Randall E. Schumacker

Interaction and Nonlinear Effects in Structural Equation Modeling

Contents: Preface. E.E. Rigdon, R.E. Schumacker, W. Wothke, A Comparative Review of Interaction and Nonlinear Modeling. F.Y. Jonsson, Modeling Interaction and Nonlinear Effects: A Step-by-Step LISREL Example. M.C. Neale, Modeling Interaction and Nonlinear Effects With Mx: A General Approach. R.A. Ping, Jr., EQS and LISREL Examples Using Survey Data. P.K. Wood, D.J. Erikson, Estimating Interaction and Nonlinear Effects With SAS. K.A. Bollen, P. Paxton, Two-Stage Least Squares Estimation of Interaction Effects. F. Li, P. Harmer, Modeling Interaction Effects: A Two-Stage Least Squares Example. R.L. Tate, Effect Decomposition in Interaction and Nonlinear Models. B. Laplante, S. Sabourin, L-G. Cournoyer, J. Wright, Estimating Nonlinear Effects Using a Structured Means Intercept Approach. K. Schermelleh-Engel, A. Klein, H. Moosbrugger, Estimating Nonlinear Effects Using a Latent Moderated Structural Equations Approach. K.G. Joreskog, Interaction and Nonlinear Modeling: Issues and Approaches.

Multiple Regression Approach to Analyzing Contingency Tables: Post Hoc and Planned Comparison Procedures

Abstract Post hoc and planned comparison procedures for interpreting chi-square contingency-table test results, not currently discussed in most standard textbooks, are presented. A planned comparison procedure that simplifies the tedious process of partitioning a contingency table by creating single-degree-of-freedom contrasts through a regression-based approach is proposed. Importantly, these post hoc methods supplement the analysis of standardized residuals by reporting the percentage contribution for each cell to the overall chi-square statistic (relative contribution) and to the percentage of variance shared by the two factors (absolute contribution). Both methods can be readily incorporated into existing statistical packages such as SAS or SPSS. The equivalence of the percentage contribution method to the more common standardized residual method is also presented along with an example of a typical application.

Latent Variable Interaction Modeling

Latent variable interaction modeling with continuous observed variables is presented using 2 different approaches. The 1st approach analyzes data using a LISREL 8.30 program where the latent interaction variable is defined by multiplying pairs of observed variables. The 2nd approach analyzes data using PRELIS2 and SIMPLIS programs where the latent interaction variable is defined by multiplying the latent variable scores of the exogeneous latent independent variables. The programs used to create the multivariate normal observed variables and conduct the analyses for the 2 different approaches are given in the appendixes. The product indicant and latent variable score approach produced similar gamma coefficients in their hypothesized models but differed in their standard errors for the gamma coefficients. The latent variable score approach holds the promise of being easier to implement and can be applied to more complex latent variable interaction models.

A Practical Approach to Monitoring Recovery: Development of a Perceived Recovery Status Scale

Laurent, CM, Green, JM, Bishop, PA, Sjökvist, J, Schumacker, RE, Richardson, MT, and Curtner-Smith, M. A practical approach to monitoring recovery: development of a perceived recovery status scale. J Strength Cond Res 25(3): 620-628, 2011-The aim of this study was to develop and test the practical utility of a perceived recovery status (PRS) scale. Sixteen volunteers (8 men, 8 women) performed 4 bouts of high-intensity intermittent sprint exercise. After completion of the baseline trial, in a repeated-measures design, subjects were given variable counterbalanced recovery periods of 24, 48, and 72 hours whereupon they repeated an identical intermittent exercise protocol. After a warm-up period, but before beginning each subsequent bout of intermittent sprinting, each individual provided their perceived level of recovery with a newly developed PRS scale. Similar to perceived exertion during exercise, PRS was based on subjective feelings. The utility of the PRS scale was assessed by measuring the level of agreement of an individuals perceived recovery relative to their performance during the exercise bout. Perceived recovery status and change (both positive and negative) in sprint performance during multiple bouts of repeated sprint exercise were moderately negative correlated (r = −0.63). Additionally, subjects were able to accurately assess level of recovery using the PRS scale indicated by correspondence with negative and positive changes in total sprint time relative to their previous session. The ability to detect changes in performance using a noninvasive psychobiological tool to identify differences in performance was independent of other psychological and physiological markers measured during testing, because there were no differences (p > 0.05) among ratings of perceived exertion (RPE), heart rate, blood lactate concentration, or session RPE values among any of the performance trials. Although further study is needed, current results indicate a subjective approach may be an effective means for assessing recovery from day to day, at least under similar conditions.

A Rasch Perspective

Measurement error is a common theme in classical measurement models used in testing and assessment. In classical measurement models, the definition of measurement error and the subsequent reliability coefficients differ on the basis of the test administration design. Internal consistency reliability specifies error due primarily to poor item sampling. Rater reliability indicates error due to inconsistency among raters. For estimates of test-retest reliability, error is attributed mainly to changes over time. In alternate-forms reliability, error is assumed to be due largely to variation between samples of items on test forms. Rasch models can also compute reliability estimates of scores under different test situations. The authors therefore present the Rasch perspective on calculating reliability (measurement error) and present Rasch measurement model programs to compute the various reliability estimates.

Confirmatory Factor Analysis With Different Correlation Types and Estimation Methods

Structural equation modeling techniques can use different correlation coefficients and different estimation methods in confirmatory factor analysis (CFA). The rationale for examining correlation types and estimation methods is related to their effect on the weight matrix (W-1) in the CFA formula for determining the fit function statistics. The results of this study help us to understand that the type of correlation matrix and estimation method effects factor loadings and fit functions. Some suggested alternatives are to use either a limited information estimator for categorical variable analysis or multinomial full information estimators based on modern item response theory.

Model specification searches in structural equation modeling using tabu search

This article introduces an alternative structural equation modeling (SEM) specification search approach that is based on the Tabu search procedure. Using data with known structure, the performance of the Tabu search is illustrated. The results demonstrate the capabilities of the Tabu search procedure for conducting specification searches in SEM.

A Comparison of Logistic Regression and Analysis of Variance Differential Item Functioning Detection Methods

Differential item functioning (DIF) detection rates were compared between logistic regression and analysis of variance for dichotomously scored items. These two DIF methods were compared using simulated binary item response data sets of varying test length (20, 40, and 60 items), sample size (200, 400, and 600 examinees), discrimination type (fixed and varying), and relative underlying ability (equal and unequal) between groups under conditions of uniform DIF, nonuniform DIF, combination DIF, and false positive errors. These test conditions were replicated 100 times. For both DIF detection methods, a test length of 20 items was sufficient for satisfactory DIF detection with detection rate increasing as sample size increased. With the exception of uniform DIF, the logistic regression method had higher mean detection rates than the analysis of variance method. Because the type of DIF present in real data is rarely known, the logistic regression method is recommended for most practical applications.

An Evaluation of Rosenthal and Rubin’s Binomial Effect Size Display

The binomial effect size display (BESD) has been proposed by Rosenthal and Rubin (1979, 1982; Rosenthal, 1990; Rosenthal & Rosnow, 1991) as a format for presenting effect sizes associated with certain experimental and nonexperimental research. An evaluation of the BESD suggests that its application is limited to presenting the results of 2 × 2 tables where φ is employed as the index of effect size. Findings indicate that the BESD provides little added information beyond an examination of the raw percentages in the 2 × 2 table and dramatically distorts effect sizes when binomial success rates vary from .50.

Predictors of Modern Homonegativity among Professional Counselors

Modern homonegativity is prejudice against gay men and lesbians based on current issues such as equality and social justice. Predictors of modern homonegativity among professional counselors were examined. Logistic regression analysis indicated that frequency of church attendance, not having a gay or lesbian friend, being a member of the Republican political party, not having participated in training about gay and lesbian sexual identities in the 12 months prior to the study, and being older predicted the probability of counselors having high modern homonegativity scores.