The Actor–Partner Interdependence Model for Longitudinal Dyadic Data: An Implementation in the SEM Framework

In dyadic research, the actor–partner interdependence model (APIM) is widely used to model the effect of a predictor measured across dyad members on one’s own and one’s partner outcome. When such dyadic data are measured repeatedly over time, both the non-independence within couples and the non-independence over time need to be accounted for. In this paper, we present a longitudinal extension of the APIM, the L-APIM, that allows for both stable and time-varying sources of non-independence. Its implementation is readily available in multilevel software, such as proc mixed in SAS, but is lacking in the structural equation modeling (SEM) framework. We tackle the computational challenges associated with its SEM-implementation and propose a user-friendly free application for the L-APIM, which can be found at http://fgisteli.shinyapps.io/Shiny_LDD. As an illustration, we explore the actor and partner effects of positive relationship feelings on next day’s intimacy using 3-week diary data of 66 heterosexual couples.     

No Need to be Discrete: A Method for Continuous Time Mediation Analysis

Mediation is one concept that has shaped numerous theories. The list of problems associated with mediation models, however, has been growing. Mediation models based on cross-sectional data can produce unexpected estimates, so much so that making longitudinal or causal inferences is inadvisable. Even longitudinal mediation models have faults, as parameter estimates produced by these models are specific to the lag between observations, leading to much debate over appropriate lag selection. Using continuous time models (CTMs) rather than commonly employed discrete time models, one can estimate lag-independent parameters. We demonstrate methodology that allows for continuous time mediation analyses, with attention to concepts such as indirect and direct effects, partial mediation, the effect of lag, and the lags at which relations become maximal. A simulation compares common longitudinal mediation methods with CTMs. Reanalysis of a published covariance matrix demonstrates that CTMs can be fit to data used in longitudinal mediation studies.     

Mediation Analysis in a Latent Growth Curve Modeling Framework

This article presents several longitudinal mediation models in the framework of latent growth curve modeling and provides a detailed account of how such models can be constructed. Logical and statistical challenges that might arise when such analyses are conducted are also discussed. Specifically, we discuss how the initial status (intercept) and change (slope) of the putative mediator variable can be appropriately included in the causal chain between the independent and dependent variables in longitudinal mediation models. We further address whether the slope of the dependent variable should be controlled for the dependent variable's intercept to improve the conceptual relevance of the mediation models. The models proposed are illustrated by analyzing a longitudinal data set. We conclude that for certain research questions in developmental science, a multiple mediation model where the dependent variable's slope is controlled for its intercept can be considered an adequate analytical model. However, such models also show several limitations.     

The Effects of Sex and Gender Role Orientation on Approach-Based Coping Strategies Across Cultures: A Moderated Mediation Model

This study explores the mediation effect of gender role orientation on the influence of sex on coping strategies and how the mediation effects differ across the two cultures of the United States and China. A total of 478 respondents (243 Americans and 235 resident Chinese) participated in this study. Employing Hayes’ (2013) PROCESS for testing moderated mediation models using conditional process analysis, we found that femininity mediated the influence of sex on both emotional and instrumental coping, and the mediation effects were significantly different between American participants and Chinese participants. We also found that national culture moderated the influence of sex on coping strategies when gender role orientation was being held constant. This study adopts an integrated model of sex, gender role orientation, culture, and coping. This model allows us to examine both general and specific relationships among interested variables, which contributes to existing literature in several ways.     

Formal Relations and an Empirical Comparison among the Bi-Factor,the Testlet,and a Second-Order Multidimensional IRT Model

Testlet effects can be taken into account by incorporating specific dimensions in addition to the general dimension into the item response theory model. Three such multidimensional models are described: the bi-factor model, the testlet model, and a second-order model. It is shown how the second-order model is formally equivalent to the testlet model. In turn, both models are constrained bi-factor models. Therefore, the efficient full maximum likelihood estimation method that has been established for the bi-factor model can be modified to estimate the parameters of the two other models. An application on a testlet-based international English assessment indicated that the bi-factor model was the preferred model for this particular data set.     

Sensitivity Analysis of the No-Omitted Confounder Assumption in Latent Growth Curve Mediation Models

Latent growth curve mediation models are increasingly used to assess mechanisms of behavior change. For latent growth mediation model, like any another mediation model, even with random treatment assignment, a critical but untestable assumption for valid and unbiased estimates of the indirect effects is that there should be no omitted variable that confounds indirect effects. One way to address this untestable assumption is to conduct sensitivity analysis to assess whether the inference about an indirect effect would change under varying degrees of confounding bias. We developed a sensitivity analysis technique for a latent growth curve mediation model. We compute the biasing effect of confounding on point and confidence interval estimates of the indirect effects in a structural equation modeling framework. We illustrate sensitivity plots to visualize the effects of confounding on each indirect effect and present an empirical example to illustrate the application of the sensitivity analysis.     

Do schools discriminate against homosexual parents? Evidence from a randomized correspondence experiment

The recognition of homosexual rights is a controversial issue in many countries. Spain was the third country in the world (after the Netherlands and Belgium) to introduce a law recognizing homosexual marriage and the adoption of children by homosexual couples. In this paper, we examine for the first time whether schools are more hesitant about giving feedback to homosexual parents during children's pre-registration period in Catalonia (Spain). To do so, we designed a correspondence experiment to be conducted in schools. We created three types of fictitious couples—one heterosexual, one gay, and one lesbian—and sent emails to schools in which the couples’ sexual orientation was explicit. Our results show that gay couples had a significantly lower (22 percentage points) call-back probability than heterosexual couples. No statistically significant differences in call-back probability were found between the lesbian and heterosexual couples.     

Power Analysis for Complex Mediational Designs Using Monte Carlo Methods

Applied researchers often include mediation effects in applications of advanced methods such as latent variable models and linear growth curve models. Guidance on how to estimate statistical power to detect mediation for these models has not yet been addressed in the literature. We describe a general framework for power analyses for complex mediational models. The approach is based on the well-known technique of generating a large number of samples in a Monte Carlo study, and estimating power as the percentage of cases in which an estimate of interest is significantly different from zero. Examples of power calculation for commonly used mediational models are provided. Power analyses for the single mediator, multiple mediators, 3-path mediation, mediation with latent variables, moderated mediation, and mediation in longitudinal designs are described. Annotated sample syntax for Mplus is appended and tabled values of required sample sizes are shown for some models.     

Analyzing Different Types of Moderated Method Effects in Confirmatory Factor Models for Structurally Different Methods

An extension of two confirmatory factor models for multitrait-multimethod measurement designs with structurally different methods to the analysis of latent interaction effects is presented: the nonlinear latent difference (NL-LD) model and the nonlinear correlated trait–correlated method-minus-one (NL-CTC[M – 1]) model. Both models are compared with regard to (a) the psychometric definition of the latent variables, (b) the capabilities of explaining latent method effects, and (c) the analysis of latent interaction effects. Using the latent moderated structural equation approach, we show how moderated method effects can be examined in the NL-CTC(M – 1) model. This fine-grained analysis of method effects is not feasible using the classical NL-LD model. We propose an extended version of the NL-LD model, which recovers the results of the NL-CTC(M – 1) model. The different versions of the nonlinear multimethod models are illustrated using real data from a multirater study. Finally, the advantages and challenges of incorporating latent interaction effects in complex CFA–MTMM models are discussed.     

Moderated Mediation Analysis Using Bayesian Methods

Conventionally, moderated mediation analysis is conducted through adding relevant interaction terms into a mediation model of interest. In this study, we illustrate how to conduct moderated mediation analysis by directly modeling the relation between the indirect effect components including a and b and the moderators, to permit easier specification and interpretation of moderated mediation. With this idea, we introduce a general moderated mediation model that can be used to model many different moderated mediation scenarios including the scenarios described in Preacher, Rucker, and Hayes (2007). Then we discuss how to estimate and test the conditional indirect effects and to test whether a mediation effect is moderated using Bayesian approaches. How to implement the estimation in both BUGS and Mplus is also discussed. Performance of Bayesian methods is evaluated and compared to that of frequentist methods including maximum likelihood (ML) with 1st-order and 2nd-order delta method standard errors and mL with bootstrap (percentile or bias-corrected confidence intervals) via a simulation study. The results show that Bayesian methods with diffuse (vague) priors implemented in both BUGS and Mplus yielded unbiased estimates, higher power than the ML methods with delta method standard errors, and the ML method with bootstrap percentile confidence intervals, and comparable power to the ML method with bootstrap bias-corrected confidence intervals. We also illustrate the application of these methods with the real data example used in Preacher et al. (2007). Advantages and limitations of applying Bayesian methods to moderated mediation analysis are also discussed.     

Three-Level Models for Indirect Effects in School- and Class-Randomized Experiments in Education

Due to the clustered nature of field data, multi-level modeling has become commonly used to analyze data arising from educational field experiments. While recent methodological literature has focused on multi-level mediation analysis, relatively little attention has been devoted to mediation analysis when three levels (e.g., student, class, school) are present in a study setting. This article presents analysis models that can be used to test indirect effects in experimental designs having three levels where random assignment is at the third (school) or second (class) level and where the indirect effect may be random. In the presentation, simulated datasets are used to illustrate model specification and results interpretation for hypothetical three-level educational experiments involving mediation and moderation of treatment effects.     

Associations between peer bullying and classroom concentration: evidence for mediation by perceived personal safety and relationship with teacher

Being bullied is associated with a psycho-social maladjustment during childhood. One hitherto largely overlooked correlate is disrupted classroom concentration. Using data collected from 364 9–11-year-old children attending seven junior schools in the UK, we tested a model in which children’s perceived safety in two contexts (classroom and playground) and their perceived relationship with their teacher were hypothesised to mediate the association between being bullied and classroom concentration. Two analytical approaches to testing multiple mediation – product of coefficients and bootstrapping – supported the model. None of the mediation effects was moderated by sex but they were by year; in all cases the mediation effect was stronger in the older children than in the younger children (but still significant among the latter). These data suggest mechanisms through which bullying might have its effects on classroom concentration. The practical and theoretical implications are discussed.     

Coparenting Among Lesbian,Gay, and Heterosexual Couples: Associations With Adopted Children's Outcomes

Coparenting is associated with child behavior in families with heterosexual parents, but less is known about coparenting among lesbian‐ and gay‐parent families. Associations were studied among self‐reported divisions of labor, coparenting observations, and child adjustment (M_age = 3 years) among 104 adoptive families headed by lesbian, gay, or heterosexual couples. Lesbian and gay couples reported sharing child care, whereas heterosexual couples reported specialization (i.e., mothers did more child care than fathers). Observations confirmed this pattern—lesbian and gay parents participated more equally than heterosexual parents during family interaction. Lesbian couples showed the most supportive and least undermining behavior, whereas gay couples showed the least supportive behavior, and heterosexual couples the most undermining behavior. Overall, supportive coparenting was associated with better child adjustment.     

Obtaining Diagnostic Classification Model Estimates Using Mplus

Diagnostic classification models (aka cognitive or skills diagnosis models) have shown great promise for evaluating mastery on a multidimensional profile of skills as assessed through examinee responses, but continued development and application of these models has been hindered by a lack of readily available software. In this article we demonstrate how diagnostic classification models may be estimated as confirmatory latent class models using Mplus, thus bridging the gap between the technical presentation of these models and their practical use for assessment in research and applied settings. Using a sample English test of three grammatical skills, we describe how diagnostic classification models can be phrased as latent class models within Mplus and how to obtain the syntax and output needed for estimation and interpretation of the model parameters. We also have written a freely available SAS program that can be used to automatically generate the Mplus syntax. We hope this work will ultimately result in greater access to diagnostic classification models throughout the testing community, from researchers to practitioners.     

Preschool selection considerations and experiences of school mistreatment among lesbian,gay, and heterosexual adoptive parents

The current study is the first to investigate the school selection considerations and school-related experiences of sexual-minority parents with young children. The sample consisted of 210 parents in 105 couples, including 35 lesbian couples, 30 gay male couples, and 40 heterosexual couples, all of whom had adopted a child three years earlier. We found that parents with less income were more likely to consider cost in choosing a preschool, and parents with less education were more likely to consider location. More educated parents tended to emphasize racial diversity and the presence of adoptive families, and, among sexual-minority parents, the presence of other lesbian/gay parents. Sexual-minority parents were more likely to consider racial diversity than heterosexual parents. In reporting on their experiences with schools, heterosexual parents were more likely to perceive mistreatment due to their adoptive status than sexual-minority parents, and sexual-minority parents living in less gay-friendly communities were more likely to perceive mistreatment due to their sexual orientation than sexual-minority parents living in more gay-friendly communities. Our findings have implications for early childhood educators and administrators seeking to create an inclusive learning community for all types of families.     

Analyzing Mixed-Dyadic Data Using Structural Equation Models

Mixed-dyadic data, collected from distinguishable (nonexchangeable) or indistinguishable (exchangeable) dyads, require statistical analysis techniques that model the variation within dyads and between dyads appropriately. The purpose of this article is to provide a tutorial for performing structural equation modeling analyses of cross-sectional and longitudinal models for mixed independent variable dyadic data, and to clarify questions regarding various dyadic data analysis specifications that have not been addressed elsewhere. Artificially generated data similar to the Newlywed Project and the Swedish Adoption Twin Study on Aging were used to illustrate analysis models for distinguishable and indistinguishable dyads, respectively. Due to their widespread use among applied researchers, the AMOS and Mplus statistical analysis software packages were used to analyze the dyadic data structural equation models illustrated here. These analysis models are presented in sufficient detail to allow researchers to perform these analyses using their preferred statistical analysis software package.     

Dyadic Curve-of-Factors Model: An Introduction and Illustration of a Model for Longitudinal Nonexchangeable Dyadic Data

The analysis of longitudinal data collected from nonexchangeable dyads presents a challenge for applied researchers for various reasons. This article introduces the dyadic curve-of-factors model (D–COFM), which extends the curve-of-factors model (COFM) proposed by McArdle (1988) for use with nonexchangeable dyadic data. The D–COFM overcomes problems with modeling composite scores across time and instead permits examination of the growth in latent constructs over time. The D–COFM also appropriately models the interdependency among nonexchangeable dyads. Different parameterizations of the D–COFM are illustrated and discussed using a real data set to aid applied researchers when analyzing dyadic longitudinal data.     

The Sensitivity of Value-Added Teacher Effect Estimates to Different Mathematics Achievement Measures

Using longitudinal data from a cohort of middle school students from a large school district, we estimate separate "value-added" teacher effects for two subscales of a mathematics assessment under a variety of statistical models varying in form and degree of control for student background characteristics. We find that the variation in estimated effects resulting from the different mathematics achievement measures is large relative to variation resulting from choices about model specification, and that the variation within teachers across achievement measures is larger than the variation across teachers. These results suggest that conclusions about individual teachers' performance based on value-added models can be sensitive to the ways in which student achievement is measured.     

An intervention to improve sibling relationship quality among youth in foster care: Results of a randomized clinical trial

Sibling programming is an important part of a prevention framework, particularly for youth in foster care. After children are removed from their families and placed into foster care in the aftermath of maltreatment, the sibling relationship is often the most viable ongoing relationship available to the child, and may be critical to a youth’s sense of connection, emotional support, and continuity. The promise of dyadic sibling programming in particular rests on the ability of interventions to enhance the quality of sibling relationships; yet little research exists that suggests that sibling interventions can improve relationship quality among foster youth. The primary aim of the current study was to examine the effects of a specific dyadic sibling-focused intervention for older and younger siblings on sibling relationship quality. One hundred sixty four dyads (328 youth) participated in the study, with each dyad consisting of an older sibling between 11 and 15 years of age at baseline and a younger sibling separated in age by less than 4 years. Hierarchical linear models were applied to self-reported, observer-reported and observational data over the 18-month study period. Findings suggest that the sibling intervention holds promise for improving sibling relationship quality among youth in foster care. Implications and future directions for research are discussed.     

Mother–child joint writing and storybook reading and their effects on kindergartners’ literacy: an intervention study

This study assessed the effects of three different intervention programs on low-SES mother?Cchild joint activities and on their kindergarten-age children??s progress in early literacy and language. Parents in three groups (119 mothers, 5 fathers) were coached to mediate child learning, respectively, in: interactive storybook reading, writing, or visuomotor skills. A group-specific workshop was followed by 7?weeks of tri-weekly structured dyadic interactions and weekly tutorial home visits. A fourth group (control) received no intervention. Results showed implementation success: Mothers coached in interactive storybook reading or writing mediation improved in the coached activity from pretest to immediate posttest and to delayed posttest. Interactive storybook reading improved less for older than younger children, whereas writing mediation improved more for older than younger children. No transfer emerged from one activity to the other: Coaching on reading had no effect on writing or visuomotor skills, and coaching of writing had an effect only on writing. Children??s alphabetic skills were enhanced in the writing mediation-coached group, whereas linguistic competencies, unexpectedly, were not enhanced in the interactive storybook reading-coached group. The significance of writing mediation as a dyadic activity promoting literacy is emphasized.