the extent and magnitude of a lack of invariance is known. This simulation study examines these methods in terms of accuracy (i.e., true positive and false positive rates) of identifying invariant referent variables.

Detection of Crossing Differential Item Functioning: A Comparison of Four Methods

Differential item functioning (DIF) continues to receive attention both in applied and methodological studies. Because DIF can be an indicator of irrelevant variance that can influence test scores, continuing to evaluate and improve the accuracy of detection methods is an essential step in gathering score validity evidence. Methods for detecting uniform DIF are well established, whereas those for identifying the presence of nonuniform or crossing DIF are less clearly understood. Four such methods were compared: simultaneous item bias test (SIBTEST), logistic regression, item response theory likelihood ratio test, and confirmatory factor analysis. Factors manipulated were sample size, ability differences between groups, percentage of DIF, and the underlying model used to generate the data. Results suggest that all methods were able to control Type I error, but SIBTEST had the highest power of the approaches compared. Problems with detection rates were evident with different underlying models.

A Comparison of Two-Group Classification Methods

The statistical classification of N individuals into G mutually exclusive groups when the actual group membership is unknown is common in the social and behavioral sciences. The results of such classification methods often have important consequences. Among the most common methods of statistical classification are linear discriminant analysis, quadratic discriminant analysis, and logistic regression. However, recent developments in the statistics literature have brought new and potentially more flexible classification models to the forefront. Although these new models are increasingly being used in the physical sciences and marketing research, they are still relatively little used in the social and behavioral sciences. The purpose of this article is to provide a comparison of these modern methods with the classical methods widely used in situations that are relevant in the social and behavioral sciences. This study uses a large-scale Monte Carlo simulation study for the comparisons, as analytic comparisons are often not tractable. Results indicate that classification and regression trees generally produced the highest classification accuracy of all techniques tested, though study design characteristics such as sample size and model complexity can greatly influence optimal choice or effectiveness of statistical classification method.

Adolescent Characteristics by Type of Long-Term Aim in Life

Surveys were administered to adolescents (N = 144) to determine if young people varied based on the type of long-term aims they held. Using cluster analysis, four groups emerged from the data: youth without clear long-term aims, youth with self-oriented long-term aims, youth with other-oriented long-term aims, and youth with both self- and other-oriented long-term aims. The latter two clusters represent potentially purposeful youth and the self-oriented cluster represents youth with meaning in their lives. Therefore, the authors were able to compare potentially purposeful youth to youth with meaning and to youth with neither purpose nor meaning in their lives. Youth with other-oriented long-term aims were more likely to be searching for a purpose, to have identified a purpose, to report higher levels of life satisfaction, and to score higher on openness. Implications for understanding the purpose construct and for fostering purpose among adolescents are addressed.

Purpose in life among high ability adolescents

Leading high ability scholars have proposed theories that suggest a purpose in life may be particularly prevalent among high ability youth; however, the prevalence of purpose has not been empirically assessed among this population. Therefore using in‐depth interviews the present study established the prevalence of purpose among a sample of high ability adolescents and compared it to the prevalence of purpose among a sample of typical youth (N= 203). Results revealed that purpose was present among high ability early and late adolescents at roughly the same rate as among more typical youth. However, high ability youth reported embracing self‐oriented life goals earlier than more typical youth, and they identified different types of inspiring life purposes. Implications, including steps practitioners can take to foster purpose among high ability youth, are addressed.

Misclassification Rates for Four Methods of Group Classification Impact of Predictor Distribution, Covariance Inequality, Effect Size, Sample Size, and Group Size Ratio

This study compares the classification accuracy of linear discriminant analysis (LDA), quadratic discriminant analysis (QDA), logistic regression (LR), and classification and regression trees (CART) under a variety of data conditions. Past research has generally found comparable performance of LDA and LR, with relatively less research on QDA and virtually none on CART. This study uses Monte Carlo simulations to assess the crossvalidated predictive accuracy of these methods, while manipulating such factors as predictor distribution, sample size, covariance matrix inequality, group separation, and group size ratio. The results indicate that QDA performs as well as or better than the other alternatives in virtually all conditions. Suggestions for practitioners are provided.

The Canonical Relationship Between Sensory-Motor Functioning and Cognitive Processing in Children with Attention-Deficit/Hyperactivity Disorder

Children with Attention-Deficit/Hyperactivity Disorder (ADHD) typically exhibits a pattern of behavioral deficits, impairment in academic achievement, and cognitive processing, and presents with sensory-motor deficits. This study examined the relationships between sensory-motor tasks, cognitive processing, and academic achievement for a group of 67 children with ADHD. Strong canonical correlations emerged between sensory-motor functioning and academic achievement (.93) and sensory-motor functioning and cognitive processing (.98). An analysis of the redundancy coefficient showed that sensory-motor skills accounted for 65% of the variance in the achievement variables and 31% of the variance in the cognitive processing variables. The strong relationship between sensory-motor skills and higher order cognitive processes indicates that early assessment of sensory-motor skills may be useful in the identification of subsequent deficits in academic performance. Neuropsychologists should carefully consider the contribution of sensory-motor functioning to the more widely studied and assessed constructs of academic, behavioral, and emotional problems in children with ADHD.

Estimation of MIMIC Model Parameters with Multilevel Data.

The purpose of this simulation study was to assess the performance of latent variable models that take into account the complex sampling mechanism that often underlies data used in educational, psychological, and other social science research. Analyses were conducted using the multiple indicator multiple cause (MIMIC) model, which is a flexible and effective tool for relating observed and latent variables. The data were simulated in a hierarchical framework (e.g., individuals nested in schools) so that a multilevel modeling approach would be appropriate. Analyses were conducted accounting for and not accounting for the nested data to determine the impact of ignoring such multilevel data structures in full structural equation models. Results highlight the differences in modeling results when the analytic strategy is congruent with the data structure and what occurs when this congruency is absent. Type I error rates and power for the standard and multilevel methods were similar for within-cluster variables and for the multilevel model with between-cluster variables. However, Type I error rates were inflated for the standard approach when modeling between-cluster variables.