James A. Bovaird

On the Merits of Orthogonalizing Powered and Product Terms: Implications for Modeling Interactions Among Latent Variables

The goals of this article are twofold: (a) briefly highlight the merits of residual centering for representing interaction and powered terms in standard regression contexts (e.g., Lance, 1988), and (b) extend the residual centering procedure to represent latent variable interactions. The proposed method for representing latent variable interactions has potential advantages over extant procedures. First, the latent variable interaction is derived from the observed covariation pattern among all possible indicators of the interaction. Second, no constraints on particular estimated parameters need to be placed. Third, no recalculations of parameters are required. Fourth, model estimates are stable and interpretable. In our view, the orthogonalizing approach is technically and conceptually straightforward, can be estimated using any structural equation modeling software package, and has direct practical interpretation of parameter estimates. Its behavior in terms of model fit and estimated standard errors is very reasonable, and it can be readily generalized to other types of latent variables where nonlinearity or collinearity are involved (e.g., powered variables).

Modeling contextual effects in longitudinal studies

Researchers often grapple with the idea that an observed relationship may be part of a more complex chain of effects. These complex relationships are described in terms such as indirect influences, distal vs. proximal causes, intermediate outcomes, and ultimate causes; all of which share the concept of mediation. Similarly, researchers must often consider that an observed relationship may be part of a more complex, qualified system. These relationships are described using concepts such as interactions, subgroup differences, and shocks; all of which share the concept of moderation. Generally speaking, a mediator can be thought of as the carrier or transporter of information along the causal chain of effects. A moderator, on the other hand, is the changer of a relationship in as ystem. In this chapter, we explore both empirical and theoretical considerations in modeling mediation and moderation using structural equation modeling. OurThe multilevel approach uses a data set in which the records are person-days. On each record variables called “couple” (couple number), “exmprt” (examinee vs. partner), and “day” indicate which kind of person and which day is represented on the record. Before the analysis is run, some new variables are created that contain the same information. The variable “daycl” is identical to “day,” but will be used to define day as a class variable. The variable “exmnee” is a dummy code with 1 for examinee and 0 for partner. The variable “partner” is the complement of the latter: It is a dummy code with 1 for partner and 0 for examinee. With these variables one can use the following PROC MIXED syntax. PROC MIXED DATA=anger COVTEST METHOD=REML; TITLE ‘Examinee and Partner random effects and correlated errors’; CLASS couple exmprt daycl ; MODEL anger=exmnee partner day / S NOINT;Contents: Preface. N.A. Card, T.D. Little, J.A. Bovaird, Modeling Ecological and Contextual Effects in Longitudinal Studies of Human Development. S.M. Hofer, L. Hoffman, Statistical Analysis With Incomplete Data: A Developmental Perspective. K.J. Preacher, L. Cai, R.C. MacCullum, Alternatives to Traditional Model Comparison Strategies for Covariance Structure Models. S.E. Embretson, Impact of Measurement Scale in Modeling Developmental Processes and Ecological Factors. P.J. Curran, M.C. Edwards, R.J. Wirth, A.M. Hussong, L. Chassin, The Incorporation of Categorical Measurement Models in the Analysis of Individual Growth. T.D. Little, N.A. Card, D.W. Slegers, E.C. Ledford, Representing Contextual Effects in Multiple-Group MACS Models. J.A. Bovaird, Multilevel Structural Equation Models for Contextual Factors. D. Hedeker, R.J. Mermelstein, Mixed-Effects Regression Models With Heterogeneous Variance: Analyzing Ecological Momentary Assessment (EMA) Data of Smoking. T.D. Little, N.A. Card, J.A. Bovaird, K.J. Preacher, C.S. Crandel, Structural Equation Modeling of Mediation and Moderation With Contextual Factors. D.B. Flora, S.T. Khoo, L. Chassin, Moderating Effects of a Risk Factor: Modeling Longitudinal Moderated Mediation in the Development of Adolescent Heavy Drinking. D.J. Bauer, M.J. Shanahan, Modeling Complex Interactions: Person-Centered and Variable-Centered Approaches. N. Bolger, P.E. Shrout, Accounting for Statistical Dependency in Longitudinal Data on Dyads. S.M. Boker, J-P. Laurenceau, Coupled Dynamics and Mutually Adaptive Context. N. Ram, J.R. Nesselroade, Modeling Intraindividual and Intracontextual Change: Rendering Developmental Contextualism Operational. J.L. Rodgers, The Shape of Things to Come: Using Developmental Curves From Adolescent Smoking and Drinking Reports to Diagnose the Type of Social Process that Generated the Curves. K.J. Grimm, J.J. McArdle, A Dynamic Structural Analysis of the Impacts of Context on Shifts in Lifespan Development. K.F. Widaman, Intrauterine Environment Affects Infant and Child Intellectual Outcomes: Environment as Direct Effect. H. Jelicic, C. Theokas, E. Phelps, R.M. Lerner, Conceptualizing and Measuring the Context Within Person Context Models of Human Development: Implications for Theory, Research, and Application.Longitudinal studies are increasingly common in psychological and social sciences research. In these studies, subjects are measured repeatedly across time and interest often focuses on characterizing their growth or development across time. Mixed-effects regression models (MRMs) have become the method of choice for modeling of longitudinal data; variants of MRMs have been developed under a variety of names: Random-effects models. Laird and Ware (1982),variance component models (Dempster, Rubin, & Tsutakawa, 1981) , multilevel models (Goldstein, 1995), hierarchical linear models (Bryk & Raudenbush, 1992), two-stage models. Bock (1989), random coefficient models (Leeuw & Kreft, 1986), mixed models (Longford, 1987; Wolfinger, 1993), empirical Bayes models (Hui & Berger, 1983; Strenio, Weisberg, & Bryk, 1983), and random regression models (Bock, 1983b, 1983a; Gibbons, Hedeker, Waternaux, & Davis, 1988). A basic characteristic of these models is the inclusion of random subject effects into regression models in order to account for the influence of subjects on their repeated observations. These random effects reflect each person’s growth or development across time, and explain the correlational structure of the longitudinal data. Additionally, they indicate the degree of subject variation that exists in the population of subjects. There are several features that make MRMs especially useful in longitudinal research. First, subjects are not assumed to be measured on the same number of timepoints, thus, subjects with incomplete data across time are included in the

Classroom Variables and Access to the General Curriculum for Students with Disabilities

This study investigated the degree to which students with intellectual and developmental disabilities have access to the general education curriculum and the degree to which such access is related to and predicted by classroom setting and ecological variables. We observed 19 students during science or social studies instruction and collected data with Access CISSAR, a computer-based observation system that uses time sampling observation. The results of the study indicated that accommodations and modifications were provided depending on the amount of time students were educated with their nondisabled peers. Further, one-on-one or independent instructional groupings were better predictors of access than whole-group instruction, as were entire or divided group physical arrangements.

Parent Engagement and School Readiness: Effects of the Getting Ready Intervention on Preschool Children’s Social–Emotional Competencies

Research Findings: Parental engagement with children has been linked to a number of adaptive characteristics in preschool children, and relationships between families and professionals are an important contributor to school readiness. Furthermore, social–emotional competence is a key component of young childrens school readiness. This study reports the results of a randomized trial of a parent engagement intervention (Getting Ready) designed to facilitate school readiness among disadvantaged preschool children, with a particular focus on social–emotional outcomes. Two hundred and twenty children were involved over the 4-year study period. Statistically significant differences were observed between treatment and control participants in the rate of change over a 2-year period on teacher reports for certain interpersonal competencies (i.e., attachment, initiative, and anxiety/withdrawal). In contrast, no statistically significant differences between groups over a 2-year period were noted for behavioral concerns (anger/aggression, self-control, or behavioral problems) as a function of the Getting Ready intervention. Practice or Policy: The intervention appears to be particularly effective at building social–emotional competencies beyond the effects experienced as a function of participation in Head Start programming alone. Limitations and implications for future research are reviewed.

Statistical analysis of data from studies on experimental autoimmune encephalomyelitis

Research in multiple sclerosis often employs animal models of the disease, especially experimental autoimmune encephalomyelitis (EAE) in rodents. The statistical analysis procedures chosen for these studies are often suboptimal, either because of violations of the assumptions of the procedure or because the analysis selected is inappropriate for the research question. In this paper, we discuss the types of research questions frequently asked in EAE studies and suggest appropriate and useful research designs and statistical methods that will optimize the information contained within the data. We also discuss other troublesome issues such as missing data, atypical disease profiles, and power analysis.

On the use of multilevel modeling as an alternative to items analysis in psycholinguistic research

The use of multilevel modeling is presented as an alternative to separate item and subject ANOVAs (F1 ×F2) in psycholinguistic research. Multilevel modeling is commonly utilized to model variability arising from the nesting of lower level observations within higher level units (e.g., students within schools, repeated measures within individuals). However, multilevel models can also be used when two random factors are crossed at the same level, rather than nested. The current work illustrates the use of the multilevel model for crossed random effects within the context of a psycholinguistic experimental study, in which both subjects and items are modeled as random effects within the same analysis, thus avoiding some of the problems plaguing current approaches.

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 Dimensionality of Language Ability in Young Children

The purpose of this study was to empirically examine the dimensionality of language ability for young children (4-8 years) from prekindergarten to third grade (n = 915), theorizing that measures of vocabulary and grammar ability will represent a unitary trait across these ages, and to determine whether discourse skills represent an additional source of variance in language ability. Results demonstrated emergent dimensionality of language across development with distinct factors of vocabulary, grammar, and discourse skills by third grade, confirming that discourse skills are an important source of variance in childrens language ability and represent an important additional dimension to be accounted for in studying growth in language skills over the course of childhood.

Advancing career counseling and employment support for survivors: an intervention evaluation.

The purpose of this research was to conduct a replication-based and extension study examining the effectiveness of a 5-week career group counseling intervention, Advancing Career Counseling and Employment Support for Survivors (ACCESS; Chronister, 2008). The present study was conducted in a markedly different geographic region within a larger community as compared with the original investigation conducted by Chronister and McWhirter (2006). Women survivors of intimate partner violence (N = 73) participated in ACCESS, with career-search self-efficacy, perceived career barriers, perceived career supports, anxiety, and depression assessed at preintervention, postintervention, and 8-week follow-up. Women survivors demonstrated significant improvements in career-search self-efficacy and perceived career barriers at postintervention. Moreover, these same improvements were maintained at the 8-week follow-up assessment with the addition of significant improvements in perceived future financial supports, anxiety, and depression compared with preintervention scores. This work replicates the initial findings regarding the effectiveness of ACCESS with respect to career-search self-efficacy (Chronister & McWhirter, 2006) as well as extends the initial research to include improvements in perceived career barriers and perceived career supports. Moreover, the present study extends the work to include the mental health outcomes of anxiety and depression; results demonstrated improvements in these areas at 8-week follow-up. This investigation begins to fill a critical need for evaluated career-focused interventions for the underserved population of women survivors of intimate partner violence.

Regression-Based Multi-Trait QTL Mapping Using a Structural Equation Model

Quantitative trait loci (QTL) mapping often results in data on a number of traits that have well-established causal relationships. Many multi-trait QTL mapping methods that account for the correlation among multiple traits have been developed to improve the statistical power and the precision of QTL parameter estimation. However, none of these methods are capable of incorporating the causal structure among the traits. Consequently, genetic functions of the QTL may not be fully understood. Structural equation modeling (SEM) allows researchers to explicitly characterize the causal structure among the variables and to decompose effects into direct, indirect, and total effects. In this paper, we developed a multi-trait SEM method of QTL mapping that takes into account the causal relationships among traits related to grain yield. Performance of the proposed method is evaluated by simulation study and applied to data from a wheat experiment. Compared with single trait analysis and the multi-trait least-squares analysis, our multi-trait SEM improves statistical power of QTL detection and provides important insight into how QTLs regulate traits by investigating the direct, indirect, and total QTL effects. The approach also helps build biological models that more realistically reflect the complex relationships among QTL and traits and is more precise and efficient in QTL mapping than single trait analysis.