When modeling psychological processes and relationships, intrinsically nonlinear models often enhance researchers' ability to draw useful theoretical and substantive conclusions. In addition, psychological theories frequently suggest that such processes and relationships are moderated; therefore, it is often important to test for, probe, and plot moderation. However, extant methods for assessing and visualizing moderation are largely restricted to linear models. Therefore, the goal of this paper is to develop novel analytical and software tools that enable researchers to specify and examine moderated parameters within intrinsically nonlinear models. First, methods for testing, plotting, and probing moderation are expanded in novel ways for use in nonlinear models; specifically, we present conceptual and mathematical extensions of the Johnson-Neyman (JN) technique. The JN technique is currently used to probe moderation of simple slopes within the linear modeling framework; our extensions enable its application to any moderated parameter of an intrinsically nonlinear model. Additionally, we introduce a Shiny application called CurveBuilder, which unifies the process of choosing, specifying, fitting, and visualizing intrinsically nonlinear models that may include moderated parameters and/or random effects. The application provides a code-free environment for users to complete all steps of the analysis process, including uploading data, visually choosing start values, specifying models, plotting results, and probing moderation with the extended JN technique. CurveBuilder examples are reviewed, and opportunities for future work in this area are discussed.

Objective Tuberculosis (TB) stigma is a critical barrier to timely diagnosis and treatment, yet few studies have quantified community-level TB stigma or its variability across geographic contexts. This study describes methods for capturing community-level TB stigma and examines stigma variability and correlations with community-level sociodemographic and TB-related factors across urban, periurban and rural communities.Design Ecological study.Setting 93 demarcated study communities in Buffalo City Metropolitan Health District, Eastern Cape, South Africa.Participants 3869 heads of household, age ≥18 years, were surveyed in a geographically clustered random sample of households across the 93 study communities.Primary outcome measures Validated scales were used to measure perceived TB stigma. Community levels of TB stigma were generated by aggregating individual responses within each study community.Results Median community TB stigma scores varied significantly by community location: compared with urban communities, rural communities had lower TB stigma scores (beta=−0.235; 95% CI −0.362 to −0.108) while periurban communities had higher scores (beta=0.136; 95% CI 0.017 to 0.254). Community TB stigma was positively associated with community HIV stigma, with the strongest associations in urban (beta=0.977 (95% CI 0.634 to 1.321) and rural (beta=0.816 (95% CI 0.186 to 1.446) communities. No associations were observed between TB stigma and TB prevalence, TB knowledge or household demographics after adjusting for community location.Conclusions TB stigma varied meaningfully across communities and was associated with urbanicity and HIV stigma. Stigma is a complex social process and there may be many other factors shaping TB stigma at the community level. Future research and stigma-reduction interventions should consider local contexts and community-level determinants beyond individual demographics, TB knowledge or community TB burden.

In both grant proposals and published studies, many research hypotheses (represented by primary parameters) are tested in the context of complex statistical models. The power to detect these primary parameters depends on the values of multiple secondary model parameters that often go unexamined, unreported, and unjustified. The result is that many a priori power analyses are incomplete, ambiguous, potentially subjective, and nearly impossible for others to evaluate. In the current article, we encourage researchers to use plausible values for secondary parameters (PVSPs), in addition to the hoped-for effect sizes for their primary parameters, in their power calculations. More specifically, upper and lower bounds for power are generated based on the highest and lowest plausible values for secondary model parameters. In the article, we demonstrate how to conduct and describe such power estimates for four increasingly complex statistical methods. We further demonstrate how such analyses can inform decisions about resource allocation in ways that improve power in the context of complex statistical models, often revealing that power can be enhanced by methods other than increasing sample size. The PVSP approach can enhance power, improve the transparency of power analyses in grant proposals, reduce the likelihood of funding underpowered research, and alleviate at least one problem underlying the replication crisis.

Model complexity is a critical consideration when evaluating a statistical model. To quantify complexity, one can examine fitting propensity (FP), or the ability of the model to fit well to diverse patterns of data. The scant foundational research on FP has focused primarily on proof of concept rather than practical application. To address this oversight, the present work joins a recently published study in examining the FP of models that are commonly applied in factor analysis. We begin with a historical account of statistical model evaluation, which refutes the notion that complexity can be fully understood by counting the number of free parameters in the model. We then present three sets of analytic examples to better understand the FP of exploratory and confirmatory factor analysis models that are widely used in applied research. We characterize our findings relative to previously disseminated claims about factor model FP. Finally, we provide some recommendations for future research on FP in latent variable modeling. (PsycInfo Database Record (c) 2025 APA, all rights reserved).

Estimating statistical power is essential for designing behavioral medicine studies efficiently and conserving finite resources. Sometimes behavioral medicine researchers are interested in calculating power for 1-sided z-tests of individual parameters (e.g., slopes) in complex models such as multilevel structural equation models or multilevel mixture regression models. For such models, calculating power for 1-sided z-tests is cumbersome because: (a) online z-test power calculator tools are inapplicable, (b) commonly-used power analysis software provides power only for 2-sided z-tests and does not allow changing alpha, and (c) published power tables typically provide power results only for 2-sided z-tests. Hence, here we introduce straightforward and resource-efficient conversion formulas to estimate the power of 1-sided z-tests of individual parameters in any model by using direct power conversions from the corresponding 2-sided tests. We then implement these conversion formulas in accessible R and Excel software. This brief report thus provides behavioral medicine researchers with a convenient and practical solution for power calculation that minimizes the time, financial, and computational resources typically needed for power estimation.

Introduction:Tuberculosis (TB) stigma is a critical barrier to timely diagnosis and treatment. Although stigma originates within communities, few studies have quantified community-level TB stigma or its variability across geographic contexts. This study describes methods for capturing community-level TB stigma and examines stigma variability across 93 urban, peri-urban, and rural communities in Buffalo City Metropolitan Health District, South Africa. Methods:As part of the MISSED TB Outcomes Study, heads of household (HoHs) were surveyed in a geographically clustered random sample of households across demarcated study communities. Validated scales were used to measure perceived community-level TB stigma, HIV stigma, and TB/HIV knowledge. Demographic data, including self-reported household TB and HIV history, were also captured. Community-level data, including TB and HIV stigma, were generated by aggregating individual responses within each study community. Associations between TB stigma and other community-level variables were analyzed using robust linear regression. Results:Surveys were completed by 3,869 households across 93 communities. Median community TB stigma scores varied significantly by community location, with rural communities reporting the lowest stigma and peri-urban communities the highest. TB stigma was positively associated with HIV stigma across all community types, with the strongest associations in urban and rural communities. No associations were observed between TB stigma and TB prevalence, TB knowledge, or household demographics after adjusting for community location. Conclusions:TB stigma varied meaningfully across communities and was influenced by urbanicity and HIV stigma. These findings suggest that stigma-reduction interventions must be tailored to local contexts and consider community-level determinants beyond individual knowledge or TB burden. The identified variability in TB stigma will inform future multilevel analyses of the TB care cascade in South Africa.

Objective: Posttrauma nightmares are recurring nightmares that begin after a traumatic experience. Research has only recently begun to identify variables that predict posttrauma nightmare occurrences. Research has identified presleep arousal-cognitive (PSA-C) and presleep arousal physiological (PSA-PHYS), sleep onset latency (SOL), and sleep-disordered breathing (SDB) as potential predictors of posttrauma nightmares. However, previous research includes methodological limitations, such as a lack of physiological measures and a homogeneous sample. To replicate previous findings and increase generalizability, the current study investigated predictors of nightmare occurrences in a sample of male inpatient veterans with mixed-trauma history. Method: Participants (n = 15) completed an initial assessment battery and seven consecutive days of pre and postsleep diaries, including measures of posttrauma nightmare triggers and posttrauma nightmare occurrences. Portable objective measurements of sleep and presleep states were used to examine sleep quality and physical arousal. Results: Analyses revealed that PSA-C and SOL both predicted posttrauma nightmare occurrences and that PSA-PHYS was significantly higher on nights when nightmares occurred. Conclusion: Results replicate earlier research which posits that PSA and SOL play a role in triggering the occurrence of posttrauma nightmares. It should be noted that the sample was relatively small, warranting cautious interpretation of results. However, when taken together with the findings of the replicated study, results could suggest the plausibility of therapies targeting presleep cognitions, SOL, and presleep arousal in the treatment of posttrauma nightmares.

In multilevel models, disaggregating predictors into level-specific parts (typically accomplished via centering) benefits parameter estimates and their interpretations. However, the importance of level-specificity has been sparsely addressed in multilevel literature concerning collinearity. In this study, we develop novel insights into the interactivity of centering and collinearity in multilevel models. After integrating the broad literatures on centering and collinearity, we review level-specific and conflated correlations in multilevel data. Next, by deriving formal relationships between predictor collinearity and multilevel model estimates, we demonstrate how the consequences of collinearity change across different centering specifications and identify data characteristics that may exacerbate or mitigate those consequences. We show that when all or some level-1 predictors are uncentered, slope estimates can be greatly biased by collinearity. Disaggregation of all predictors eliminates the possibility that fixed effect estimates will be biased due to collinearity alone; however, under some data conditions, collinearity is associated with biased standard errors and random effect (co)variance estimates. Finally, we illustrate the importance of disaggregation for diagnosing collinearity in multilevel data and provide recommendations for the use of level-specific collinearity diagnostics. Overall, the necessity of disaggregation for identifying and managing collinearity's consequences in multilevel models is clarified in novel ways.

Variability in treatment effects is common in intervention studies using cluster randomized controlled trial (C-RCT) designs. Such variability is often examined in multilevel modeling (MLM) to understand how treatment effects (TRT) differ based on the level of a covariate (COV), called TRT × COV. In detecting TRT × COV effects using MLM, relationships between covariates and outcomes are assumed to vary across clusters linearly. However, this linearity assumption may not hold in all applications and an incorrect assumption may lead to biased statistical inference about TRT × COV effects. In this study, we present generalized additive mixed model (GAMM) specifications in which cluster-specific functional relationships between covariates and outcomes can be modeled using by-variable smooth functions. In addition, the implementation for GAMM specifications is explained using the mgcv R package (Wood, 2021). The usefulness of the GAMM specifications is illustrated using intervention data from a C-RCT. Results of simulation studies showed that parameters and by-variable smooth functions were recovered well in various multilevel designs and the misspecification of the relationship between covariates and outcomes led to biased estimates of TRT × COV effects. Furthermore, this study evaluated the extent to which the GAMM can be treated as an alternative model to MLM in the presence of a linear relationship.

This study's first purpose was to investigate effects of a fourth- and fifth-grade “next-generation” fraction intervention, which included six enhancements over a previously validated fraction intervention, designed to address career- and college-readiness standards. The study's second purpose was to assess effects of the next-generation fraction intervention at follow-up, 1 year after intervention ended. The third purpose was to isolate the effects of one of the six intervention enhancements: interleaved fraction calculations instruction. Students with intensive intervention needs were randomized to next-generation fraction intervention (Super Solvers [SSINT]) with blocked calculations instruction (SSINT_B), SSINT with interleaved calculations instruction (SSINT_I), and control. On a mix of proximal and transfer outcomes, SSINT (across conditions) produced strong, significant effects over control at posttest. At follow-up, effect sizes were weaker but remained significant on calculations: g = 1.22. On other measures, follow-up g was 0.39 to 0.58. The effect of SSINT_I over SSINT_B, although not significant at posttest ( g = 0.28), was statistically significant and large at follow-up ( g = 0.65), in line with the cognitive science literature showing long-term advantages for interleaved instruction. Results suggest next-generation fraction intervention efficacy for intensive-needs students and the importance of interleaved instruction.

Background/objectives Nutrition and obesity researchers often dichotomize or discretize continuous independent variables to conduct an analysis of variance to examine group differences. We describe consequences associated with dichotomizing and discretizing continuous variables using two cross-sectional studies related to nutrition. Subjects/methods Study 1 investigated the effects of health literacy and nutrition knowledge on nutrition label accuracy ( n = 612). Study 2 investigated the effects of cognitive restraint and BMI on fruit and vegetable (F/V) intake ( n = 586). We compare analytic approaches where continuous independent variables were either discretized/dichotomized or analyzed as continuous variables. Results In Study 1, dichotomization of health literacy and nutrition knowledge for 2 × 2 ANOVA revealed health literacy had an effect on nutrition label accuracy. Nutrition knowledge has an effect on nutrition label accuracy, but the health literacy by nutrition knowledge interaction was not significant. When analyzed using regression, the nutrition knowledge effect was significant. The simple effect of health literacy was also significant when health literacy equals zero. Finally, the quadratic effect of health literacy was negative and significant. In Study 2, dichotomization and discretization of cognitive restraint and BMI were used for three ANOVAs, which discretized BMI in three ways. For all ANOVAs, the BMI main effect for predicting fruit and vegetable intake was significant, the interaction between BMI and cognitive restraint was non-significant, and cognitive restraint was only significant when both variables were dichotomized. When analyzed using regression, the continuous mean-centered variables, and their interaction each significantly predicted F/V intake. Conclusions Dichotomizing continuous independent variables resulted in distortions of effect sizes across studies, an inability to assess the quadratic effect of health literacy, and an inability to detect the moderating effect of BMI. We discourage researchers from dichotomizing and discretizing continuous independent variables and instead use multiple regression to examine relationships between continuous independent and dependent variables.

Purpose Fear of recurrence (FoR) is a prevalent and difficult experience among cancer patients. Most research has focused on FoR among breast cancer patients, with less attention paid to characterizing levels and correlates of FoR among oral and oropharyngeal cancer survivors. The purpose was to characterize FoR with a measure assessing both global fears and the nature of specific worries as well as evaluate the role of sociodemographic and clinical factors, survivorship care transition practices, lifestyle factors, and depressive symptoms in FoR. Methods Three hundred eighty-nine oral and oropharyngeal survivors recruited from two cancer registries completed a survey assessing demographics, cancer treatment, symptoms, alcohol and tobacco use, survivorship care practices, depression, and FoR. Results Forty percent reported elevated global FoR, with similar percentages for death (46%) and health worries (40.3%). Younger, female survivors and survivors experiencing more physical and depressive symptoms reported more global fears and specific fears about the impact of recurrence on roles, health, and identity, and fears about death. Depression accounted for a large percent of the variance. Lower income was associated with more role and identity/sexuality worries, and financial hardship was associated with more role worries. Conclusions FoR is a relatively common experience for oral and oropharyngeal cancer survivors. Many of its correlates are modifiable factors that could be addressed with multifocal, tailored survivorship care interventions. Implications for Cancer Survivors Assessing and addressing depressive symptoms, financial concerns, expected physical symptoms in the first several years of survivorship may impact FoR among oral and oropharyngeal cancer survivors.

The topic of centering in multilevel modeling (MLM) has received substantial attention from methodologists, as different centering choices for lower-level predictors present important ramifications for the estimation and interpretation of model parameters. However, the centering literature has focused almost exclusively on continuous predictors, with little attention paid to whether and how categorical predictors should be centered, despite their ubiquity across applied fields. Alongside this gap in the methodological literature, a review of applied articles showed that researchers center categorical predictors infrequently and inconsistently. Algebraically and statistically, continuous and categorical predictors behave the same, but researchers using them do not, and for many, interpreting the effects of categorical predictors is not intuitive. Thus, the goals of this tutorial article are twofold: to clarify why and how categorical predictors should be centered in MLM, and to explain how multilevel regression coefficients resulting from centered categorical predictors should be interpreted. We first provide algebraic support showing that uncentered coding variables result in a conflated blend of the within- and between-cluster effects of a multicategorical predictor, whereas appropriate centering techniques yield level-specific effects. Next, we provide algebraic derivations to illuminate precisely how the within- and between-cluster effects of a multicategorical predictor should be interpreted under dummy, contrast, and effect coding schemes. Finally, we provide a detailed demonstration of our conclusions with an empirical example. Implications for practice, including relevance of our findings to categorical control variables (i.e., covariates), interaction terms with categorical focal predictors, and multilevel latent variable models, are discussed. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

OBJECTIVE:Individuals with autism spectrum disorder (ASD) have significant impairment in social competence and reduced social salience. SENSE Theatre, a peer-mediated, theater-based intervention has demonstrated posttreatment gains in face memory and social communication. The multisite randomized clinical trial compared the Experimental (EXP; SENSE Theatre) to an Active Control Condition (ACC; Tackling Teenage Training, TTT) at pretest, posttest, and follow-up. It was hypothesized that the EXP group would demonstrate greater incidental face memory (IFM) and better social behavior (interaction with novel peers) and social functioning (social engagement in daily life) than the ACC group, and posttest IFM would mediate the treatment effect on follow-up social behavior and functioning. METHOD:Two hundred ninety participants were randomized to EXP (N = 144) or ACC (N = 146). Per protocol sample (≥ 7/10 sessions) resulted in 207 autistic children 10-16 years. Event-related potentials measured IFM. Naive examiners measured social behavior (Vocal Expressiveness, Quality of Rapport, Social Anxiety) and functioning (Social Communication). Structural equation modeling was used to assess treatment effects. RESULTS:SENSE Theatre participants showed significantly better IFM (b = .874, p = .039) at posttest, and significant indirect effects on follow-up Vocal Expressiveness a × b = .064, with 90% CI [.014, .118] and Quality of Rapport a × b = .032, with 90% CI [.002, .087] through posttest IFM. CONCLUSIONS:SENSE Theatre increases social salience as reflected by IFM, which in turn affected Vocal Expressiveness and Quality of Rapport. Results indicate that a neural mechanism supporting social cognition and driven by social salience is engaged by the treatment and has a generalized, indirect effect on clinically meaningful functional outcomes related to core symptoms of autism. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

BACKGROUND:Statistical tests of mediation are important for advancing implementation science; however, little research has examined the sample sizes needed to detect mediation in 3-level designs (e.g., organization, provider, patient) that are common in implementation research. Using a generalizable Monte Carlo simulation method, this paper examines the sample sizes required to detect mediation in 3-level designs under a range of conditions plausible for implementation studies. METHOD:Statistical power was estimated for 17,496 3-level mediation designs in which the independent variable (X) resided at the highest cluster level (e.g., organization), the mediator (M) resided at the intermediate nested level (e.g., provider), and the outcome (Y) resided at the lowest nested level (e.g., patient). Designs varied by sample size per level, intraclass correlation coefficients of M and Y, effect sizes of the two paths constituting the indirect (mediation) effect (i.e., X→M and M→Y), and size of the direct effect. Power estimates were generated for all designs using two statistical models-conventional linear multilevel modeling of manifest variables (MVM) and multilevel structural equation modeling (MSEM)-for both 1- and 2-sided hypothesis tests. RESULTS:For 2-sided tests, statistical power to detect mediation was sufficient (≥0.8) in only 463 designs (2.6%) estimated using MVM and 228 designs (1.3%) estimated using MSEM; the minimum number of highest-level units needed to achieve adequate power was 40; the minimum total sample size was 900 observations. For 1-sided tests, 808 designs (4.6%) estimated using MVM and 369 designs (2.1%) estimated using MSEM had adequate power; the minimum number of highest-level units was 20; the minimum total sample was 600. At least one large effect size for either the X→M or M→Y path was necessary to achieve adequate power across all conditions. CONCLUSIONS:While our analysis has important limitations, results suggest many of the 3-level mediation designs that can realistically be conducted in implementation research lack statistical power to detect mediation of highest-level independent variables unless effect sizes are large and 40 or more highest-level units are enrolled. We suggest strategies to increase statistical power for multilevel mediation designs and innovations to improve the feasibility of mediation tests in implementation research.

A cluster randomized controlled trial (C-RCT) is common in educational intervention studies. Multilevel modelling (MLM) is a dominant analytic method to evaluate treatment effects in a C-RCT. In most MLM applications intended to detect an interaction effect, a single interaction effect (called a conflated effect) is considered instead of level-specific interaction effects in a multilevel design (called unconflated multilevel interaction effects), and the linear interaction effect is modelled. In this paper we present a generalized additive mixed model (GAMM) that allows an unconflated multilevel interaction to be estimated without assuming a prespecified form of the interaction. R code is provided to estimate the model parameters using maximum likelihood estimation and to visualize the nonlinear treatment-by-covariate interaction. The usefulness of the model is illustrated using instructional intervention data from a C-RCT. Results of simulation studies showed that the GAMM outperformed an alternative approach to recover an unconflated logistic multilevel interaction. In addition, the parameter recovery of the GAMM was relatively satisfactory in multilevel designs found in educational intervention studies, except when the number of clusters, cluster sizes, and intraclass correlations were small. When modelling a linear multilevel treatment-by-covariate interaction in the presence of a nonlinear effect, biased estimates (such as overestimated standard errors and overestimated random effect variances) and incorrect predictions of the unconflated multilevel interaction were found.

Objectives Mindfulness has been linked to better emotion regulation and more adaptive responses to stress across a number of studies, but the mechanisms underlying these links remain to be fully understood. The present study examines links between trait mindfulness (Five Facets of Mindfulness Questionnaire; FFMQ) and participants' responses to common emotional challenges, focusing specifically on the roles of reduced avoidance and more self-distanced engagement as key potential mechanisms driving the adaptive benefits of trait mindfulness. Methods Adults (n = 305, age range: 40-72) from the Second Generation Study of the Harvard Study of Adult Development completed two laboratory-based challenges-public speaking combined with difficult math tasks (the Trier Social Stress Test) and writing about a memory of a difficult moment. State anxiety and sadness were assessed immediately before and after the two stressors. To capture different ways of engaging, measures of self-distancing, avoidance, and persistent worry were collected during the lab session. Results As predicted, individuals who scored higher on the FFMQ experienced less anxiety and persistent worry in response to the social stressors. The FFMQ was also linked to less anxiety and sadness when writing about a difficult moment. The links between mindfulness and negative emotions after the writing task were independently mediated by self-distanced engagement and lower avoidance. Conclusions Affective benefits of trait mindfulness under stress are associated with both the degree and the nature of emotional engagement. Specifically, reduced avoidance and self-distanced engagement may facilitate reflection on negative experiences that is less affectively aversive.

Past research suggests that higher coherence between feelings and physiology under stress may confer regulatory advantages. Research and theory also suggest that higher resting vagal tone (rVT) may promote more adaptive responses to stress. The present study examines the roles of response system coherence (RSC; defined as the within-individual covariation between feelings and heart rate over time) and rVT in mediating the links between childhood adversity and later-life responses to acute stressors. Using data from 279 adults from the Second Generation Study of the Harvard Study of Adult Development who completed stressful public speaking and mental arithmetic tasks, we find that individuals who report more childhood adversity have lower RSC, but not lower rVT. We further find that lower RSC mediates the association between adversity and slower cardiovascular recovery. Higher rVT in the present study is linked to less intense cardiovascular reactivity to stress, but not to quicker recovery or to the subjective experience of negative affect after the stressful tasks. Additional analyses indicate links between RSC and mindfulness and replicate previous findings connecting RSC to emotion regulation and well-being outcomes. Taken together, these findings are consistent with the idea that uncoupling between physiological and emotional streams of affective experiences may be one of the mechanisms connecting early adversity to later-life affective responses. These findings also provide evidence that RSC and rVT are associated with distinct aspects of self-regulation under stress.

The purposes of this study were to assess the effects of fractions intervention for students who are at risk for poor outcomes and to examine whether a component that combines self-regulated learning with growth-mindset instruction (SR-GM) provides added value for improving outcomes. At-risk students ( N = 84) were randomly assigned to three conditions: fractions intervention, fractions intervention with embedded SR-GM, and a control group. Intervention was conducted three times per week for 35 min per session for 13 weeks. Multilevel models indicated both fractions intervention conditions produced strong effects, with no added value for SR-GM. Posttest fractions achievement gaps for both intervention conditions held steady, narrowed, or closed, whereas the control group’s gaps remained sizeable or grew. Results suggest that intervention can address challenging mathematics standards for at-risk learners and that SR-GM instruction may not be necessary in the context of strong intervention.