Optimal Scaling of Interaction Effects in Generalized Linear Models

This study involved two phases: first, when classification was based on the calibration sample; and second, in a cross-validation setting. Computer generated data were used. Results obtained from rules based on probabilities of group membership were compared for accuracy when classifying in the discriminant space and in the predictor variable spaces. In the first phase accuracy was greater in the predictor variable spaces, while the reverse was true in the second phase. In general, rules based on probabilities of group membership were approximately equally accurate and more accurate than a rule related to a multiple regression analysis. Other findings are also discussed.     

Erratum to: Beyond the Mean: A Flexible Framework for Studying Causal Effects Using Linear Models

Psychometrika - The original version of the article contains the below listed errors.     

Beyond the Mean: A Flexible Framework for Studying Causal Effects Using Linear Models

Psychometrika - Graph-based causal models are a flexible tool for causal inference from observational data. In this paper, we develop a comprehensive framework to define, identify, and estimate a...     

An Idiographic Approach to Estimating Models of Dyadic Interactions with Differential Equations

We present an idiographic approach to modeling dyadic interactions using differential equations. Using data representing daily affect ratings from romantic relationships, we examined several models conceptualizing different types of dyadic interactions. We fitted each model to each of the dyads and the resulting AICc values were used to classify the most likely configuration of interaction for each dyad. Additionally, the AICc from the different models were used in parameter averaging across models. Averaged parameters were used in models involving predictors of relationship dynamics, as indexed by these parameters, as well as models wherein the parameters predicted distal outcomes of the dyads such as relationship satisfaction and status. Results indicated that, within our sample, the most likely interaction style was that of independence, without evidence of emotional interrelations between the two individuals in the couple. Attachment-related avoidance and anxiety showed significant relations with model parameters, such that ideal levels of affect for males were negatively influenced by higher levels of avoidance from their partner while their own levels of anxiety had positive effects on their levels of dyadic coregulation. For females coregulation was negatively influenced by both time in the relationship and their partner’s level of avoidance. Analysis involving distal outcomes showed modest influences from the individual’s level of ideal affect.     

Analysis of School Context Effects on Differential Item Functioning Using Hierarchical Generalized Linear Models

This article considers and illustrates a strategy to study effects of school context on differential item functioning (DIF) in large-scale assessment. The approach employs a hierarchical generalized linear modeling framework to (a) detect DIF, and (b) identify school-level correlates of the between-group differences in item performance. To illustrate, I investigated (a) whether any of the civic skills items used in the U.S. Civic Education Study of the International Association for the Evaluation of Educational Achievement displayed ethnic–racial DIF, and (b) the extent to which the ethnic–racial DIF was related to teacher-reported opportunity to learn (OTL) major civic-related topics. The results indicated that 3 of the 13 items displayed ethnic–racial DIF. After adjusting for OTL, two of the three flagged items ceased to exhibit DIF. Implications of this approach are discussed.     

Autoregressive Generalized Linear Mixed Effect Models with Crossed Random Effects: An Application to Intensive Binary Time Series Eye-Tracking Data

As a method to ascertain person and item effects in psycholinguistics, a generalized linear mixed effect model (GLMM) with crossed random effects has met limitations in handing serial dependence across persons and items. This paper presents an autoregressive GLMM with crossed random effects that accounts for variability in lag effects across persons and items. The model is shown to be applicable to intensive binary time series eye-tracking data when researchers are interested in detecting experimental condition effects while controlling for previous responses. In addition, a simulation study shows that ignoring lag effects can lead to biased estimates and underestimated standard errors for the experimental condition effects.     

Structural Modeling of Measurement Error in Generalized Linear Models with Rasch Measures as Covariates

This paper proposes a structural analysis for generalized linear models when some explanatory variables are measured with error and the measurement error variance is a function of the true variables. The focus is on latent variables investigated on the basis of questionnaires and estimated using item response theory models. Latent variable estimates are then treated as observed measures of the true variables. This leads to a two-stage estimation procedure which constitutes an alternative to a joint model for the outcome variable and the responses given to the questionnaire. Simulation studies explore the effect of ignoring the true error structure and the performance of the proposed method. Two illustrative examples concern achievement data of university students. Particular attention is given to the Rasch model.     

Extensions of the Johnson-Neyman Technique to Linear Models With Curvilinear Effects: Derivations and Analytical Tools

The past decade has witnessed renewed interest in the use of the Johnson-Neyman (J-N) technique for calculating the regions of significance for the simple slope of a focal predictor on an outcome variable across the range of a second, continuous independent variable. Although tools have been developed to apply this technique to probe 2- and 3-way interactions in several types of linear models, this method has not been extended to include quadratic terms or more complicated models involving quadratic terms and interactions. Curvilinear relations of this type are incorporated in several theories in the social sciences. This article extends the J-N method to such linear models along with presenting freely available online tools that implement this technique as well as the traditional pick-a-point approach. Algebraic and graphical representations of the proposed J-N extension are provided. An example is presented to illustrate the use of these tools and the interpretation of findings. Issues of reliability as well as “spurious moderator” effects are discussed along with recommendations for future research.     

Doubly-Latent Models of School Contextual Effects: Integrating Multilevel and Structural Equation Approaches to Control Measurement and Sampling Error

This article is a methodological-substantive synergy. Methodologically, we demonstrate latent-variable contextual models that integrate structural equation models (with multiple indicators) and multilevel models. These models simultaneously control for and unconfound measurement error due to sampling of items at the individual (L1) and group (L2) levels and sampling error due the sampling of persons in the aggregation of L1 characteristics to form L2 constructs. We consider a set of models that are latent or manifest in relation to sampling items (measurement error) and sampling of persons (sampling error) and discuss when different models might be most useful. We demonstrate the flexibility of these 4 core models by extending them to include random slopes, latent (single-level or cross-level) interactions, and latent quadratic effects.

Substantively we use these models to test the big-fish-little-pond effect (BFLPE), showing that individual student levels of academic self-concept (L1-ASC) are positively associated with individual level achievement (L1-ACH) and negatively associated with school-average achievement (L2-ACH)—a finding with important policy implications for the way schools are structured. Extending tests of the BFLPE in new directions, we show that the nonlinear effects of the L1-ACH (a latent quadratic effect) and the interaction between gender and L1-ACH (an L1 × L1 latent interaction) are not significant. Although random-slope models show no significant school-to-school variation in relations between L1-ACH and L1-ASC, the negative effects of L2-ACH (the BFLPE) do vary somewhat with individual L1-ACH.

We conclude with implications for diverse applications of the set of latent contextual models, including recommendations about their implementation, effect size estimates (and confidence intervals) appropriate to multilevel models, and directions for further research in contextual effect analysis.     

The Effects of Scrambling on Spanish and Korean Agrammatic Interpretation: Why Linear Models Fail and Structural Models Survive

Several models of comprehension deficits in agrammatic aphasia rely heavily on linear considerations in the assignment of thematic roles to structural positions (e.g., the Trace-Deletion Hypothesis, the Mapping Hypothesis, and the Argument-Linking Hypothesis). These accounts predict that constructions in languages with rules that affect syntactic structure but preserve relative linear order should be unimpaired. Other models [e.g., the Double-Dependency Hypothesis, (DDH)] do not resort to linearity but are purely structural in conception and therefore should be immune to word-order effects. We tested linear and nonlinear accounts with scrambling structures in Korean and topicalization structures in Spanish. The results are very clear. The (nonlinear) DDH is entirely compatible with the evidence, but the linear accounts are not.     

Parent and Adolescent Responses to PovertyRelated Stress: Tests of Mediated and Moderated Coping Models

We tested several models of the associations among economic strain, life stress, coping, involuntary stress responses, and psychological symptoms in a sample of 57 parent-adolescent dyads from rural, lower-income families. Economic strain and life stress predicted symptoms for both parents and adolescents. Stressor-symptom specificity was found for parents, such that economic strain uniquely predicted depression, whereas negative life events predicted hostility. Involuntary stress responses were associated with higher levels of symptoms for both parents and the adolescent children. Secondary control coping was associated with fewer symptoms for both parents and adolescents. Results support a mediational role of coping and responses to stress during adolescence, with a shift to moderational status in adulthood. Implications of these results are discussed with regard to developmental coping theory and potential interventions with at-risk families.     

Hierarchical Diagnostic Classification Models: A Family of Models for Estimating and Testing Attribute Hierarchies

Although latent attributes that follow a hierarchical structure are anticipated in many areas of educational and psychological assessment, current psychometric models are limited in their capacity to objectively evaluate the presence of such attribute hierarchies. This paper introduces the Hierarchical Diagnostic Classification Model (HDCM), which adapts the Log-linear Cognitive Diagnosis Model to cases where attribute hierarchies are present. The utility of the HDCM is demonstrated through simulation and by an empirical example. Simulation study results show the HDCM is efficiently estimated and can accurately test for the presence of an attribute hierarchy statistically, a feature not possible when using more commonly used DCMs. Empirically, the HDCM is used to test for the presence of a suspected attribute hierarchy in a test of English grammar, confirming the data is more adequately represented by hierarchical attribute structure when compared to a crossed, or nonhierarchical structure.     

内隐记忆研究的新进展:概念、实验和模型

本文回顾了近年来内隐记忆研究的新进展。内隐记忆概念的描述性和模糊性正受到研究者的批评。对此概念进行更准确地把握在当前愈显紧迫和必要。多数研究者仍继续沿用这一术语．最近的实验研究修改了部分早期结论．并开始与学习和记忆研究的其他领域,尤其是涉及无意识过程的领域互相结合。内隐记忆的解释和建模呈现出从定性到定量的发展趋势。     

A Computationally Efficient State Space Approach to Estimating Multilevel Regression Models and Multilevel Confirmatory Factor Models

Although the state space approach for estimating multilevel regression models has been well established for decades in the time series literature, it does not receive much attention from educational and psychological researchers. In this article, we (a) introduce the state space approach for estimating multilevel regression models and (b) extend the state space approach for estimating multilevel factor models. A brief outline of the state space formulation is provided and then state space forms for univariate and multivariate multilevel regression models, and a multilevel confirmatory factor model, are illustrated. The utility of the state space approach is demonstrated with either a simulated or real example for each multilevel model. It is concluded that the results from the state space approach are essentially identical to those from specialized multilevel regression modeling and structural equation modeling software. More importantly, the state space approach offers researchers a computationally more efficient alternative to fit multilevel regression models with a large number of Level 1 units within each Level 2 unit or a large number of observations on each subject in a longitudinal study.     

Conditional Direction Dependence Analysis: Evaluating the Causal Direction of Effects in Linear Models with Interaction Terms

Abstract

Direction dependence analysis (DDA) makes use of higher than second moment information of variables (x and y) to detect potential confounding and to probe the causal direction of linear variable relations (i.e., whether x?→?y or y?→?x better approximates the underlying causal mechanism). The “true” predictor is assumed to be a continuous nonnormal exogenous variable. Existing methods compatible with DDA, however, are of limited use when the relation of a focal predictor and an outcome is affected by a moderator. This study presents a conditional direction dependence analysis (CDDA) framework which enables researchers to evaluate the causal direction of conditional regression effects. Monte–Carlo simulations were used to evaluate two different moderation scenarios: Study 1 evaluates the performance of CDDA tests when a moderator affects the strength of the causal effect x?→?y. Study 2 evaluates cases in which the causal direction itself (x?→?y vs y?→?x) depends on moderator values. Study 3 evaluates the robustness of DDA tests in the presence of functional model misspecifications. Results suggest that significance tests compatible with CDDA are suitable in both moderation scenarios, i.e., CDDA allows one to discern regions of a moderator in which the causal direction is uniquely identifiable. An empirical example is provided to illustrate the approach.     

Generalized Processing Tree Models: Jointly Modeling Discrete and Continuous Variables

Multinomial processing tree models assume that discrete cognitive states determine observed response frequencies. Generalized processing tree (GPT) models extend this conceptual framework to continuous variables such as response times, process-tracing measures, or neurophysiological variables. GPT models assume finite-mixture distributions, with weights determined by a processing tree structure, and continuous components modeled by parameterized distributions such as Gaussians with separate or shared parameters across states. We discuss identifiability, parameter estimation, model testing, a modeling syntax, and the improved precision of GPT estimates. Finally, a GPT version of the feature comparison model of semantic categorization is applied to computer-mouse trajectories.     

有中介的调节模型检验方法：甄别和整合*

在心理和教育研究中,经常遇到调节和中介效应。模型包含不止3个变量时,可能同时包含调节和中介变量,一种常见的模型是有中介的调节模型。本文评介了文献上可以找到的五种检验有中介的调节模型的方法,逐一甄别,指出其中一些不合理之处,并推荐较好的方法。整合其中主要方法,总结出检验有中介的调节模型的流程,用偏差校正的百分位 Bootstrap 法或马尔科夫链蒙特卡罗法检验其中的中介效应,并用一个实际例子演示如何用此流程检验有中介的调节模型。     

Correction for Item Response Theory Latent Trait Measurement Error in Linear Mixed Effects Models

Psychometrika - When latent variables are used as outcomes in regression analysis, a common approach that is used to solve the ignored measurement error issue is to take a multilevel perspective on...