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This study's purpose was to investigate effects of 3 intervention approaches for building working memory (WM) and improving word-problem solving (WPS). Children with mathematics difficulties (n = 240; 7.51 years [SD = 0.33]) were randomized to 4 conditions: a control group, general WM training with contiguous math practice, WPS intervention without WM training, and WPS intervention with domain-specific WM training. WM, WPS, and arithmetic were assessed before and 1-3 weeks after intervention; delayed WPS and arithmetic posttesting occurred 4-6 weeks later. Multilevel modeling of main effects and mediation effects were employed. Compared to control, general WM training with contiguous math practice and WPS intervention without WM training increased WM and WPS. The 3rd training condition, WPS intervention with domain-specific WM training, which minimized WM training time, improved WPS but without effects on WM. Both WPS intervention conditions outperformed general WM training on WPS. Conclusions are as follows. (a) General WM training with contiguous math practice improves WM and WPS. (b) WM training is not a substitute for WPS intervention when the goal is to strengthen WPS. (c) WPS intervention without WM training improves WM but is not a substitute for WM training when the goal is to strengthen WM. (d) For WM effects to accrue, WM training needs to occur with sufficient intensity. (e) WM plays a causal role in WPS, but not in arithmetic. Implications are drawn for research and practice, including assessing instructional supports in future research to build cognitive-academic bidirectionality. [For the grantee submission, see ED620371.]

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[superscript 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 ([delta]"R[superscript 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.

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

A common theme uniting articles in this special issue is a focus on aptitude-by-treatment interactions (ATIs). This timely and welcome focus allows the field to synthesize current substantive findings on ATIs in educational intervention research in both reading and math domains. In this methodological commentary, we begin by reviewing traditional approaches for detecting and reporting interactions in single-level and multilevel models. Next, we discuss some limitations of traditional approaches for theorizing about and modeling ATIs, and we suggest some solutions. These solutions include interpreting level-specific (unconflated) ATIs, understanding and ameliorating threats to adequate power for detecting ATIs, expanding focus beyond linear ATIs, and increasing the number of measurement occasions beyond two to allow use of a growth modeling framework for investigating ATIs. Incorporating some of these advances into future research can motivate new research questions about educational interventions and lead to new discoveries in the search for ATIs.

The purpose of this set of analyses, conducted on a randomized control trial examining the effects of a fourth-grade fraction intervention, was to assess the initial academic deficit severity hypothesis. With this hypothesis, at-risk students with more severe initial academic deficits are expected to profit less from intervention than do students with less severe initial academic deficits. Moderation analyses indicated that students with varying degrees of initial academic deficits benefited comparably from the intervention, such that effect sizes comparing intervention against control students were similar across the range of initial academic deficits. In a similar way, across the range of initial academic deficits, intervention students' posttest (spring) calculation performance was normalized (one standard error of measurement above the 25th percentile of a not-at-risk normative group's spring performance). On the most distal fractions outcome, however, normalized performance was achieved for intervention students with less severe initial academic deficits. Findings are discussed in terms of methods for judging intervention efficacy and for making individual decisions about when students should exit intervention.

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. (Contains 7 figures and 13 footnotes.)

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. (Contains 10 figures, 11 footnotes and 6 tables.)

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., [less than or equal to] 50 clusters). (Contains 7 tables, 8 footnotes and 7 figures.)

This article relates a still-popular motivation for using parceling to an unrecognized cost. The still-popular motivation is improvement in fit with respect to the item-solution. The cost is uncertainty in fit due to the selection of one out of many possible item-to-parcel allocations. A theoretical framework establishes the reason for this relationship: The same mechanisms that cause larger item- versus parcel-solution differences in the minimized discrepancy function also cause larger allocation to allocation variability in the parcel-solution's minimized discrepancy function. Study 1 illustrates that these shared causal mechanisms lead to a strong positive association between average item-parcel differences in minimized discrepancy function values and parcel-allocation variability in those values. Study 2 extends these results from discrepancy function values to fit indexes, showing that the association remains positive, but varies in magnitude depending on what quantities other than the discrepancy function are involved in computing the fit index. The important implication for practice is that when item-parcel fit differences are large enough to alter conclusions about model adequacy, parcel-allocation variability tends to be large enough for parcel-solution model adequacy to depend on the particular allocation chosen. (Contains 4 figures, 7 tables and 12 footnotes.)

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.

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. (Contains 8 figures, 5 tables and 8 footnotes.)

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. (Contains 10 figures, 1 table, and 4 footnotes.)

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. (Contains 2 tables, 3 figures and 15 footnotes.)

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. (Contains 1 table and 8 footnotes.)

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. [ABSTRACT FROM AUTHOR]

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 posfintervention (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. Keywords: parental depression, children, prevention, family, cognitive-behavioral DOI: 10.1037/a0016930

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 ah 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. Keywords: self-injury, self-harm, suicide, EMA, self-mutilation, suicidal Supplemental materials: http://dx.doi.org/10.1037/a0016948.supp Journal of Abnormal Pshychology 2009, Vol. No. 4, 816-827 [c] 2009 American Psychological Association 0021-843X/09/$12.00 DOI: 10.1037/a0016948

Reading comprehension (RC) and word-problem solving (WPS) both involve text processing. Yet, despite evidence that RC text-structure intervention (RC.INT) improves RC, transfer to WPS has not been investigated. Similarly, despite evidence that WPS text-structure intervention (WP.INT) improves WPS, transfer to RC has not been examined. The purpose of this randomized controlled trial was to assess effects of single-domain text-structure intervention (RC or WPS intervention) for simultaneously improving RC and WPS. Second-grade children with comorbid learning difficulty across RC and WPS were randomly assigned to three conditions: RC.INT, WP.INT, or the standard school program (the control group). Inferential tests for acquisition effects in multilevel models were significant. RC.INT's effect sizes (ESs) (vs. control) on RC were g = 1.16 and 0.83; WP.INT's ESs (vs. control) on WPS were g = 1.36 and 1.05. Inferential tests for cross-domain transfer effects in multilevel models were also significant. RC.INT's ESs (vs. control) on WPS were g = 0.41 and 0.68; WP.INT's ES (vs. control) on RC were g = 0.91 and 0.54. Children's text-structure knowledge in passages and word problems mediated acquisition and cross-domain transfer effects in multilevel models. Findings suggest that text-structure intervention may help address the complex needs of children with comorbid RC and WPS difficulty. Educational Impact and Implications Statement: For children with difficulty across reading comprehension (RC) and word-problem solving (WPS), RC text-structure intervention transfers to WPS; WPS text-structure intervention transfers to RC; and text-structure knowledge mediates effects. Findings indicate a causal relation between RC and WPS; that learning in one domain contributes to learning in the other; that WPS may be viewed as a form of text comprehension; and that single-focus text-structure intervention is a promising approach for this population. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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; Mage = 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. [ABSTRACT FROM AUTHOR]

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 (SEs) 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 SEs 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 . [ABSTRACT FROM AUTHOR]