Simple matrix methods for analyzing diffusion models of choice probability, choice response time, and simple response time

Diffusion processes (e.g., Wiener process, Ornstein-Uhlenbeck process) are powerful approaches to model human information processes in a variety of psychological tasks. Lack of mathematical tractability, however, has prevented broad applications of these models to empirical data. This tutorial explains step by step, using a matrix approach, how to construct these models, how to implement them on a computer, and how to calculate the predictions made by these models. In particular, we present models for binaries choices for unidimensional and multiattribute choice alternatives; for simple reaction time tasks; and for three alternatives choice problems.     

What Does Successful Aging Sound Like? Profiling Communication About Aging

We draw on the recently developed communicative ecology model of successful aging (CEMSA) to examine how adults communicate about aging and how these communication patterns relate to experiences of successful aging. Using latent class analysis across 2 datasets collected in New Zealand and the United States, we identify 3 distinct classes of agers (disengaged, engaged, and bantering) defined by different profiles of communication behavior. Across samples, an engaged profile was generally associated with the most positive experiences of aging, whereas a disengaged profile was associated with the least positive experiences, although these differences were surprisingly small. Our results highlight the diverse ways in which individuals communicatively engage with the process of aging and experience aging as positive and successful.     

Efficient nonparametric approaches for estimating the operating characteristics of discrete item responses

Rationale and the actual procedures of two nonparametric approaches, called Bivariate P.D.F. Approach and Conditional P.D.F. Approach, for estimating the operating characteristic of a discrete item response, or the conditional probability, given latent trait, that the examinee's response be that specific response, are introduced and discussed. These methods are featured by the facts that: (a) estimation is made without assuming any mathematical forms, and (b) it is based upon a relatively small sample of several hundred to a few thousand examinees.Some examples of the results obtained by the Simple Sum Procedure and the Differential Weight Procedure of the Conditional P.D.F. Approach are given, using simulated data. The usefulness of these nonparametric methods is also discussed.This research was mostly supported by the Office of Naval Research (N00014-77-C-0360, N00014-81-C-0569, N00014-87-K-0320, N00014-90-J-1456).     

Latent profiles of work motivation in adolescents in relation to work expectations,goal engagement,and changes in work experiences

Motivation plays a key role in successful entry into working life. Based on a cross-sectional and a one-year longitudinal study, we used a person-centered approach to explore work-related motivation (i.e., autonomous goals, positive affect, and occupational self-efficacy) among 577 students in 8th grade (Study 1) and 949 adolescents in vocational training (Study 2). Based on latent profile analysis, in both studies we identified four groups that were characterized by different levels of overall motivation and one group characterized by low positive affect and mean levels in autonomous goals and self-efficacy. Profiles characterized by high levels of motivation showed the highest levels of positive work expectations and goal engagement and the lowest levels of negative work expectations in Study 1 and the highest levels of person-job fit, work engagement, and job satisfaction in Study 2. Moreover, latent difference score analysis showed that motivational profiles predicted changes in person-job fit and work engagement across one year but not in job satisfaction. The results imply that career counselors should be aware of characteristic motivational patterns of clients that may require specific counseling approaches.     

Do people reason rationally about causally related events? Markov violations,weak inferences,and failures of explaining away

Making judgments by relying on beliefs about the causal relationships between events is a fundamental capacity of everyday cognition. In the last decade, Causal Bayesian Networks have been proposed as a framework for modeling causal reasoning. Two experiments were conducted to provide comprehensive data sets with which to evaluate a variety of different types of judgments in comparison to the standard Bayesian networks calculations. Participants were introduced to a fictional system of three events and observed a set of learning trials that instantiated the multivariate distribution relating the three variables. We tested inferences on chains X₁ → Y → X₂, common cause structures X₁ ← Y → X₂, and common effect structures X₁ → Y ← X₂, on binary and numerical variables, and with high and intermediate causal strengths. We tested transitive inferences, inferences when one variable is irrelevant because it is blocked by an intervening variable (Markov Assumption), inferences from two variables to a middle variable, and inferences about the presence of one cause when the alternative cause was known to have occurred (the normative “explaining away” pattern). Compared to the normative account, in general, when the judgments should change, they change in the normative direction. However, we also discuss a few persistent violations of the standard normative model. In addition, we evaluate the relative success of 12 theoretical explanations for these deviations.     

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.     

Dealing with Multiple Solutions in Structural Vector Autoregressive Models

Structural vector autoregressive models (VARs) hold great potential for psychological science, particularly for time series data analysis. They capture the magnitude, direction of influence, and temporal (lagged and contemporaneous) nature of relations among variables. Unified structural equation modeling (uSEM) is an optimal structural VAR instantiation, according to large-scale simulation studies, and it is implemented within an SEM framework. However, little is known about the uniqueness of uSEM results. Thus, the goal of this study was to investigate whether multiple solutions result from uSEM analysis and, if so, to demonstrate ways to select an optimal solution. This was accomplished with two simulated data sets, an empirical data set concerning children's dyadic play, and modifications to the group iterative multiple model estimation (GIMME) program, which implements uSEMs with group- and individual-level relations in a data-driven manner. Results revealed multiple solutions when there were large contemporaneous relations among variables. Results also verified several ways to select the correct solution when the complete solution set was generated, such as the use of cross-validation, maximum standardized residuals, and information criteria. This work has immediate and direct implications for the analysis of time series data and for the inferences drawn from those data concerning human behavior.     

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.     

A Note on Recurring Misconceptions When Fitting Nonlinear Mixed Models

Nonlinear mixed-effects (NLME) models are used when analyzing continuous repeated measures data taken on each of a number of individuals where the focus is on characteristics of complex, nonlinear individual change. Challenges with fitting NLME models and interpreting analytic results have been well documented in the statistical literature. However, parameter estimates as well as fitted functions from NLME analyses in recent articles have been misinterpreted, suggesting the need for clarification of these issues before these misconceptions become fact. These misconceptions arise from the choice of popular estimation algorithms, namely, the first-order linearization method (FO) and Gaussian-Hermite quadrature (GHQ) methods, and how these choices necessarily lead to population-average (PA) or subject-specific (SS) interpretations of model parameters, respectively. These estimation approaches also affect the fitted function for the typical individual, the lack-of-fit of individuals’ predicted trajectories, and vice versa.