Christina S. Werner

Advanced nonlinear latent variable modeling: Distribution analytic LMS and QML estimators of interaction and quadratic effects

Interaction and quadratic effects in latent variable models have to date only rarely been tested in practice. Traditional product indicator approaches need to create product indicators (e.g., x 1 2, x 1 x 4) to serve as indicators of each nonlinear latent construct. These approaches require the use of complex nonlinear constraints and additional model specifications and do not directly address the nonnormal distribution of the product terms. In contrast, recently developed, easy-to-use distribution analytic approaches do not use product indicators, but rather directly model the nonlinear multivariate distribution of the measured indicators. This article outlines the theoretical properties of the distribution analytic Latent Moderated Structural Equations (LMS; Klein & Moosbrugger, 2000) and Quasi-Maximum Likelihood (QML; Klein & Muthén, 2007) estimators. It compares the properties of LMS and QML to those of the product indicator approaches. A small simulation study compares the two approaches and illustrates the advantages of the distribution analytic approaches as multicollinearity increases, particularly in complex models with multiple nonlinear terms. An empirical example from the field of work stress applies LMS and QML to a model with an interaction and 2 quadratic effects. Example syntax for the analyses with both approaches is provided.

Methoden der Reliabilitätsbestimmung

Angenommen, Sie sollen bei einer schulpsychologischen Begutachtung entscheiden, ob ein Kind am Unterricht einer normalen Klasse teilnehmen kann oder Sonderunterricht fur Lern behinderte erhalten soll. Wenn Sie hierfur einen Intelligenztest durchfuhren, sollten Sie sich darauf verlassen konnen, dass das Testergebnis messgenau ist, d. h. dass es die „wahre“ Leistungsfahigkeit operationalisiert am IQ moglichst genau widerspiegelt und nicht bei einer Testwiederholung kurze Zeit spater ein deutlich anderes Ergebnis herauskame — die Entscheidung hat schlieslich zentrale Bedeutung fur die Zukunft des Kindes. Messgenauigkeit ist insofern ein ausgesprochen wichtiges Gutekriterium furTests, gerade bei der Individualdiagnostik.

Psychological Resources, Appraisals, and Coping and Their Relationship to Participation in Spinal Cord Injury: A Path Analysis

OBJECTIVE To test the Spinal Cord Injury Adjustment Model and gain a better understanding about whether and how the psychological resources general self-efficacy (SE), purpose in life (PIL), appraisals, and coping influence participation in persons with spinal cord injury (SCI). DESIGN Cross-sectional data collection within the Swiss Spinal Cord Injury Cohort. SETTING Community setting. PARTICIPANTS Persons with SCI (N=516) who are ≥ 16 years old and living in the community in Switzerland. INTERVENTIONS Not applicable. MAIN OUTCOME MEASURES Participation was measured with the restrictions subscale of the Utrecht Scale for Evaluation of Rehabilitation-Participation, General SE with the General Self-Efficacy Scale, PIL with the Purpose in Life Test-Short Form, appraisals with the Appraisal of Life Events Scale, and coping with the Brief COPE. RESULTS General SE (r=.32) and PIL (r=.23) were associated with less participation restrictions. The initial model yielded a poor model fit. The modified final model had an acceptable fit (χ(2)11=36.2; P<.01; root mean square error of approximation=.067 [90% confidence interval: .045-.09]; comparative fit index=.98). A total of 15% of the variance of participation was explained. In the final model, general SE had a moderate direct effect (β=.24) and mediated effects via threat appraisal and challenge appraisal and humor on participation, indicating a partial mediation effect. The association between PIL and participation was indirect: challenge appraisal and humor acted as mediators. CONCLUSIONS The results only partly support the double-mediating effect as suggested in the SCI adjustment model because both direct and indirect effects on participation were observed. Individuals with higher general SE and PIL perceive less participation restrictions. General SE seems an appropriate target to enhance participation. Longitudinal studies are needed to support our findings.

Measurement bias detection through factor analysis

Measurement bias is defined as a violation of measurement invariance, which can be investigated through multigroup factor analysis (MGFA), by testing across-group differences in intercepts (uniform bias) and factor loadings (nonuniform bias). Restricted factor analysis (RFA) can also be used to detect measurement bias. To also enable nonuniform bias detection, we extend RFA with latent moderated structures (LMS) or use a random slope parameterization (RSP). In a simulation study we compare the MGFA, RFA/LMS, and RFA/RSP methods in detecting measurement bias, varying type of bias (uniform, nonuniform), type of the variable that violates measurement invariance (dichotomous, continuous), and its relationship with the trait that we want to measure (independent, dependent). For each condition, 500 sets of data are generated and analyzed with each of the three detection methods, in single run and in an iterative procedure. The RFA methods outperform MGFA when the violating variable is continuous.

Learning through online peer discourse: Structural equation modeling points to the role of discourse activities in individual understanding

Although learning through discourse activities seems well-documented, it is unclear which mechanisms and behavioral variables are involved. What exactly contributes to learning when two or more learners interact in online learning environments? To analyze interrelations between central discourse activities and individual learning outcomes at the level of constructs, we applied structural equation modeling to data collected from 160 dyads engaging in written online learning discourses within a series of homogeneous experiments. We analyzed three theory-based indicators of conceptual elaboration activities during online discourse: the number of questions asked to receive information and expand knowledge, the number of explanations formulated to express individual knowledge, and the amount of on-task discourse. Individual conceptual understanding was represented by objective learning parameters that varied in each particular experimental task. These measured general understanding of the topic addressed and particular understanding of conceptual terms, complemented by the gain in individual self-assessed knowledge. Results of structural equation modeling revealed a strong effect of dyadic conceptual elaboration on individual understanding at the construct level, demonstrating that dyadic elaboration fosters the development of an elaborated individual understanding of specialist concepts and general content knowledge. Moreover, conceptual elaboration was best measured by the number of explanations during discourse. Implications regarding which features of collaborative learning settings promote mutual conceptual elaboration are discussed.

Social Skills: A Resource for More Social Support, Lower Depression Levels, Higher Quality of Life, and Participation in Individuals With Spinal Cord Injury?

OBJECTIVE To examine the relevance of social skills and their different dimensions (ie, expressivity, sensitivity, control) in relation to social support, depression, participation, and quality of life (QOL) in individuals with spinal cord injury (SCI). DESIGN Cross-sectional data collection within the Swiss Spinal Cord Injury Cohort. SETTING Community-based. PARTICIPANTS Individuals with SCI (N=503). INTERVENTIONS Not applicable. MAIN OUTCOME MEASURES Depression, participation, and QOL were measured using the Hospital Anxiety and Depression Scale, the Utrecht Scale for Evaluation of Rehabilitation-Participation, and 5 selected items of the World Health Organization Quality of Life Scale. The Social Skills Inventory and the Social Support Questionnaire were used to assess social skills (expressivity, sensitivity, control) and social support, respectively. RESULTS Structural equation modeling was conducted. In model 1 (χ(2)=27.81; df=19; P=.087; root mean square error of approximation=.033; 90% confidence interval=.000-.052), social skills as a latent variable was related to social support (β=.31; R(2)=.10), depression (β=-.31; total R(2)=.42), and QOL (β=.46; R(2)=.25). Social support partially mediated the effect of social skills on QOL (indirect effect: β=.04; P=.02) but not on depression or participation. In model 2 (χ(2)=27.96; df=19; P=.084; root mean square error of approximation=.031; 90% confidence interval=.000-.053), the social skills dimension expressivity showed a path coefficient of β=.20 to social support and β=.18 to QOL. Sensitivity showed a negative path coefficient to QOL (β=-.15) and control a path coefficient of β=-.15 to depression and β=.24 to QOL. CONCLUSIONS Social skills are a resource related to more social support, lower depression scores, and higher QOL.

Depression in spinal cord injury: assessing the role of psychological resources.

PURPOSE To test the spinal cord injury adjustment model (SCIAM) and to examine how psychological resources may influence depressive symptoms in persons with spinal cord injury (SCI). We expect that (a) higher general self-efficacy (GSE) and higher purpose in life (PIL) are associated with lower levels of depressive symptoms, and that (b) the effect of GSE and PIL on depressive symptoms is mediated by appraisals and coping strategies, as proposed by the SCIAM. METHOD A nationwide cross-sectional survey (the Swiss Spinal Cord Injury Cohort Study) was conducted with individuals with SCI living in the Swiss community (N = 516). Structural equation modeling was used to test relationships between variables as specified in the SCIAM. RESULTS Higher GSE (r = -.54) and PIL (r = -.62) were significantly associated with lower depressive symptoms. The initial model yielded poor model fit. However, the final modified model fitted well, with χ2(21) = 54.00, p < .01, RMSEA = .055 (90% CI [.038, .073]), CFI = .98, explaining 62.9% of the variance of depressive symptoms. PIL had a direct large effect and an indirect effect on depressive symptoms via appraisals and coping strategies. The influence of GSE on depressive symptoms was fully mediated by appraisals and coping strategies. CONCLUSIONS Psychological resources of individuals with SCI can have a direct effect on depressive symptoms. The mediated pathways are present, but not exclusive in our data, yielding only partial support for the mechanism proposed by the SCIAM.