Regression Mixture Models: Does Modeling the Covariance Between Independent Variables and Latent Classes Improve the Results?

Regression mixture models are increasingly used as an exploratory approach to identify heterogeneity in the effects of a predictor on an outcome. In this simulation study, we tested the effects of violating an implicit assumption often made in these models; that is, independent variables in the model are not directly related to latent classes. Results indicate that the major risk of failing to model the relationship between predictor and latent class was an increase in the probability of selecting additional latent classes and biased class proportions. In addition, we tested whether regression mixture models can detect a piecewise relationship between a predictor and outcome. Results suggest that these models are able to detect piecewise relations but only when the relationship between the latent class and the predictor is included in model estimation. We illustrate the implications of making this assumption through a reanalysis of applied data examining heterogeneity in the effects of family resources on academic achievement. We compare previous results (which assumed no relation between independent variables and latent class) to the model where this assumption is lifted. Implications and analytic suggestions for conducting regression mixture based on these findings are noted.     

A Simple Simulation Technique for Nonnormal Data with Prespecified Skewness,Kurtosis, and Covariance Matrix

We present and investigate a simple way to generate nonnormal data using linear combinations of independent generator (IG) variables. The simulated data have prespecified univariate skewness and kurtosis and a given covariance matrix. In contrast to the widely used Vale-Maurelli (VM) transform, the obtained data are shown to have a non-Gaussian copula. We analytically obtain asymptotic robustness conditions for the IG distribution. We show empirically that popular test statistics in covariance analysis tend to reject true models more often under the IG transform than under the VM transform. This implies that overly optimistic evaluations of estimators and fit statistics in covariance structure analysis may be tempered by including the IG transform for nonnormal data generation. We provide an implementation of the IG transform in the R environment.     

Accounting for Parcel-Allocation Variability in Practice: Combining Sources of Uncertainty and Choosing the Number of Allocations

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.     

Bayesian Factor Analysis as a Variable-Selection Problem: Alternative Priors and Consequences

Factor analysis is a popular statistical technique for multivariate data analysis. Developments in the structural equation modeling framework have enabled the use of hybrid confirmatory/exploratory approaches in which factor-loading structures can be explored relatively flexibly within a confirmatory factor analysis (CFA) framework. Recently, Muthén & Asparouhov proposed a Bayesian structural equation modeling (BSEM) approach to explore the presence of cross loadings in CFA models. We show that the issue of determining factor-loading patterns may be formulated as a Bayesian variable selection problem in which Muthén and Asparouhov's approach can be regarded as a BSEM approach with ridge regression prior (BSEM-RP). We propose another Bayesian approach, denoted herein as the Bayesian structural equation modeling with spike-and-slab prior (BSEM-SSP), which serves as a one-stage alternative to the BSEM-RP. We review the theoretical advantages and disadvantages of both approaches and compare their empirical performance relative to two modification indices-based approaches and exploratory factor analysis with target rotation. A teacher stress scale data set is used to demonstrate our approach.     

The two roads of passionate goal pursuit: links with appraisal,coping, and academic achievement

Background and Objectives: In this research, we tested the role of cognitive appraisals in explaining why harmonious and obsessive passion dimensions are related to distinct forms of coping and explored if performance was impacted by these appraisal and coping processes. Design: Undergraduate students (N = 489) participated in a longitudinal study and completed three surveys throughout the course of an academic year. Methods: Participants completed assessments of both passion dimensions (Time 1), reported how they were appraising and coping with the mid-year examination period (Time 2), and provided consent to obtain their final grade in Introductory Psychology (Time 3). The hypothesized model was tested using structural equation modeling. Results: Harmonious and obsessive passion dimensions were linked with approach and avoidant coping responses, respectively. Cognitive appraisals, particularly appraisals of challenge and uncontrollability, played an indirect role in these relationships. In addition, both appraisals and coping responses had an indirect effect in the relationship between passion dimensions and final grade. Conclusions: These results identify cognitive appraisal as a reason why passion dimensions are linked with distinct coping tendencies and demonstrate the role of appraisal and coping processes in the journey to passionate goal attainment.     

Analysis of factors affecting drivers’ choice to engage with a mobile phone while driving in Beijing

In the current work, we examined reasons that drivers choose to engage with a mobile phone while driving in Beijing. An Internet survey was administered to collect data about talking and texting while driving. Conversations were sorted into different types. Respondents were requested to indicate the frequency of initiating a call or text, perceived risk, perceived importance and emotionality of the call or text. A structural equation model of talking and texting while driving was developed with perceived risk, perceived importance and emotionality of the call as predictors and compared to a similar model with U.S. drivers. Unlike the U.S. data, perceived risk has a significant negative impact on the choice to call or text among drivers in Beijing. Results also show that perceived importance of the call is a major factor affecting the usage of phone while driving. Even though drivers know it is dangerous and illegal, Beijing drivers choose to talk on mobile phones while driving, but they prefer not to text.     

Diversity and Community Can Coexist

We examine the (in)compatibility of diversity and sense of community by means of agent‐based models based on the well‐known Schelling model of residential segregation and Axelrod model of cultural dissemination. We find that diversity and highly clustered social networks, on the assumptions of social tie formation based on spatial proximity and homophily, are incompatible when agent features are immutable, and this holds even for multiple independent features. We include both mutable and immutable features into a model that integrates Schelling and Axelrod models, and we find that even for multiple independent features, diversity and highly clustered social networks can be incompatible on the assumptions of social tie formation based on spatial proximity and homophily. However, this incompatibility breaks down when cultural diversity can be sufficiently large, at which point diversity and clustering need not be negatively correlated. This implies that segregation based on immutable characteristics such as race can possibly be overcome by sufficient similarity on mutable characteristics based on culture, which are subject to a process of social influence, provided a sufficiently large “scope of cultural possibilities” exists.     

Diverging Paths: Understanding Racial Differences in Civic Engagement Among White,African American,and Latina/o Adolescents Using Structural Equation Modeling

There is increasing concern about the large civic engagement gap between Whites and Latina/o and African American youth. Some suggest this may be because traditional models and measures of civic engagement may not be as applicable for youth from historically marginalized groups. With an urban sample of middle and high school‐age youth (n = 903, 52% female), we used structural equation modeling to identify differences in civic pathways between youth from different racial/ethnic backgrounds. We found significant differences between groups including much stronger relationships between exposure to democratic practices and civic self‐efficacy and knowledge for African American and Latina/o youth than for White youth and a stronger relationship between civic knowledge and future civic engagement for Whites and Latina/os than for African Americans. These findings suggest that educators and researchers interested need to take into account the diversity of youths' racial experiences when examining youth civic development.     

Feature Statistics Modulate the Activation of Meaning During Spoken Word Processing

Understanding spoken words involves a rapid mapping from speech to conceptual representations. One distributed feature‐based conceptual account assumes that the statistical characteristics of concepts’ features—the number of concepts they occur in (distinctiveness/sharedness) and likelihood of co‐occurrence (correlational strength)—determine conceptual activation. To test these claims, we investigated the role of distinctiveness/sharedness and correlational strength in speech‐to‐meaning mapping, using a lexical decision task and computational simulations. Responses were faster for concepts with higher sharedness, suggesting that shared features are facilitatory in tasks like lexical decision that require access to them. Correlational strength facilitated responses for slower participants, suggesting a time‐sensitive co‐occurrence‐driven settling mechanism. The computational simulation showed similar effects, with early effects of shared features and later effects of correlational strength. These results support a general‐to‐specific account of conceptual processing, whereby early activation of shared features is followed by the gradual emergence of a specific target representation.     

A Computational Evaluation of Sentence Processing Deficits in Aphasia

Individuals with agrammatic Broca's aphasia experience difficulty when processing reversible non‐canonical sentences. Different accounts have been proposed to explain this phenomenon. The Trace Deletion account (Grodzinsky, 1995, 2000, 2006) attributes this deficit to an impairment in syntactic representations, whereas others (e.g., Caplan, Waters, Dede, Michaud, & Reddy, 2007; Haarmann, Just, & Carpenter, 1997) propose that the underlying structural representations are unimpaired, but sentence comprehension is affected by processing deficits, such as slow lexical activation, reduction in memory resources, slowed processing and/or intermittent deficiency, among others. We test the claims of two processing accounts, slowed processing and intermittent deficiency, and two versions of the Trace Deletion Hypothesis (TDH), in a computational framework for sentence processing (Lewis & Vasishth, 2005) implemented in ACT‐R (Anderson, Byrne, Douglass, Lebiere, & Qin, 2004). The assumption of slowed processing is operationalized as slow procedural memory, so that each processing action is performed slower than normal, and intermittent deficiency as extra noise in the procedural memory, so that the parsing steps are more noisy than normal. We operationalize the TDH as an absence of trace information in the parse tree. To test the predictions of the models implementing these theories, we use the data from a German sentence—picture matching study reported in Hanne, Sekerina, Vasishth, Burchert, and De Bleser (2011). The data consist of offline (sentence‐picture matching accuracies and response times) and online (eye fixation proportions) measures. From among the models considered, the model assuming that both slowed processing and intermittent deficiency are present emerges as the best model of sentence processing difficulty in aphasia. The modeling of individual differences suggests that, if we assume that patients have both slowed processing and intermittent deficiency, they have them in differing degrees.