Equivalent Structural Equation Models: A Challenge and Responsibility

Relevant aspects of the example provided by Raykov and Marcoulides (2001) Raykov, T. and Marcoulides, G. A. 2001. Can there be infinitely many models equivalent to a given covariance structure model?. Structural Equation Modeling, 8: 142–149. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar] are emphasized, specifically the distinctiveness of infinitely many members of its sequence of equivalent structural equation models. This emphasis appears to be needed in light of recent statements by Markus (2002) Markus, K. A. 2002. Statistical equivalence, semantic equivalence, eliminative induction and the Raykov–Marcoulides proof of infinite equivalence. Structural Equation Modeling, 9: 503–522. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar], whose intended counterexamples do not present a disconfirmation of any of the developments of Raykov and Marcoulides (2001) Raykov, T. and Marcoulides, G. A. 2001. Can there be infinitely many models equivalent to a given covariance structure model?. Structural Equation Modeling, 8: 142–149. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]. Issues pertaining to differentiation between equivalent models 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.     

Validation of the child sex abuse attitude scale through confirmatory factor analysis

A validation study was conducted on the Child Sex Abuse Attitude Scale (CSAAS) using confirmatory factor analysis (CFA) to examine factor structure. The CSAAS was developed based on Festinger's (1957) theory of attitude development resulting in a 4‐factor first‐order structure (cognition, value, affect, and behavior) and a single‐factor 2nd‐order structure (attitude). A sample of 215 school psychologists, members of the National Association of School Psychologists, responded to the CSAAS survey. CFA results supported the hypothesized factor structure of the CSAAS, thus indicating the plausibility of a 4‐factor 1st‐order and a single‐factor higher order structure of the CSAAS.     

Residual Structures in Latent Growth Curve Modeling

This article presents relevant research on Bayesian methods and their major applications to modeling in an effort to lay out differences between the frequentist and Bayesian paradigms and to look at the practical implications of these differences. Before research is reviewed, basic tenets and methods of the Bayesian approach to modeling are presented and contrasted with basic estimation results from a frequentist perspective. It is argued that Bayesian methods have become a viable alternative to traditional maximum likelihood-based estimation techniques and may be the only solution for more complex psychometric data structures. Hence, neither the applied nor the theoretical measurement community can afford to neglect the exciting new possibilities that have opened up on the psychometric horizon.     

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.     

Improving Instructional Practices, Policies, and Student Outcomes for Early Childhood Language and Literacy Through Data-Driven Decision Making

Since the passage of No Child Left Behind, data-driven decision making has become one of the central foci in schools in their attempt to attain and maintain adequate levels of student academic performance. The importance of early childhood education is well established with language and literacy proficiency in the early years being viewed as a leading indicator in children’s educational development. It provides schools with the initial signs of progress towards academic achievement. In this article, a conceptual framework for improving instructional practice and student outcomes in early childhood language and literacy through data-driven decision making was described. Four questions served as the structure around which the conceptual framework was built. These questions include (1) Why do data need to be collected? (2) What kinds of data need to be collected? (3) How are the data collected? (4) How are the data used for making decisions? Responses to these questions serve as tenets for guiding the decision making process.     

Orthographic Learning During Oral and Silent Reading

This study examined orthographic learning in oral and silent reading conditions. Dutch third graders read, either aloud or silently, short texts containing novel target (pseudo) words. The acquisition of new word-specific orthographic knowledge was assessed several days later by comparing target spellings with homophonic spellings in tasks requiring orthographic choice, spelling, and naming. It was predicted that orthographic learning would be evident in both oral and silent conditions but stronger in the oral condition. As expected, orthographic learning was evident in both oral and silent conditions. This finding suggests that support for the self-teaching hypothesis of orthographic learning obtained in studies of unassisted oral reading can be generalized to the more common form of independent reading: silent reading. In addition, the results on the naming task provided some evidence for stronger orthographic learning during oral reading, but the two spelling tasks did not.     

Supplemental Fluency Intervention and Determinants of Reading Outcomes

This study replicates research on the efficacy of a repeated reading intervention with word-level instruction for students in Grades 2 and 3 with low to moderate fluency skills, examines differences between treatment implementers, and tests unique contributions of treatment-related variables on outcomes. Students from 13 schools were randomly assigned to dyads; dyads were randomly assigned to treatment or control conditions. Schools were matched into treatment implementer groups (teachers or paraeducators) at study onset. Tutoring occurred during school hours for 15 weeks (M = 25.5 hr). Multilevel model results showed treatment students (n = 98) gained more than controls (n = 104) on measures of letter-sound knowledge (d = .41), fluency (d = .37–.38), and comprehension (d = .30–.31); students tutored by teachers gained more than their paraeducator-tutored peers on word reading and fluency. Finally, dyads tutored with greater fidelity gained more in word reading and fluency; dyads that read more complex words in their texts gained less on letter-sounds, fluency, and comprehension.