Parametric g-formula for Testing Time-Varying Causal Effects: What It Is, Why It Matters, and How to Implement It in Lavaan.

Psychologists leverage longitudinal designs to examine the causal effects of a focal predictor (i.e., treatment or exposure) over time. But causal inference of naturally observed time-varying treatments is complicated by treatment-dependent confounding in which earlier treatments affect confounders of later treatments. In this tutorial article, we introduce psychologists to an established solution to this problem from the causal inference literature: the parametric g-computation formula. We explain why the g-formula is effective at handling treatment-dependent confounding. We demonstrate that the parametric g-formula is conceptually intuitive, easy to implement, and well-suited for psychological research. We first clarify that the parametric g-formula essentially utilizes a series of statistical models to estimate the joint distribution of all post-treatment variables. These statistical models can be readily specified as standard multiple linear regression functions. We leverage this insight to implement the parametric g-formula using lavaan, a widely adopted R package for structural equation modeling. Moreover, we describe how the parametric g-formula may be used to estimate a marginal structural model whose causal parameters parsimoniously encode time-varying treatment effects. We hope this accessible introduction to the parametric g-formula will equip psychologists with an analytic tool to address their causal inquiries using longitudinal data.

Mitigating Multiple Sources of Bias in a Quasi-Experimental Integrative Data Analysis: Does Treating Childhood Anxiety Prevent Substance Use Disorders in Late Adolescence/Young Adulthood?

Psychiatric epidemiologists, developmental psychopathologists, prevention scientists, and treatment researchers have long speculated that treating child anxiety disorders could prevent alcohol and other drug use disorders in young adulthood. A primary challenge in examining long-term effects of anxiety disorder treatment from randomized controlled trials is that all participants receive an immediate or delayed study-related treatment prior to long-term follow-up assessment. Thus, if a long-term follow-up is conducted, a comparison condition no longer exists within the trial. Quasi-experimental designs (QEDs) pairing such clinical samples with comparable untreated epidemiological samples offer a method of addressing this challenge. Selection bias, often a concern in QEDs, can be mitigated by propensity score weighting. A second challenge may arise because the clinical and epidemiological studies may not have used identical measures, necessitating Integrative Data Analysis (IDA) for measure harmonization and scale score estimation. The present study uses a combination of propensity score weighting, zero-inflated mixture moderated nonlinear factor analysis (ZIM-MNLFA), and potential outcomes mediation in a child anxiety treatment QED/IDA (n = 396). Under propensity score-weighted potential outcomes mediation, CBT led to reductions in substance use disorder severity, the effects of which were mediated by reductions in anxiety severity in young adulthood. Sensitivity analyses highlighted the importance of attending to multiple types of bias. This study illustrates how hybrid QED/IDAs can be used in secondary prevention contexts for improved measurement and causal inference, particularly when control participants in clinical trials receive study-related treatment prior to long-term assessment.

Hidden framings and hidden asymmetries in the measurement of personality--A combined lens-model and frame-of-reference perspective.

OBJECTIVE: The symmetry principle and the frame-of-reference perspective have each made contributions to improving the measurement of personality. Although each perspective is valuable in its own right, we argue that even greater improvement can be achieved through the combination of both. Therefore, the goal of the current article was to show the value of a combined lens-model and frame-of-reference perspective. METHOD: We conducted a literature review to summarize relevant research findings that shed light on the interplay of both perspectives and developed an integrative model. RESULTS: Based on the literature review and on theoretical grounds, we argue that a basic premise of the frame-of-reference literature--that personality items are open to interpretation and allow individuals to impose their own contextual framings--should be considered from a symmetry perspective. Unintended context-specificity in items may "spread" to personality facets and domains, and thus, impact the symmetry of personality measures with other criteria. As the individuals´ frames-of-reference and (a)symmetric relationships are not always apparent, we term them as "hidden." CONCLUSIONS: The proposed combination of lens-model and frame-of-reference perspectives provides further insights into current issues in personality research and uncovers important avenues for future research.

A Tribute to the Mind, Methodology and Mentoring of Wayne Velicer.

Wayne Velicer is remembered for a mind where mathematical concepts and calculations intrigued him, behavioral science beckoned him, and people fascinated him. Born in Green Bay, Wisconsin on March 4, 1944, he was raised on a farm, although early influences extended far beyond that beginning. His Mathematics BS and Psychology minor at Wisconsin State University in Oshkosh, and his PhD in Quantitative Psychology from Purdue led him to a fruitful and far-reaching career. He was honored several times as a high-impact author, was a renowned scholar in quantitative and health psychology, and had more than 300 scholarly publications and 54,000+ citations of his work, advancing the arenas of quantitative methodology and behavioral health. In his methodological work, Velicer sought out ways to measure, synthesize, categorize, and assess people and constructs across behaviors and time, largely through principal components analysis, time series, and cluster analysis. Further, he and several colleagues developed a method called Testing Theory-based Quantitative Predictions, successfully applied to predicting outcomes and effect sizes in smoking cessation, diet behavior, and sun protection, with the potential for wider applications. With $60,000,000 in external funding, Velicer also helped engage a large cadre of students and other colleagues to study methodological models for a myriad of health behaviors in a widely applied Transtheoretical Model of Change. Unwittingly, he has engendered indelible memories and gratitude to all who crossed his path. Although Wayne Velicer left this world on October 15, 2017 after battling an aggressive cancer, he is still very present among us.

Analysis of Interactions and Nonlinear Effects with Missing Data: A Factored Regression Modeling Approach Using Maximum Likelihood Estimation.

When estimating multiple regression models with incomplete predictor variables, it is necessary to specify a joint distribution for the predictor variables. A convenient assumption is that this distribution is a multivariate normal distribution, which is also the default in many statistical software packages. This distribution will in general be misspecified if predictors with missing data have nonlinear effects (e.g., x2) or are included in interaction terms (e.g., x·z). In the present article, we introduce a factored regression modeling approach for estimating regression models with missing data that is based on maximum likelihood estimation. In this approach, the model likelihood is factorized into a part that is due to the model of interest and a part that is due to the model for the incomplete predictors. In three simulation studies, we showed that the factored regression modeling approach produced valid estimates of interaction and nonlinear effects in regression models with missing values on categorical or continuous predictor variables under a broad range of conditions. We developed the R package mdmb, which facilitates a user-friendly application of the factored regression modeling approach, and present a real-data example that illustrates the flexibility of the software.

Effect of Early Grade Retention on School Completion: A Prospective Study.

This 14 year prospective study investigated the effect of retention in grades 1-5 on high school completion (diploma, GED, or drop out). Participants were 734 (52.7% males) ethnically diverse, academically at-risk students recruited from Texas schools into the study when they were in first grade (mean age = 6.57). Propensity score weighting successfully equated the 256 retained students and the 478 students continuously promoted students on 65 covariates assessed in grade 1. At the end of 14 years, 477 had earned a diploma, 21 had obtained a GED, 110 had dropped out, and 126 were missing school completion status. Using multinomial logistic regression with high school graduation as the reference outcome, retention led to a significant increase in the likelihood of dropping out of high school (odds ratio = 2.61), above students' propensity to be retained and additional covariates. The contrast between graduation and GED outcomes was not significant. A significant Retention X Ethnicity X Gender interaction was obtained: The negative effect of retention was strongest for African American and Hispanic girls. Even though grade retention in the elementary grades does not harm students in terms of their academic achievement or educational motivation at the transition to high school, retention increases the odds that a student will drop out of school before obtaining a high school diploma.

Opportunities and Issues in Modeling Intensive Longitudinal Data: Learning from the COGITO Project.

Technological developments increasingly permit the collection of longitudinal data sets in which the data structure contains a large number of participants N and a large number of measurement occasions T. Promising new dynamical systems approaches to the analysis of large N, large T data sets have been proposed that utilize both between-subjects and within-subjects information. The COGITO project, begun over a decade ago, is an early large N = 204, large T = 100 study that collected high quality cognitive and psychosocial data. In this introduction, I describe the COGITO project and conceptual and statistical issues that arise in the analysis of large N, large T data sets. I provide a brief overview of the five papers in the special section which include conceptual pieces, a didactic presentation of a dynamic structural equation approach, and papers reporting new statistical analyses of the COGITO data set to answer substantive questions. Although many challenges remain, these new approaches offer the promise of improving scientific inquiry in the behavioral sciences.

Tests of Simple Slopes in Multiple Regression Models with an Interaction: Comparison of Four Approaches.

In multiple regression researchers often follow up significant tests of the interaction between continuous predictors X and Z with tests of the simple slope of Y on X at different sample-estimated values of the moderator Z (e.g., ±1 SD from the mean of Z). We show analytically that when X and Z are randomly sampled from the population, the variance expression of the simple slope at sample-estimated values of Z differs from the traditional variance expression obtained when the values of X and Z are fixed. A simulation study using randomly sampled predictors compared four approaches: (a) the Aiken and West ( 1991 ) test of simple slopes at fixed population values of Z, (b) the Aiken and West test at sample-estimated values of Z, (c) a 95% percentile bootstrap confidence interval approach, and (d) a fully Bayesian approach with diffuse priors. The results showed that approach (b) led to inflated Type 1 error rates and 95% confidence intervals with inadequate coverage rates, whereas other approaches maintained acceptable Type 1 error rates and adequate coverage of confidence intervals. Approach (c) had asymmetric rejection rates at small sample sizes. We used an empirical data set to illustrate these approaches.

An experimental test of the Bridges to High School intervention on harsh parenting and early age intercourse among Mexican American adolescents.

OBJECTIVE: Can an intervention that contained no content on sex or contraception reduce rates of early-age intercourse among Mexican American adolescents? The current study examined whether the Bridges to High School intervention designed, in part, to decrease harsh parenting, had a longitudinal effect on decreasing rates of early-age intercourse in the treatment versus control groups, as well as the moderating role of gender and linguistic acculturation. METHOD: The sample consisted of 516 Mexican American adolescents (Mage = 12.31 years; 50.8% female) and their mothers who participated in a randomized, intervention trial. A series of longitudinal, meditational path models were used to examine the effects of the intervention on harsh parenting practices and early-age intercourse. RESULTS: Our findings revealed that participation in the treatment versus control group was indirectly linked to a lower likelihood of early-age intercourse through decreased maternal harsh parenting. Tests of mediation were significant. These findings did not vary across gender and linguistic acculturation. CONCLUSION: Results suggest that the Bridges to High School intervention successfully decreased early-age intercourse among Mexican American adolescents through reduced harsh parenting among mothers. This finding is consistent with positive youth development programs that have been found to have broad, and sometimes nontargeted, effects on adolescent sexual behaviors. (PsycINFO Database Record

Weekly Cycles in Daily Report Data: An Overlooked Issue.

Daily diaries and other everyday experience methods are increasingly used to study relationships between two time-varying variables X and Y. Although daily data potentially often have weekly cyclical patterns (e.g., stress may be higher on weekdays and lower on weekends), the majority of daily diary studies have ignored this possibility. In this study, we investigated the effect of ignoring existing weekly cycles. We reanalyzed an empirical dataset (stress and alcohol consumption) and performed Monte Carlo simulations to investigate the impact of omitting weekly cycles. In the empirical dataset, ignoring cycles led to the inference of a significant within-person X-Y relation whereas modeling cycles suggested that this relationship did not exist. Simulation results indicated that ignoring cycles that existed in both X and Y led to bias in the estimated within-person X-Y relationship. The amount and direction of bias depended on the magnitude of the cycles, magnitude of the true within-person X-Y relation, and synchronization of the cycles. We encourage researchers conducting daily diary studies to address potential weekly cycles in their data. We provide guidelines for detecting and modeling cycles to remove their influence and discuss challenges of causal inference in daily experience studies.

Nesselroade and Molenaar's Measurement Concerns and Proposals: An Introduction.

In this special section Nesselroade and Molenaar (N & M) propose a provocative new approach to measurement invariance. When measures are collected repeatedly over time (e.g., daily diary studies), a potentially unique measurement model relating the items to the underlying construct can be created for each individual. If hypothesized causal paths specified between constructs (e.g., frustration → aggression) can be constrained to be equal across the individuals, a model with idiographic measurement of the constructs, but with nomothetic structural relationships can be specified. Three commentaries react to N & M's proposal. Revelle and Wilt challenge the priority given by N & M to unique individual measurement structures, arguing that between subjects differences in structural relationships are empirically important and meaningful. Markus's uses David Hume's framework to raise philosophy of science challenges for N & M's approach. Maydeu-Olivares challenges the incremental validity of N & M's approach, arguing that N & M's approach is unlikely to improve the prediction of between subjects criteria. Finally, N & M present a rejoinder to the three commentaries.

Analyzing Complex Treatment Effects in Nonrandomized Observational Studies: The Case of Retention of Students in Grade.

Should low-achieving students be promoted to the next grade or be retained (held back) in the prior grade? This special section presents a discussion of the application of marginal structural models to the challenging problem of estimating the effect of promotion versus retention in grade on math scores in elementary school. Vandecandelaere, De Fraine, Van Damme, and Vansteelandt provide a didactic presentation of the marginal structural modeling approach, noting retention is a time-varying treatment because promoted low-achieving students may be retained in a subsequent grade. Steiner, Park, and Kim's commentary presents a detailed analysis of the treatment effects being estimated in same-age versus same-grade comparisons from the perspective of the potential outcomes model. Reshetnyak, Cham, and Kim's commentary clarifies the conditions under which same-age versus same-grade comparisons might be preferred; they also identify methods of further improving the estimation of retention effects. In their rejoinder, Vandecandelaere and Vansteelandt discuss tradeoffs in comparing the promoted and retained groups and highlight sensitivity analysis as a method of probing the robustness of treatment effect estimates. Our hope is that this combined didactic presentation and critical evaluation will encourage researchers to add marginal structural models to their methodological toolkits.

Improving the dependability of research in personality and social psychology: recommendations for research and educational practice.

In this article, the Society for Personality and Social Psychology (SPSP) Task Force on Publication and Research Practices offers a brief statistical primer and recommendations for improving the dependability of research. Recommendations for research practice include (a) describing and addressing the choice of N (sample size) and consequent issues of statistical power, (b) reporting effect sizes and 95% confidence intervals (CIs), (c) avoiding "questionable research practices" that can inflate the probability of Type I error, (d) making available research materials necessary to replicate reported results, (e) adhering to SPSP's data sharing policy, (f) encouraging publication of high-quality replication studies, and (g) maintaining flexibility and openness to alternative standards and methods. Recommendations for educational practice include (a) encouraging a culture of "getting it right," (b) teaching and encouraging transparency of data reporting, (c) improving methodological instruction, and (d) modeling sound science and supporting junior researchers who seek to "get it right."

Theory and Analysis of Total, Direct, and Indirect Causal Effects.

Mediation analysis, or more generally models with direct and indirect effects, are commonly used in the behavioral sciences. As we show in our illustrative example, traditional methods of mediation analysis that omit confounding variables can lead to systematically biased direct and indirect effects, even in the context of a randomized experiment. Therefore, several definitions of causal effects in mediation models have been presented in the literature (Baron & Kenny, 1986 ; Imai, Keele, & Tingley, 2010 ; Pearl, 2012 ). We illustrate the stochastic theory of causal effects as an alternative foundation of causal mediation analysis based on probability theory. In this theory we define total, direct, and indirect effects and show how they can be identified in the context of our illustrative example. A particular strength of the stochastic theory of causal effects are the causality conditions that imply causal unbiasedness of effect estimates. The causality conditions have empirically testable implications and can be used for covariate selection. In the discussion, we highlight some similarities and differences of the stochastic theory of causal effects with other theories of causal effects.

Preventing Mental Health Problems in Children After High Conflict Parental Separation/Divorce Study: An Optimization Randomized Controlled Trial Protocol.

Parental divorce is a childhood stressor that affects approximately 1.1 million children in the U.S. annually. The children at greatest risk for deleterious mental health consequences are those exposed to high interparental conflict (IPC) following the separation/divorce. Research shows that children's emotional security and coping efficacy mediate the impact of IPC on their mental health. Interventions targeting their adaptive coping in response to IPC events may bolster their emotional security and coping efficacy. However, existing coping interventions have not been tested with children exposed to high post-separation/divorce IPC, nor has any study assessed the effects of individual intervention components on children's coping with IPC and their mental health. This intensive longitudinal intervention study examines the mechanisms through which coping intervention components impact children's responses to interactions in interparental relationships. A 23 factorial experiment will assess whether, and to what extent, three candidate intervention components demonstrate main and interactive effects on children's coping and mental health. Children aged 9-12 (target N = 144) will be randomly assigned to one of eight combinations of three components with two levels each: (1) reappraisal (present vs. absent), (2) distraction (present vs. absent), (3) relaxation (present vs. absent). The primary outcomes are child-report emotional security and coping efficacy at one-month post-intervention. Secondary outcomes include internalizing and externalizing problems at the three-month follow-up. Based on data from this optimization phase RCT, intervention components will be selected to comprise a multi-component intervention and assessed for effectiveness in a subsequent evaluation phase RCT.

Distinguishing between-person and within-person relationships in longitudinal health research: arthritis and quality of life.

BACKGROUND: Many health measures (e.g., blood pressure, quality of life) have meaningful fluctuation over time around a relatively stable mean level for each person. PURPOSE: This didactic paper describes two closely related statistical models for examining between-person and within-person relationships between two or more sets of measures collected over time: the latent intercept model with correlated residuals (LI) in structural equation modeling framework and the multivariate multilevel model (MVML) in multilevel modeling framework. RESULTS: We illustrated that the basic LI model and the MVML model are equivalent. We presented an illustrative example using a national arthritis data resource to examine between-person and within-person relationships of symptom status, functional health, and quality of life in arthritis patients. DISCUSSION: Additional design and modeling issues for the treatment of missing data are considered. We discuss contexts in which one of the two models may be preferred. Mplus and SAS syntax are available.

Establishing measurement invariance: English and Spanish Paediatric Asthma Quality of Life Questionnaire.

BACKGROUND: Registered nurses and nurse researchers often use questionnaires to measure patient outcomes. When questionnaires or other multiple-item instruments have been developed using a relatively homogeneous sample, the suitability of even a psychometrically well-developed instrument for the new population comes into question. Bias or lack of equivalence can be introduced into instruments through differences in perceptions of the meaning of the measured items, constructs, or both in the two groups. OBJECTIVE: To explain measurement invariance and illustrate how it can be tested using the English and Spanish versions of the Paediatric Asthma Quality of Life Questionnaire (PAQLQ). METHODS: A sample of 607 children from the Phoenix Children's Hospital Breathmobile was selected for this analysis. The children were of ages 6-18 years; 61.2% completed the PAQLQ in Spanish. Testing measurement invariance using multiple-group confirmatory factor analysis, a series of hierarchical nested models, is demonstrated. In assessing the adequacy of the fit of each model at each stage, both χ2 tests and goodness-of-fit indexes were used. RESULTS: The test of measurement invariance for the one-factor model showed that the English and Spanish versions of the scale met the criteria for measurement invariance. The level of strict invariance (equal factor loadings, intercepts, and residual variances between groups) was achieved. DISCUSSION: Confirmatory factor analysis is used to evaluate the structural integrity of a measurement instrument; multiple confirmatory factor analyses are used to assess measurement invariance across different groups and to stamp the data as valid or invalid. The PAQLQ, a widely used instrument having evidence to support reliability and validity was used separately in English- and Spanish-speaking groups. Traditional methods for evaluating measurement instruments have been less than thorough, and this article demonstrates a well-developed approach, allowing for confident comparisons between populations.

Trajectories of Math and Reading Achievement in Low Achieving Children in Elementary School: Effects of Early and Later Retention in Grade.

This study investigated the effects of retention or promotion in first grade on growth trajectories in mathematics and reading achievement over the elementary school years (grades 1-5). From a large multiethnic sample (n = 784) of children who were below the median in literacy at school entrance, 363 children who were either promoted (n = 251) or retained (n = 112) in first grade could be successfully matched on 72 background variables. Achievement was measured annually using Woodcock-Johnson W scores; scores of retained children were shifted back one year to permit same-grade comparisons. Using longitudinal growth curve analysis, trajectories of math and reading scores for promoted and retained children were compared. Retained children received a one year boost in achievement; this boost fully dissipated by the end of elementary school. The pattern of subsequent retention in grades 2, 3 and 4 and placement in special education of the sample during the elementary school years is also described and their effects are explored. Policy implications for interventions for low achieving children are considered.

Estimating Latent Variable Interactions With Non-Normal Observed Data: A Comparison of Four Approaches.

A Monte Carlo simulation was conducted to investigate the robustness of four latent variable interaction modeling approaches (Constrained Product Indicator [CPI], Generalized Appended Product Indicator [GAPI], Unconstrained Product Indicator [UPI], and Latent Moderated Structural Equations [LMS]) under high degrees of non-normality of the observed exogenous variables. Results showed that the CPI and LMS approaches yielded biased estimates of the interaction effect when the exogenous variables were highly non-normal. When the violation of non-normality was not severe (normal; symmetric with excess kurtosis < 1), the LMS approach yielded the most efficient estimates of the latent interaction effect with the highest statistical power. In highly non-normal conditions, the GAPI and UPI approaches with ML estimation yielded unbiased latent interaction effect estimates, with acceptable actual Type-I error rates for both the Wald and likelihood ratio tests of interaction effect at N ≥ 500. An empirical example illustrated the use of the four approaches in testing a latent variable interaction between academic self-efficacy and positive family role models in the prediction of academic performance.

Beyond Experiments.

It is often claimed that only experiments can support strong causal inferences and therefore they should be privileged in the behavioral sciences. We disagree. Overvaluing experiments results in their overuse both by researchers and decision makers and in an underappreciation of their shortcomings. Neglect of other methods often follows. Experiments can suggest whether X causes Y in a specific experimental setting; however, they often fail to elucidate either the mechanisms responsible for an effect or the strength of an effect in everyday natural settings. In this article, we consider two overarching issues. First, experiments have important limitations. We highlight problems with external, construct, statistical-conclusion, and internal validity; replicability; and conceptual issues associated with simple X causes Y thinking. Second, quasi-experimental and nonexperimental methods are absolutely essential. As well as themselves estimating causal effects, these other methods can provide information and understanding that goes beyond that provided by experiments. A research program progresses best when experiments are not treated as privileged but instead are combined with these other methods.