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Fraudulent analysis and reporting of psychological data have the potential to contaminate the scientific knowledge base and eventuate in the unjustified expenditure of public money and scientific effort (Koocher & Keith-Spiegel, 1998). Traditionally, the field has relied on quantitative methodologists to educate researchers in proper analysis and reporting practices, and to examine these via peer review. The field has also relied on psychologists with training or board service in ethics to establish standards and implement strategies to discourage misconduct. However, this division of responsibility for examination, standard setting, and deterrence is shown to compromise the effectiveness of methodologists' and ethicists' respective gatekeeping efforts. Methodologically and ethically trained specialists instead need to coordinate efforts to safeguard analysis and reporting procedures. Researchers also need to increase self-monitoring. Potential obstacles to achieving these ends are considered, and three tactics are proposed to overcome them. [ABSTRACT FROM AUTHOR]

It is unappreciated that there are four different approaches to power analysis for detecting misspecification by testing overall fit of structural equation models (SEMs) and, moreover, that common approaches can yield radically diverging results for SEMs with many items (high p ). Here we newly relate these four approaches. Analytical power analysis methods using theoretical null and theoretical alternative distributions (Approach 1) have a long history, are widespread, and are often contrasted with "the" Monte Carlo method-which is an oversimplification. Actually, three Monte Carlo methods can be distinguished; all use an empirical alternative distribution but differ regarding whether the null distribution is theoretical (Approach 2), empirical (Approach 3), or-as we newly propose and demonstrate the need for-adjusted empirical (Approach 4). Because these four approaches can yield radically diverging power results under high p (as demonstrated here), researchers need to "match" their a priori SEM power analysis approach to their later SEM data analysis approach for testing overall fit, once data are collected. Disturbingly, the most common power analysis approach for a global test-of-fit is mismatched with the most common data analysis approach for a global test-of-fit in SEM. Because of this mismatch, researchers' anticipated versus actual/obtained power can differ substantially. We explain how/why to "match" across power-analysis and data-analysis phases of a study and provide software to facilitate doing so. As extensions, we explain how to relate and implement all four approaches to power analysis (a) for testing overall fit using χ² versus root-mean-square error of approximation and (b) for testing overall fit versus testing a target parameter/effect. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

For multilevel models (MLMs) with fixed slopes, it has been widely recognized that a level-1 variable can have distinct between-cluster and within-cluster fixed effects, and that failing to disaggregate these effects yields a conflated, uninterpretable fixed effect. For MLMs with random slopes, however, we clarify that two different types of slope conflation can occur: that of the fixed component (termed fixed conflation) and that of the random component (termed random conflation). The latter is rarely recognized and not well understood. Here we explain that a model commonly used to disaggregate the fixed component-the contextual effect model with random slopes-troublingly still yields a conflated random component. Negative consequences of such random conflation have not been demonstrated. Here we show that they include erroneous interpretation and inferences about the substantively important extent of between-cluster differences in slopes, including either underestimating or overestimating such slope heterogeneity. Furthermore, we show that this random conflation can yield inappropriate standard errors for fixed effects. To aid researchers in practice, we delineate which types of random slope specifications yield an unconflated random component. We demonstrate the advantages of these unconflated models in terms of estimating and testing random slope variance (i.e., improved power, Type I error, and bias) and in terms of standard error estimation for fixed effects (i.e., more accurate standard errors), and make recommendations for which specifications to use for particular research purposes.

Applications of multilevel models (MLMs) with three or more levels have increased alongside expanding software capability and dataset availability. Though researchers often express interest in R-squared measures as effect sizes for MLMs, R-squareds previously proposed for MLMs with three or more levels cover a limited subset of choices for how to quantify explained variance in these models. Additionally, analytic relationships between total and level-specific versions of MLM R-squared measures have not been clarified, despite such relationships becoming increasingly important to understand when there are more levels. Furthermore, the impact of predictor centering strategy on R-squared computation and interpretation has not been explicated for MLMs with any number of levels. To fill these gaps, we extend the Rights and Sterba two-level MLM R-squared framework to three or more levels, providing a general set of measures that includes preexisting three-level measures as special cases and yields additional results not obtainable from existing measures. We mathematically and pedagogically relate total and level-specific R-squareds, and show how all total and level-specific R-squared measures in our framework can be computed under any centering strategy. Finally, we provide and empirically demonstrate software (available in the r2mlm R package) to compute measures and graphically depict results.

Objective: Comorbidity of disordered eating (DE) behaviors and nonsuicidal self-injury (NSSI) is linked to increased functional impairment. The present study identified subtypes of DE and NSSI comorbidity in a non-Western, low- and middle-income country where there has been particularly little research in this area., Method: Latent profile analyses (LPA) were conducted to identify patterns of subgroup comorbidity in self-reported DE behaviors and NSSI behaviors, in a sample of Vietnamese high-school students (N = 1451, 51% female). Parallel-process LPA was used to predict NSSI subgroup membership from DE subgroup membership., Results: A seven-class LPA model was identified for DE: (1) Low frequencies of all DE behaviors; (2) Frequent levels of all DE behaviors; (3) Frequent fasting and purging behaviors; (4) Frequent binge eating only; (5) Moderate binge eating; (6) Moderate fasting and purging behaviors; (7) Exercise and fasting. A two-class (high versus low) model was identified for NSSI. Odds of membership in the high-NSSI class were significantly increased for all DE classes except the class characterized by moderate binge eating. Odds of belonging to the high-NSSI class were highest for those in DE classes involving purging behaviors. Males predominated in classes characterized by high behavior dysregulation., Discussion: DE and NSSI represent important clinical concerns among Vietnamese youth in urban contexts, and males may show particular vulnerability for certain risk behaviors. The association of classes of DE behaviors to NSSI was particularly strong for classes that involved purging, highlighting the importance of this specific behavior for understanding comorbidity of DE and NSSI., Public Significance: Disordered eating and nonsuicidal self-injury (NSSI; hurting oneself without intending to die) commonly co-occur. There has been less research on disordered eating and NSSI among individuals from non-Western or low/middle-income countries. We examined patterns of these behaviors in a school-based sample of Vietnamese adolescents. We found that patterns of disordered eating distinguished by purging showed particular links to NSSI, which could have implications for screening and treatment., (© 2022 Wiley Periodicals LLC. This article has been contributed to by U.S. Government employees and their work is in the public domain in the USA.)

The main purpose of this study was to test the effects of word-problem intervention, with versus without embedded language comprehension instruction, on at-risk 1 st graders' word-problem performance. We also isolated the need for a structured approach to word-problem intervention and tested the efficacy of schema-based instruction at 1 st grade. Children (n=391; mean age = 6.53, SD = 0.32) were randomly assigned to 4 conditions: schema-based word-problem intervention with embedded language instruction, the same word-problem intervention but without language comprehension instruction, structured number knowledge intervention without a structured word-problem component, and a control group. Each intervention included 45 30-min sessions. Multilevel models, accounting for classroom and school effects, revealed the efficacy of schema-based word-problem intervention at 1 st grade, with both word-problem conditions outperforming the number knowledge condition and the control group. Yet, word-problem performance was significantly stronger for the schema-based condition with embedded language comprehension instruction compared to the schema-based condition without language comprehension instruction. Number knowledge intervention conveyed no word-problem advantage over the control group, even though all 3 intervention conditions outperformed the control group on arithmetic. Results demonstrate the importance of a structured approach to word-problem intervention; the efficacy of schema-based instruction at 1 st grade; and the added value of language comprehension instruction within word-problem intervention. Results also provide causal evidence on the role of language comprehension in word-problem solving.

Developmental researchers commonly utilize multilevel models (MLMs) to describe and predict individual differences in change over time. In such growth model applications, researchers have been widely encouraged to supplement reporting of statistical significance with measures of effect size, such as R-squareds (R 2 ) that convey variance explained by terms in the model. An integrative framework for computing R-squareds in MLMs with random intercepts and/or slopes was recently introduced by Rights and Sterba and it subsumed pre-existing MLM R-squareds as special cases. However, this work focused on cross-sectional applications, and hence did not address how the computation and interpretation of MLM R-squareds are affected by modeling considerations typically arising in longitudinal settings: (a) alternative centering choices for time (e.g., centering-at-a-constant vs. person-mean-centering), (b) nonlinear effects of predictors such as time, (c) heteroscedastic level-1 errors and/or (d) autocorrelated level-1 errors. This paper addresses these gaps by extending the Rights and Sterba R-squared framework to longitudinal contexts. We: (a) provide a full framework of total and level-specific R-squared measures for MLMs that utilize any type of centering, and contrast these with Rights and Sterba's measures assuming cluster-mean-centering, (b) explain and derive which measures are applicable for MLMs with nonlinear terms, and extend the R-squared computation to accommodate (c) heteroscedastic and/or (d) autocorrelated errors. Additionally, we show how to use differences in R-squared (ΔR 2 ) measures between growth models (adding, for instance, time-varying covariates as level-1 predictors or time-invariant covariates as level-2 predictors) to obtain effects sizes for individual terms. We provide R software (r2MLMlong) and a running pedagogical example analyzing growth in adolescent self-efficacy to illustrate these methodological developments. With these developments, researchers will have greater ability to consider effect size when analyzing and predicting change using MLMs., (© 2021 Wiley Periodicals LLC.)

When comparing multilevel models (MLMs) differing in fixed and/or random effects, researchers have had continuing interest in using R-squared differences to communicate effect size and importance of included terms. However, there has been longstanding confusion regarding which R-squared difference measures should be used for which kind of MLM comparisons. Furthermore, several limitations of recent studies on R-squared differences in MLM have led to misleading or incomplete recommendations for practice. These limitations include computing measures that are by definition incapable of detecting a particular type of added term, considering only a subset of the broader class of available R-squared difference measures, and incorrectly defining what a given R-squared difference measure quantifies. The purpose of this paper is to elucidate and resolve these issues. To do so, we define a more general set of total, within-cluster, and between-cluster R-squared difference measures than previously considered in MLM comparisons and give researchers concrete step-by-step procedures for identifying which measure is relevant to which model comparison. We supply simulated and analytic demonstrations of limitations of previous MLM studies on R-squared differences and show how application of our step-by-step procedures and general set of measures overcomes each. Additionally, we provide and illustrate graphical tools and software allowing researchers to automatically compute and visualize our set of measures in an integrated manner. We conclude with recommendations, as well as extensions involving (a) how our framework relates to and can be used to obtain pseudo-R-squareds, and (b) how our framework can accommodate both simultaneous and hierarchical model-building approaches.

Researchers often mention the utility and need for R-squared measures of explained variance for multilevel models (MLMs). Although this topic has been addressed by methodologists, the MLM R-squared literature suffers from several shortcomings: (a) analytic relationships among existing measures have not been established so measures equivalent in the population have been redeveloped 2 or 3 times; (b) a completely full partitioning of variance has not been used to create measures, leading to gaps in the availability of measures to address key substantive questions; (c) a unifying approach to interpreting and choosing among measures has not been provided, leading to researchers' difficulty with implementation; and (d) software has inconsistently and infrequently incorporated available measures. We address these issues with the following contributions. We develop an integrative framework of R-squared measures for MLMs with random intercepts and/or slopes based on a completely full decomposition of variance. We analytically relate 10 existing measures from different disciplines as special cases of 5 measures from our framework. We show how our framework fills gaps by supplying additional total and level-specific measures that answer new substantive research questions. To facilitate interpretation, we provide a novel and integrative graphical representation of all the measures in the framework; we use it to demonstrate limitations of current reporting practices for MLM R-squareds, as well as benefits of considering multiple measures from the framework in juxtaposition. We supply and empirically illustrate an R function, r2MLM, that computes all measures in our framework to help researchers in considering effect size and conveying practical significance. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

In structural equation modeling applications, parcels-averages or sums of subsets of item scores-are often used as indicators of latent constructs. Parcel-allocation variability (PAV) is variability in results that arises within sample across alternative item-to-parcel allocations. PAV can manifest in all results of a parcel-level model (e.g., model fit, parameter estimates, standard errors, and inferential decisions). It is a source of uncertainty in parcel-level model results that can be investigated, reported, and accounted for. Failing to do so raises representativeness and replicability concerns. However, in recent methodological literature (Cole, Perkins, & Zelkowitz, 2016 ; Little, Rhemtulla, Gibson, & Shoemann, 2013 ; Marsh, Ludtke, Nagengast, Morin, & von Davier, 2013 ; Rhemtulla, 2016 ) parceling has been justified and recommended in several situations without quantifying or accounting for PAV. In this article, we explain and demonstrate problems with these rationales. Overall, we find that: (1) using a purposive parceling algorithm for a multidimensional construct does not avoid PAV; (2) passing a test of unidimensionality of the item-level model need not avoid PAV; and (3) a desire to improve power for detecting structural misspecification does not warrant parceling without addressing PAV; we show how to simultaneously avoid PAV and obtain even higher power by comparing item-level models differing in structural constraints. Implications for practice are discussed.

Previous research has linked sleep disturbance to anxiety. However, evidence for this relation has been inconsistent, largely limited to retrospective reports that do not account for daily variability, and silent on when the association is most pronounced. Thus, the present study utilized ecological momentary assessment (EMA) to examine the effects of daily deviations in total sleep time (TST) and person-average TST on anxiety and whether these effects varied as a function of time of day in a sample of unselected adults (N = 138). Results indicate that the amount of TST on a given night, relative to personal average TST, negatively predicted anxiety, and this relation was significant in the morning and afternoon, but not evening. In contrast, person-average TST was unrelated to average anxiety. Relations between TST and anxiety did not differ across objective (e.g., actigraphy) and subjective (e.g., sleep diary) measures. Furthermore, the pattern of results remained the same when controlling for previous day's anxiety and were not bidirectional. These findings suggest that getting less sleep than is typical for the individual predicts subsequent anxiety, and this effect is particularly strong in the morning. Average sleep duration may be less important to the experience of anxiety than deviations from that average. These findings highlight the importance of EMA to examine how and when variability in sleep confers vulnerability for anxiety symptoms., (Copyright © 2018 Elsevier Ltd. All rights reserved.)

Psychologists commonly apply regression mixture models in single-level (i.e., unclustered) and multilevel (i.e., clustered) data analysis contexts. Though researchers applying nonmixture regression models typically report R-squared measures of explained variance, there has been no general treatment of R-squared measures for single-level and multilevel regression mixtures. Consequently, it is common for researchers to summarize results of a fitted regression mixture by simply reporting class-specific regression coefficients and their associated p values, rather than considering measures of effect size. In this article, we fill this gap by providing an integrative framework of R-squared measures for single-level regression mixture models and multilevel regression mixture models (with classes at Level-2 or both levels). Specifically, we describe 11 R-squared measures that are distinguished based on what the researcher chooses to consider as outcome variance and what sources the researcher chooses to contribute to predicted variance. We relate these measures analytically and through simulated graphical illustrations. Further, we demonstrate how these R-squared measures can be decomposed in novel ways into substantively meaningful sources of explained variance. We describe and demonstrate new software tools to allow researchers to compute these R-squared measures and decompositions in practice. Using 2 empirical examples, we show how researchers can answer distinct substantive questions with each measure and can gain insights by interpreting the set of measures in juxtaposition to each other. (PsycINFO Database Record, ((c) 2018 APA, all rights reserved).)

The current study examined effects of a preventive intervention on patterns of change in symptoms of anxiety and depression in a sample of children of depressed parents. Parents with a history of depression (N = 180) and their children (N = 242; 50% female; M age  = 11.38; 74% Euro-American) enrolled in an intervention to prevent psychopathology in youth. Families were randomized to a family group cognitive behavioral intervention (FGCB) or a written information (WI) control condition. Parents and youth completed the Child Behavior Checklist and Youth Self Report at baseline, 6-, 12-, 18-, and 24-month follow up. Youth in the FGCB intervention reported significantly greater declines in symptoms of both anxiety and depression at 6, 12, and 18 months compared to youth in the WI condition. Youth with higher baseline levels of each symptom (e.g., anxiety) reported greater declines in the other symptom (e.g., depression) from 0 to 6 months in the FGCB intervention only. Changes in anxiety symptoms from 0 to 6 months predicted different patterns of subsequent changes in depressive symptoms from 6 to 12 months for the two conditions, such that declines in anxiety preceded and predicted greater declines in depression for FGCB youth but lesser increases in depression for WI youth. Findings inform transdiagnostic approaches to preventive interventions for at-risk youth, suggesting that both initial symptom levels and initial magnitude of change in symptoms are important to understand subsequent patterns of change in response to intervention.

The current study investigated the consequences of ignoring a multilevel structure for a mixture item response model to show when a multilevel mixture item response model is needed. Study 1 focused on examining the consequence of ignoring dependency for within-level latent classes. Simulation conditions that may affect model selection and parameter recovery in the context of a multilevel data structure were manipulated: class-specific ICC, cluster size, and number of clusters. The accuracy of model selection (based on information criteria) and quality of parameter recovery were used to evaluate the impact of ignoring a multilevel structure. Simulation results indicated that, for the range of class-specific ICCs examined here (.1 to .3), mixture item response models which ignored a higher level nesting structure resulted in less accurate estimates and standard errors ( SE s) of item discrimination parameters when the number of clusters was larger than 24 and the cluster size was larger than six. Class-varying ICCs can have compensatory effects on bias. Also, the results suggested that a mixture item response model which ignored multilevel structure was not selected over the multilevel mixture item response model based on Bayesian information criterion (BIC) if the number of clusters and cluster size was at least 50, respectively. In Study 2, the consequences of unnecessarily fitting a multilevel mixture item response model to single-level data were examined. Reassuringly, in the context of single-level data, a multilevel mixture item response model was not selected by BIC, and its use would not distort the within-level item parameter estimates or SE s when the cluster size was at least 20. Based on these findings, it is concluded that, for class-specific ICC conditions examined here, a multilevel mixture item response model is recommended over a single-level item response model for a clustered dataset having cluster size > 20 and the number of clusters > 50 ., Competing Interests: Declaration of Conflicting Interests: The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Objective: Individually-randomized psychotherapy trials are often partially nested. For instance, individuals assigned to a treatment arm may be clustered into therapy groups for purposes of treatment administration, whereas individuals assigned to a wait-list control are unclustered. The past several years have seen rapid expansion and investigation of methods for analyzing partially nested data. Yet partial nesting often remains ignored in psychotherapy trials., Methods: This review integrates and disseminates developments in the analysis of partially nested data that are particularly relevant for psychotherapy researchers., Results: First, we differentiate among alternative partially nested designs. Then, we present adaptations of multilevel model specifications that accommodate each design. Next, we address how moderation by treatment as well as mediation of the treatment effect can be investigated in partially nested designs. Model fitting results, annotated software syntax, and illustrative data sets are provided and key methodological issues are discussed., Conclusions: We emphasize that cluster-level variability in the treatment arm need not be considered a nuisance; it can be modeled to yield insights about the treatment process.

Research interest often lies in comparing structural model specifications implying different relationships among latent factors. In this context parceling is commonly accepted, assuming the item-level measurement structure is well known and, conservatively, assuming items are unidimensional in the population. Under these assumptions, researchers compare competing structural models, each specified using the same parcel-level measurement model. However, little is known about consequences of parceling for model selection in this context-including whether and when model ranking could vary across alternative item-to-parcel allocations within-sample. This article first provides a theoretical framework that predicts the occurrence of parcel-allocation variability (PAV) in model selection index values and its consequences for PAV in ranking of competing structural models. These predictions are then investigated via simulation. We show that conditions known to manifest PAV in absolute fit of a single model may or may not manifest PAV in model ranking. Thus, one cannot assume that low PAV in absolute fit implies a lack of PAV in ranking, and vice versa. PAV in ranking is shown to occur under a variety of conditions, including large samples. To provide an empirically supported strategy for selecting a model when PAV in ranking exists, we draw on relationships between structural model rankings in parcel- versus item-solutions. This strategy employs the across-allocation modal ranking. We developed software tools for implementing this strategy in practice, and illustrate them with an example. Even if a researcher has substantive reason to prefer one particular allocation, investigating PAV in ranking within-sample still provides an informative sensitivity analysis. (PsycINFO Database Record, ((c) 2017 APA, all rights reserved).)

Random coefficient-dependent (RCD) missingness is a non-ignorable mechanism through which missing data can arise in longitudinal designs. RCD, for which we cannot test, is a problematic form of missingness that occurs if subject-specific random effects correlate with propensity for missingness or dropout. Particularly when covariate missingness is a problem, investigators typically handle missing longitudinal data by using single-level multiple imputation procedures implemented with long-format data, which ignores within-person dependency entirely, or implemented with wide-format (i.e., multivariate) data, which ignores some aspects of within-person dependency. When either of these standard approaches to handling missing longitudinal data is used, RCD missingness leads to parameter bias and incorrect inference. We explain why multilevel multiple imputation (MMI) should alleviate bias induced by a RCD missing data mechanism under conditions that contribute to stronger determinacy of random coefficients. We evaluate our hypothesis with a simulation study. Three design factors are considered: intraclass correlation (ICC; ranging from .25 to .75), number of waves (ranging from 4 to 8), and percent of missing data (ranging from 20 to 50%). We find that MMI greatly outperforms the single-level wide-format (multivariate) method for imputation under a RCD mechanism. For the MMI analyses, bias was most alleviated when the ICC is high, there were more waves of data, and when there was less missing data. Practical recommendations for handling longitudinal missing data are suggested.

Multilevel data structures are common in the social sciences. Often, such nested data are analysed with multilevel models (MLMs) in which heterogeneity between clusters is modelled by continuously distributed random intercepts and/or slopes. Alternatively, the non-parametric multilevel regression mixture model (NPMM) can accommodate the same nested data structures through discrete latent class variation. The purpose of this article is to delineate analytic relationships between NPMM and MLM parameters that are useful for understanding the indirect interpretation of the NPMM as a non-parametric approximation of the MLM, with relaxed distributional assumptions. We define how seven standard and non-standard MLM specifications can be indirectly approximated by particular NPMM specifications. We provide formulas showing how the NPMM can serve as an approximation of the MLM in terms of intraclass correlation, random coefficient means and (co)variances, heteroscedasticity of residuals at level 1, and heteroscedasticity of residuals at level 2. Further, we discuss how these relationships can be useful in practice. The specific relationships are illustrated with simulated graphical demonstrations, and direct and indirect interpretations of NPMM classes are contrasted. We provide an R function to aid in implementing and visualizing an indirect interpretation of NPMM classes. An empirical example is presented and future directions are discussed., (© 2016 The British Psychological Society.)

Psychologists often use latent transition analysis (LTA) to investigate state-to-state change in discrete latent constructs involving delinquent or risky behaviors. In this setting, latent-state-dependent nonignorable missingness is a potential concern. For some longitudinal models (e.g., growth models), a large literature has addressed extensions to accommodate nonignorable missingness. In contrast, little research has addressed how to extend the LTA to accommodate nonignorable missingness. Here we present a shared parameter LTA that can reduce bias due to latent-state-dependent nonignorable missingness: a parallel-process missing-not-at-random (MNAR-PP) LTA. The MNAR-PP LTA allows outcome process parameters to be interpreted as in the conventional LTA, which facilitates sensitivity analyses assessing changes in estimates between LTA and MNAR-PP LTA. In a sensitivity analysis for our empirical example, previous and current membership in high-delinquency states predicted adolescents' membership in missingness states that had high nonresponse probabilities for some or all items. A conventional LTA overestimated the proportion of adolescents ending up in a low-delinquency state, compared to an MNAR-PP LTA.

Item parceling remains widely used under conditions that can lead to parcel-allocation variability in results. Hence, researchers may be interested in quantifying and accounting for parcel-allocation variability within sample. To do so in practice, three key issues need to be addressed. First, how can we combine sources of uncertainty arising from sampling variability and parcel-allocation variability when drawing inferences about parameters in structural equation models? Second, on what basis can we choose the number of repeated item-to-parcel allocations within sample? Third, how can we diagnose and report proportions of total variability per estimate arising due to parcel-allocation variability versus sampling variability? This article addresses these three methodological issues. Developments are illustrated using simulated and empirical examples, and software for implementing them is provided.

Clinical psychology researchers studying adolescents and young adults long have been interested in characterizing the latent categorical (classes/profiles) versus continuous (factors) nature of psychological syndromes. To inform this debate, researchers sometimes compare the fit of finite mixture versus factor analysis models to symptom data. This study explains and evaluates how missing data handling methods can impact results of this important model fit comparison. Via simulation, we assess three missing data-handling methods previously recommended to researchers fitting these models: multiple imputation using a saturated multivariate normal imputation model, multiple imputation using a hypothesized model, or full information maximum likelihood using the EM algorithm (FIML-EM). Results show that, under certain conditions, the method used to handle missing data can interfere with clinical psychologists' ability to accurately discriminate latent classes from continua. For instance, certain imputation methods increase the chance of selecting latent continua when latent classes truly exist. FIML-EM performed best overall. Recommendations for practice are discussed.

Mixture modeling is a popular method that accounts for unobserved population heterogeneity using multiple latent classes that differ in response patterns. Psychologists use conditional mixture models to incorporate covariates into between-class and/or within-class regressions. Although psychologists often have missing covariate data, conditional mixtures are currently fit with a conditional likelihood, treating covariates as fixed and fully observed. Under this exogenous-x approach, missing covariates are handled primarily via listwise deletion. This sacrifices efficiency and does not allow missingness to depend on observed outcomes. Here we describe a modified joint likelihood approach that (a) allows inference about parameters of the exogenous-x conditional mixture even with nonnormal covariates, unlike a conventional multivariate mixture; (b) retains all cases under missing at random assumptions; (c) yields lower bias and higher efficiency than the exogenous-x approach under a variety of conditions with missing covariates; and (d) is straightforward to implement in available commercial software. The proposed approach is illustrated with an empirical analysis predicting membership in latent classes of conduct problems. Recommendations for practice are discussed.

Prior research has shown cognitive reactivity to be a diathesis for depression. Seeking evidence for the developmental origins of such diatheses, the current study examined peer victimization and harsh parenting as developmental correlates of cognitive reactivity in 571 children and adolescents (ages 8-13 years). Four major findings emerged. First, a new method for assessing cognitive reactivity in children and adolescents showed significant reliability and demonstrated construct validity vis-à-vis its relation to depression. Second, history of more severe peer victimization was significantly related to cognitive reactivity, with verbal victimization being more strongly tied to cognitive reactivity than other subtypes of peer victimization. Third, harsh parenting was also significantly related to cognitive reactivity. Fourth, both peer victimization and harsh parenting made unique statistical contributions to cognitive reactivity, after controlling for the effects of the other. Taken together, these findings provide preliminary support for a developmental model pertaining to origins of cognitive reactivity in children and adolescents.

Study designs involving clustering in some study arms, but not all study arms, are common in clinical treatment-outcome and educational settings. For instance, in a treatment arm, persons may be nested in therapy groups, whereas in a control arm there are no groups. Methodological approaches for handling such partially nested designs have recently been developed in a multilevel modeling framework (MLM-PN) and have proved very useful. We introduce two alternative structural equation modeling (SEM) approaches for analyzing partially nested data: a multivariate single-level SEM (SSEM-PN) and a multiple-arm multilevel SEM (MSEM-PN). We show how SSEM-PN and MSEM-PN can produce results equivalent to existing MLM-PNs and can be extended to flexibly accommodate several modeling features that are difficult or impossible to handle in MLM-PNs. For instance, using an SSEM-PN or MSEM-PN, it is possible to specify complex structural models involving cluster-level outcomes, obtain absolute model fit, decompose person-level predictor effects in the treatment arm using latent cluster means, and include traditional factors as predictors/outcomes. Importantly, implementation of such features for partially nested designs differs from that for fully nested designs. An empirical example involving a partially nested depression intervention combines several of these features in an analysis of interest for treatment-outcome studies.

The methodological literature on mixture modeling has rapidly expanded in the past 15 years, and mixture models are increasingly applied in practice. Nonetheless, this literature has historically been diffuse, with different notations, motivations, and parameterizations making mixture models appear disconnected. This pedagogical review facilitates an integrative understanding of mixture models. First, 5 prototypic mixture models are presented in a unified format with incremental complexity while highlighting their mutual reliance on familiar probability laws, common assumptions, and shared aspects of interpretation. Second, 2 recent extensions-hybrid mixtures and parallel-process mixtures-are discussed. Both relax a key assumption of classic mixture models but do so in different ways. Similarities in construction and interpretation among hybrid mixtures and among parallel-process mixtures are emphasized. Third, the combination of both extensions is motivated and illustrated by means of an example on oppositional defiant and depressive symptoms. By clarifying how existing mixture models relate and can be combined, this article bridges past and current developments and provides a foundation for understanding new developments.

Researchers in psychology are increasingly using model selection strategies to decide among competing models, rather than evaluating the fit of a given model in isolation. However, such interest in model selection outpaces an awareness that one or a few cases can have disproportionate impact on the model ranking. Though case influence on the fit of a single model in isolation has been often studied, case influence on model selection results is greatly underappreciated in psychology. This article introduces the issue of case influence on model selection and proposes 3 influence diagnostics for commonly used selection indices: the chi-square difference test, Bayesian information criterion, and Akaike's information criterion. These 3 diagnostics can be obtained simply from the byproducts of full information maximum likelihood estimation without heavy computational burden. We provide practical information on the interpretation and behavior of these diagnostics for applied researchers and provide software code to facilitate their use. Simulated and empirical examples involving different kinds of model comparison scenarios encountered in cross-sectional, longitudinal, and multilevel research as well as involving different kinds of outcome distributions illustrate the generality of the proposed diagnostics. An awareness of how cases influence model selection results is shown to aid researchers in understanding how representative their sample level results are at the case level., (PsycINFO Database Record (c) 2013 APA, all rights reserved.)

Psychologists have long been interested in characterizing individual differences in change over time. It is often plausible to assume that the distribution of these individual differences is continuous in nature, yet theory is seldom so specific as to designate its parametric form (e.g., normal). Semiparametric groups-based trajectory models (SPGMs) were thus developed to provide a discrete approximation for continuously distributed growth of unknown form. Previous research has demonstrated the adequacy of the approximation provided by SPGM but only under relatively narrow, theoretically optimal conditions. Under alternative conditions, which may be more common in practice (e.g., higher dimension random effects, smaller sample sizes), this study shows that approximation adequacy can suffer. Furthermore, this study also evaluates whether SPGM's discrete approximation is preferable to a parametric trajectory model that assumes normally distributed random effects when in fact the distribution is modestly nonnormal. The answer is shown to depend on distributional characteristics of both repeated measures (binary or continuous) and random effects (bimodal or skewed). Implications for practice are discussed in light of empirical examples on externalizing behavior.

Previous research has compared methods of estimation for fitting multilevel models to binary data, but there are reasons to believe that the results will not always generalize to the ordinal case. This article thus evaluates (a) whether and when fitting multilevel linear models to ordinal outcome data is justified and (b) which estimator to employ when instead fitting multilevel cumulative logit models to ordinal data, maximum likelihood (ML), or penalized quasi-likelihood (PQL). ML and PQL are compared across variations in sample size, magnitude of variance components, number of outcome categories, and distribution shape. Fitting a multilevel linear model to ordinal outcomes is shown to be inferior in virtually all circumstances. PQL performance improves markedly with the number of ordinal categories, regardless of distribution shape. In contrast to binary data, PQL often performs as well as ML when used with ordinal data. Further, the performance of PQL is typically superior to ML when the data include a small to moderate number of clusters (i.e., ≤ 50 clusters).

Background: The differentiation hypothesis posits that the underlying liability distribution for psychopathology is of low dimensionality in young children, inflating diagnostic comorbidity rates, but increases in dimensionality with age as latent syndromes become less correlated. This hypothesis has not been adequately tested with longitudinal psychiatric symptom data., Methods: Confirmatory factor analyses of DSM-IV symptoms from seven common Axis I syndromes--major depression, generalized anxiety, separation anxiety, social anxiety, attention deficient hyperactivity, conduct, and oppositional defiant disorders--were conducted longitudinally, from ages 9 to 16, using the general-population Great Smoky Mountains Study sample., Results: An eight-syndrome model fit well at all ages, and in both genders. It included social anxiety, separation anxiety, oppositional defiant, and conduct syndromes, along with a multidimensional attention deficit-hyperactivity syndrome (i.e., inattention, hyperactivity, and impulsivity) and a unidimensional major depression/generalized anxiety syndrome. A high degree of measurement invariance across age was found for all syndromes, except for major depression/generalized anxiety. Major depression and generalized anxiety syndromes slightly diverged at age 14-16, when they also began to explain more symptom variance. Additionally, correlations between some emotional and disruptive syndromes showed slight differentiation., Conclusions: Marked developmental differentiation of psychopathology, as implied by the orthogenetic principle, is not a prominent cause of preadolescent and adolescent psychiatric comorbidity.

The person-oriented approach seeks to match theories and methods that portray development as a holistic, highly interactional, and individualized process. Over the past decade, this approach has gained popularity in developmental psychopathology research, particularly as model-based varieties of person-oriented methods have emerged. Although these methods allow some principles of person-oriented theory to be tested, little attention has been paid to the fact that these methods cannot test other principles, and may actually be inconsistent with certain principles. Lacking clarification regarding which aspects of person-oriented theory are testable under which person-oriented methods, assumptions of the methods have sometimes been presented as testable hypotheses or interpreted as affirming the theory. This general blurring of the line between person-oriented theory and method has even led to the occasional perception that the method is the theory and vice versa. We review assumptions, strengths, and limitations of model-based person-oriented methods, clarifying which theoretical principles they can test and the compromises and trade-offs required to do so.

Different random or purposive allocations of items to parcels within a single sample are thought not to alter structural parameter estimates as long as items are unidimensional and congeneric. If, additionally, numbers of items per parcel and parcels per factor are held fixed across allocations, different allocations of items to parcels within a single sample are thought not to meaningfully alter model fit-at least when items are normally distributed. We show analytically that, although these statements hold in the population, they do not necessarily hold in the sample. We show via a simulation that, even under these conservative conditions, the magnitude of within-sample item-to-parcel-allocation variability in structural parameter estimates and model fit can alter substantive conclusions when sampling error is high (e.g., low N, low item communalities, few items per few parcels). We supply a software tool that facilitates reporting and ameliorating the consequences of item-to-parcel-allocation variability. The tool's utility is demonstrated on an empirical example involving the Neuroticism-Extroversion-Openness (NEO) Personality Inventory and the Computer Assisted Panel Study data set.

A family cognitive-behavioral preventive intervention for parents with a history of depression and their 9-15-year-old children was compared with a self-study written information condition in a randomized clinical trial (n = 111 families). Outcomes were assessed at postintervention (2 months), after completion of 4 monthly booster sessions (6 months), and at 12-month follow-up. Children were assessed by child reports on depressive symptoms, internalizing problems, and externalizing problems; by parent reports on internalizing and externalizing problems; and by child and parent reports on a standardized diagnostic interview. Parent depressive symptoms and parent episodes of major depression also were assessed. Evidence emerged for significant differences favoring the family group intervention on both child and parent outcomes; strongest effects for child outcomes were found at the 12-month assessment with medium effect sizes on most measures. Implications for the prevention of adverse outcomes in children of depressed parents are highlighted.

A model-based framework, due originally to R. A. Fisher, and a design-based framework, due originally to J. Neyman, offer alternative mechanisms for inference from samples to populations. We show how these frameworks can utilize different types of samples (nonrandom or random vs. only random) and allow different kinds of inference (descriptive vs. analytic) to different kinds of populations (finite vs. infinite). We describe the extent of each framework's implementation in observational psychology research. After clarifying some important limitations of each framework, we describe how these limitations are overcome by a newer hybrid model/design-based inferential framework. This hybrid framework allows both kinds of inference to both kinds of populations, given a random sample. We illustrate implementation of the hybrid framework using the High School and Beyond data set.

Self-injurious behaviors are among the leading causes of death worldwide. However, the basic nature of self-injurious thoughts and behaviors (SITBs) is not well understood because prior studies have relied on long-term, retrospective, aggregate, self-report assessment methods. The authors used ecological momentary assessment methods to measure suicidal and nonsuicidal SITBs as they naturally occur in real time. Participants were 30 adolescents and young adults with a recent history of self-injury who completed signal- and event-contingent assessments on handheld computers over a 14-day period, resulting in the collection of data on 1,262 thought and behavior episodes. Participants reported an average of 5.0 thoughts of nonsuicidal self-injury (NSSI) per week, most often of moderate intensity and short duration (1-30 min), and 1.6 episodes of NSSI per week. Suicidal thoughts occurred less frequently (1.1 per week), were of longer duration, and led to self-injurious behavior (i.e., suicide attempts) less often. Details are reported about the contexts in which SITBs most often occur (e.g., what participants were doing, who they were with, and what they were feeling before and after each episode). This study provides a first glimpse of how SITBs are experienced in everyday life and has significant implications for scientific and clinical work on self-injurious behaviors., (PsycINFO Database Record 2009 APA, all rights reserved.)

The graphical presentation of any scientific finding enhances its description, interpretation, and evaluation. Research involving latent variables is no exception, especially when potential nonlinear effects are suspect. This article has multiple aims. First, it provides a nontechnical overview of a semiparametric approach to modeling nonlinear relationships among latent variables using mixtures of linear structural equations. Second, it provides several examples showing how the method works and how it is implemented and interpreted in practical applications. In particular, this article examines the potentially nonlinear relationships between positive and negative affect and cognitive processing. Third, a recommended display format for illustrating latent bivariate relationships is demonstrated. Finally, the article describes an R package and an online utility that generate these displays automatically.

Conventional growth models assume that the random effects describing individual trajectories are conditionally normal. In practice, this assumption may often be unrealistic. As an alternative, Nagin (2005) suggested a semiparametric group-based approach (SPGA) which approximates an unknown, continuous distribution of individual trajectories with a mixture of group trajectories. Prior simulations ( Brame, Nagin, & Wasserman, 2006 ; Nagin, 2005 ) indicated that SPGA could generate nearly-unbiased estimates of means and variances of a nonnormal distribution of individual trajectories, as functions of group-trajectory estimates. However, these studies used few random effects-usually only a random intercept. Based on the analytical relationship between SPGA and adaptive quadrature, we hypothesized that SPGA's ability to approximate (a) random effect variances/covariances and (b) effects of time-invariant predictors of growth should deteriorate as the dimensionality of the random effects distribution increases. We expected this problem to be mitigated by correlations among the random effects (highly correlated random effects functioning as fewer dimensions) and sample size (larger N supporting more groups). We tested these hypotheses via simulation, varying the number of random effects (1, 2, or 3), correlation among the random effects (0 or .6), and N (250, 500). Results indicated that, as the number of random effects increased, SPGA approximations remained acceptable for fixed effects, but became increasingly negatively biased for random effect variances. Whereas correlated random effects and larger N reduced this underestimation, correlated random effects sometimes distorted recovery of predictor effects. To illustrate this underestimation, Figure 1 depicts SPGA's approximation of the intercept variance from a three correlated random effect generating model (N < eqid1 > 500). These results suggest SPGA approximations are inadequate for the nonnormal, high-dimensional distributions of individual trajectories often seen in practice.[Figure: see text].

Individually randomized treatments are often administered within a group setting. As a consequence, outcomes for treated individuals may be correlated due to provider effects, common experiences within the group, and/or informal processes of socialization. In contrast, it is often reasonable to regard outcomes for control participants as independent, given that these individuals are not placed into groups. Although this kind of design is common in intervention research, the statistical models applied to evaluate the treatment effects are usually inconsistent with the resulting data structure, potentially leading to biased inferences. This article presents an alternative model that explicitly accounts for the fact that only treated participants are grouped. In addition to providing a useful test of the overall treatment effect, this approach also permits one to formally determine the extent to which treatment effects vary over treatment groups and whether there is evidence that individuals within treatment groups become similar to one another. This strategy is demonstrated with data from the Reconnecting Youth program for high school students at risk of school failure and behavioral disorders.

Developmental psychopathology theory speaks to the existence of early-manifesting internalizing problems with a heterogeneous longitudinal course. However, the course of internalizing problems has been investigated largely from late childhood onward, with methods that assume children's problem trajectories vary more so in rate than in qualitative functional form. This can obscure heterogeneity in symptom process and course, obscure onset of early gender differences in internalizing problems, and obscure the relevance of early sociocontextual risks for long-term internalizing outcomes. The present study addressed these issues by using person-oriented (latent growth mixture) methods to model heterogeneity in maternal-reported internalizing symptoms from age 2 to 11 years (N = 1,364). Three latent trajectory classes were supported for each gender: two-thirds of children followed a low-stable trajectory; smaller proportions followed decreasing/increasing or elevated-stable trajectories. Although the number, shape, and predictive validity of internalizing trajectory classes were similar across gender, trajectory classes' initial values and rates of change varied significantly across gender, as did the impact of maternal postpartum depression and anxiety on latent growth factors. Extracted latent trajectories were differentially predicted by postpartum maternal psychopathology, and themselves, in several respects, differentially predicted self-reported depressive symptoms in preadolescence. However, discussion focuses on the need for further external validation of extracted latent classes.