Zhonglin Wen

Monotonicity of effect sizes: Questioning kappa-squared as mediation effect size measure.

Mediation analysis is important for research in psychology and other social and behavioral sciences. Great progress has been made in testing mediation effects and in constructing their confidence intervals. Mediation effect sizes have also been considered. Preacher and Kelley (2011) proposed and recommended κ² as an effect size measure for a mediation effect. In this article, we argue that κ² is not an appropriate effect size measure for mediation models, because of its lack of the property of rank preservation (e.g., the magnitude of κ² may decrease when the mediation effect that κ² represents increases). Furthermore, κ² can lead to paradoxical results in multiple mediation models. We show that the problem of κ² is due to (a) the improper calculation of the maximum possible value of the indirect effect, and (b) mathematically, the maximum possible indirect effect is infinity, implying that the definition of κ² is mathematically incorrect. At this time, it appears that the traditional mediation effect size measure PM (the ratio of the indirect effect to the total effect), together with some other statistical information, should be preferred for basic mediation models. But for inconsistent mediation models where the indirect effect and the direct effect have opposite signs, the situation is less clear. Other considerations and suggestions for future research are also discussed.

Unconstrained Structural Equation Models of Latent Interactions: Contrasting Residual- and Mean-Centered Approaches

Little, Bovaird and Widaman (2006) proposed an unconstrained approach with residual centering for estimating latent interaction effects as an alternative to the mean-centered approach proposed by Marsh, Wen, and Hau (2004, 2006). Little et al. also differed from Marsh et al. in the number of indicators used to infer the latent interaction factor and how they were represented, but this issue is separate from the mean versus residual centering distinction that was their primary focus. However, their implementation of the Marsh et al. mean-centered approach failed to incorporate the mean structure that Marsh et al. argued was necessary to obtain unbiased estimates. One might suppose that their new approach would suffer this same problem, an issue not addressed by Little et al. However, we demonstrate here why the Little et al. approach obviates this requirement that heretofore was thought to be necessary for all constrained, partially constrained, and unconstrained approaches. Both the Marsh et al. and Little et al. unconstrained approaches typically result in similar results and are much easier to implement than traditional constrained approaches. They differ primarily in that the Little et al. approach is a 2-step approach involving a potentially large number of separate analyses prior to estimating the structural equation model that apparently does not require the estimation of a mean structure, whereas the Marsh et al. approach is a 1-step approach that includes a mean structure.

The Mediating and Moderating Effects of Teacher Preference on the Relations between Students' Social Behaviors and Peer Acceptance

Tested on a sample of 1,365 Hong Kong primary school students from five grades, teacher preference or the extent to which the classroom teacher likes a child in the class was found to both mediate and, to a lesser extent, moderate the relations between childrens social behaviors and peer acceptance across age groups. The mediating effect suggests that peer acceptance responds not only to the behavior of a student but also to how much the classroom teacher likes or dislikes the student. The moderating effect suggests that the associations between student social behaviors and peer acceptance differ as functions of teacher preference. The mediating teacher preference was stronger with younger children, whereas a stronger moderating teacher preference was found for the older children. These findings confirm the supposition that three social processes involving the teacher, children, and peers contribute to childrens social status and relations in the classroom.

Structural Equation Models of Latent Interactions: Clarification of Orthogonalizing and Double-Mean-Centering Strategies

The purpose of this investigation is to compare a new (double-mean-centering) strategy to estimating latent interactions in structural equation models with the (single) mean-centering strategy (Marsh, Wen, & Hau, 2004, 2006) and the orthogonalizing strategy (Little, Bovaird, & Widaman, 2006; Marsh et al., 2007). A key benefit of the orthogonalizing strategy is that it eliminated the need to estimate a mean structure as required by the mean-centering strategy, but required a potentially cumbersome 2-step estimation procedure. In contrast, the double-mean-centering strategy eliminates both the need for the mean structure and the cumbersome 2-stage estimation procedure. Furthermore, although the orthogonalizing and double-mean-centering strategies are equivalent when all indicators are normally distributed, the double-mean-centering strategy is superior when this normality assumption is violated. In summary, we recommend that applied researchers wanting to estimate latent interaction effects use the double-mean-centering strategy instead of either the single-mean-centering or orthogonalizing strategies, thus allowing them to ignore the cumbersome mean structure.

Mediating Teacher Liking and Moderating Authoritative Teachering on Chinese Adolescents' Perceptions of Antisocial and Prosocial Behaviors

The authors present a model of adolescents’ peer relations in the classroom that integrates 3 social processes involving the adolescent students, the classroom teacher, and peers. One of the hypotheses was that teacher liking of students mediated the relation between students’ social behaviors (e.g., antisocial disruption and prosocial leadership) and peer acceptance. This mediating teacher influence was also hypothesized to be moderated by the extent to which adolescent students perceived their teacher to be authoritative in teachering. These hypotheses were tested and supported on the basis of a sample of 659 Chinese middle school students. A discussion of these results focuses on the classroom teacher as a social context in the study of children’s social interactions in the classroom. Social developmental research is often approached in one of two ways. One focuses on age-related developmental processes internal to children and adolescents. In peer relations research, the investigation of peer perceptions of antisocial and prosocial behaviors, for example, constitutes an internal approach. The other approach emphasizes how these internal processes interact with social settings that contextualize development. An examination of

Structural Equation Models of Latent Interactions: An Appropriate Standardized Solution and Its Scale-Free Properties.

Standardized parameter estimates are routinely used to summarize the results of multiple regression models of manifest variables and structural equation models of latent variables, because they facilitate interpretation. Although the typical standardization of interaction terms is not appropriate for multiple regression models, straightforward alternatives are well known (Aiken & West, 1991; Friedrich, 1982). Whereas the analogous problem exists for the estimation of latent interactions in structural equation modeling (SEM), the problem is more complex and apparently has not been resolved. Here we demonstrate that the appropriate “standardized” parameter estimates are easily formulated from parameter estimates routinely available from existing SEM software packages. Some properties of the appropriate “standardized” solution are mathematically derived, including the demonstration that the main and interaction effects are scale-free, as are the factor loadings. These desirable properties of the standardized solution are illustrated with a simulation data set using the unconstrained approach (Marsh, Wen, & Hau, 2004) to estimating latent interactions. These results support the use of the appropriate “standardized” solutions in interpreting and comparing SEM estimates of latent interactions.

Interaction Effects in Growth Modeling: A Full Model.

In substantively important research, Li, Duncan, and Acock (2000) and Duncan, Duncan, Strycker, Li, and Alpert (1999) extended Jöreskog and Yangs (1996) structural equation model of latent interactions to latent growth modeling. We address 2 concerns with their approach: (a) Parameter constraints specified in their models were apparently inappropriate, and (b) they did not specify a full interaction model. Here we present more appropriate constraints and demonstrate a full interaction model for latent growth modeling that simultaneously estimates (a) the interaction between rates of change (slopes) of 2 predictors on the rate of change (slope) of the outcome and (b) the interaction between initial levels of growth (intercepts) of 2 predictors on the initial level (intercept) of outcome. Based on mathematical derivation and a comparison of alternative models fitted to simulated data, we show that our model is more appropriate and that their models can result in seriously biased parameter estimates.

A Comparison of Strategies for Forming Product Indicators for Unequal Numbers of Items in Structural Equation Models of Latent Interactions

This Monte Carlo simulation study investigated different strategies for forming product indicators for the unconstrained approach in analyzing latent interaction models when the exogenous factors are measured by unequal numbers of indicators under both normal and nonnormal conditions. Product indicators were created by (a) multiplying parcels of the larger scale by items of the smaller scale, and (b) matching items according to reliability to create several product indicators, ignoring those items with lower reliability. Two scaling approaches were compared where parceling was not involved: (a) fixing the factor variances, and (b) fixing 1 loading to 1 for each factor. The unconstrained approach was compared with the latent moderated structural equations (LMS) approach. Results showed that under normal conditions, the LMS approach was preferred because the biases of its interaction estimates and associated standard errors were generally smaller, and its power was higher than that of the unconstrained approach. Under nonnormal conditions, however, the unconstrained approach was generally more robust than the LMS approach. It is recommended to form product indicators by using items with higher reliability (rather than parceling) in the matching and then to specify the model by fixing 1 loading of each factor to unity when adopting the unconstrained approach.

Examining and Controlling for Wording Effect in a Self-Report Measure: A Monte Carlo Simulation Study

Wording effect refers to the systematic method variance caused by positive and negative item wordings on a self-report measure. This Monte Carlo simulation study investigated the impact of ignoring wording effect on the reliability and validity estimates of a self-report measure. Four factors were considered in the simulation design: (a) the number of positively and negatively worded items, (b) the loadings on the trait and the wording effect factors, (c) sample size, and (d) the magnitude of population validity coefficient. The findings suggest that the unidimensional model that ignores the negative wording effect would underestimate the composite reliability and criterion-related validity, but overestimate the homogeneity coefficient. The magnitude of relative bias of the composite reliability was generally small and acceptable, whereas the relative bias for the homogeneity coefficient and criterion-related validity coefficient was negatively correlated with the strength of the general trait factor.

The music self-perception inventory: Development of a short form

Music self-concept integrates perceptions, beliefs, and self-schemas about a person’s musical abilities and potential. Like other self-concept dimensions, it is multifaceted, hierarchically organized and has implications for motivation toward musical practice. The Music Self-Perception Inventory (MUSPI) is a theoretically based instrument assessing six specific music self-concept dimensions, as well as global music self-concept. Nonetheless, its applicability is limited by its length (84 items). In this study, we developed and validated a 28-item short form of the MUSPI, and showed that the short form yielded equivalent psychometric properties as the original. We validated the original MUSPI on a first sample and used these results to develop a shorter version (MUSPI-S), which we then cross-validated using a new independent sample. We also tested whether the MUSPI-S psychometric properties generalized (were invariant) across gender and grade-differentiated subgroups. Finally, we examined the convergent validity of the MUSPI and MUSPI-S. Results highlighted the psychometric soundness of the MUSPI-S on all criteria, and showed that it presented patterns of associations with other constructs equivalent to those observed with the original MUSPI.