Analysis of multivariate mixed longitudinal data: A flexible latent process approach

Multivariate ordinal and quantitative longitudinal data measuring the same latent construct are frequently collected in psychology. We propose an approach to describe change over time of the latent process underlying multiple longitudinal outcomes of different types (binary, ordinal, quantitative). By relying on random‐effect models, this approach handles individually varying and outcome‐specific measurement times. A linear mixed model describes the latent process trajectory while equations of observation combine outcome‐specific threshold models for binary or ordinal outcomes and models based on flexible parameterized non‐linear families of transformations for Gaussian and non‐Gaussian quantitative outcomes. As models assuming continuous distributions may be also used with discrete outcomes, we propose likelihood and information criteria for discrete data to compare the goodness of fit of models assuming either a continuous or a discrete distribution for discrete data. Two analyses of the repeated measures of the Mini‐Mental State Examination, a 20‐item psychometric test, illustrate the method. First, we highlight the usefulness of parameterized non‐linear transformations by comparing different flexible families of transformation for modelling the test as a sum score. Then, change over time of the latent construct underlying directly the 20 items is described using two‐parameter longitudinal item response models that are specific cases of the approach.     

The use of artificial neural networks and multiple linear regression in modelling work–health relationships: Translating theory into analytical practice

Although psychological theory acknowledges the existence of complex systems and the importance of nonlinear effects, linear statistical models have been traditionally used to examine relationships between environmental stimuli and outcomes. The way we analyse these relationships does not seem to reflect the way we conceptualize them. The present study investigated the application of connectionism (artificial neural networks) to modelling the relationships between work characteristics and employee health by comparing it with a more conventional statistical linear approach (multiple linear regression) on a sample of 1003 individuals in employment. Comparisons of performance metrics indicated differences in model fit, with neural networks to some extent outperforming the linear regression models, such that R ² for worn-out and job satisfaction were significantly higher in the neural networks. Most importantly, comparisons revealed that the predictors in the two approaches differed in their relative importance for predicting outcomes. The improvement is attributed to the ability of the neural networks to model complex nonlinear relationships. Being unconstrained by assumptions of linearity, they can provide a better approximation of such psychosocial phenomena. Nonlinear approaches are often better fitted for purpose, as they conform to the need for correspondence between theory, method, and data.     

Support for a continuous (single-process) model of recognition memory and source memory

Does memory retrieval occur in a continuous or an all-or-none manner? The shape of the receiver operating characteristic (ROC) has been used to answer this question, with curvilinear and linear memory ROCs indicating continuous and all-or-none retrieval processes, respectively. Signal detection models (e.g., the unequal variance model) correspond to a continuous retrieval process, whereas threshold models (including the multinomial model and the recollection component of the dual-process model) correspond to an all-or-none process. In studies of source memory, Slotnick et al. (2000) and others have observed curvilinear ROCs (supporting the unequal variance model), whereas Yonelinas (1999) observed linear ROCs (supporting the dual-process model). We resolve these seemingly inconsistent results, showing that source memory ROCs are naturally curvilinear but can appear linear when nondiagnostic source information is included in the analysis. Furthermore, the unequal variance model accounted for both recognition memory and source memory ROCs, supporting a continuous process of memory retrieval.     

Conditional mixed models with crossed random effects

The analysis of continuous hierarchical data such as repeated measures or data from meta‐analyses can be carried out by means of the linear mixed‐effects model. However, in some situations this model, in its standard form, does pose computational problems. For example, when dealing with crossed random‐effects models, the estimation of the variance components becomes a non‐trivial task if only one observation is available for each cross‐classified level. Pseudolikelihood ideas have been used in the context of binary data with standard generalized linear multilevel models. However, even in this case the problem of the estimation of the variance remains non‐trivial. In this paper, we first propose a method to fit a crossed random‐effects model with two levels and continuous outcomes, borrowing ideas from conditional linear mixed‐effects model theory. We also propose a crossed random‐effects model for binary data combining ideas of conditional logistic regression with pseudolikelihood estimation. We apply this method to a case study with data coming from the field of psychometrics and study a series of items (responses) crossed with participants. A simulation study assesses the operational characteristics of the method.     

The role of nonlinear factor-to-indicator relationships in tests of measurement equivalence

Measurement invariance is a necessary condition for the evaluation of factor mean differences over groups or time. This article considers the potential problems that can arise for tests of measurement invariance when the true factor-to-indicator relationship is nonlinear (quadratic) and invariant but the linear factor model is nevertheless applied. The factor loadings and indicator intercepts of the linear model will diverge across groups as the factor mean difference increases. Power analyses show that even apparently small quadratic effects can result in rejection of measurement invariance at moderate sample sizes when the factor mean difference is medium to large. Recommendations include the identification of nonlinear relationships using diagnostic plots and consideration of newly developed methods for fitting nonlinear factor models.     

The mediating effects of social exchange relationships in predicting workplace outcomes from multifoci organizational justice

This study tests a social exchange model of multifoci justice. We compared perceptions of justice emanating from the supervisor to those emanating from the organization as a whole. In presenting our model, we hypothesize that the link between multifoci justice and multifoci outcomes (e.g. performance and OCB) is mediated by the formation of multifoci social exchange relationships. We further expected organizationally focused justice and relationships to predict organizationally relevant outcomes and supervisory focused justice and relationships to predict both supervisory and organizationally relevant outcomes. Findings generally supported our expectations, but more so for interactional justice and less so for procedural justice.     

The job demand-control(-support) model and physical health outcomes: A review of the strain and buffer hypotheses

Abstract

This review of the Job Demand-Control (JDC) model and the expanded Job Demand-Control-Support (JDCS) model and employees' physical health, focuses on the two prevalent views on these models. According to their view on the models researchers study different hypotheses: (a) the (iso)strain hypothesis, stating that the highest level of ill health is expected when the job is characterized by high demand and low control (and low social sup port), ot (b) the buffer hypothesis, predicting that control (and social support) can buffer the potential negative effects of high demands on physical health. It is argued that these hypotheses reflect theoretical distinct models, and that the practical implications associated with these models differ.

The review of 51 studies on the JDC(S) model reveals that the “strain” hypothesis predominates in studies of all-cause mortality, cardiovascular disease (CVD) related and specific non-CVD related health outcomes. In contrast, the “buffer” hypothesis is most prevalent in research on self-reported (psycho)somatic complaints. For the strain hypothesis as well as the buffer hypothesis the results are equivocal. Working in a high (iso)strain job appears to be associated with an elevated risk for cardiovascular disease and negative pregnancy outcomes, and increased (psycho)somatic complaints. Conclusions on other physical outcomes seem premature, considering the limited number of studies. The buffer hypothesis is supported in the few studies on CVD endpoints and in some studies on (psycho)somatic complaints.

A comparison of the validity of the two hypotheses is problematic, because they are mostly applied to a different set of outcomes. Furthermore, the analyses employed in the testing of the two hypotheses are of a different nature (non-linear versus linear).

The main recommendation for future research is to examine the validity of the strain and the buffer hypothesis concurrently, and to further explore the nature of the relationships.     

The nature and outcomes of work: a replication and extension of interdisciplinary work-design research

Research into the changing nature of work requires comprehensive models of work design. One such model is the interdisciplinary framework (M. A. Campion, 1988), which integrates 4 work-design approaches (motivational, mechanistic, biological, perceptual-motor) and links each approach to specific outcomes. Unfortunately, studies of this framework have used methods that disregard measurement error, overlook dimensions within each work-design approach, and treat each approach and outcome separately. This study reanalyzes data from M. A. Campion (1988), using structural equation models that incorporate measurement error, specify multiple dimensions for each work-design approach, and examine the work-design approaches and outcomes jointly. Results show that previous studies underestimate relationships between work-design approaches and outcomes and that dimensions within each approach exhibit relationships with outcomes that differ in magnitude and direction.     

A New Multilevel CART Algorithm for Multilevel Data with Binary Outcomes

The multilevel logistic regression model (M-logit) is the standard model for modeling multilevel data with binary outcomes. However, many assumptions and restrictions should be considered when applying this model for unbiased estimation. To overcome these limitations, we proposed a multilevel CART (M-CART) algorithm which combines the M-logit and single level CART (S-CART) within the framework of the expectation-maximization. Simulation results showed that the proposed M-CART provided substantial improvements on classification accuracy, sensitivity, and specific over the M-logit, S-CART, and single level logistic regression model when modeling multilevel data with binary outcomes. This benefit of using M-CART was consistently found across different conditions of sample size, intra-class correlation, and when relationships between predictors and outcomes were nonlinear and nonadditive.     

Prime and probability: causal knowledge affects inferential and predictive effects on self-agency experiences

Experiences of having caused a certain outcome may arise from motor predictions based on action–outcome probabilities and causal inferences based on pre-activated outcome representations. However, when and how both indicators combine to affect such self-agency experiences is still unclear. Based on previous research on prediction and inference effects on self-agency, we propose that their (combined) contribution crucially depends on whether people have knowledge about the causal relation between actions and outcomes that is relevant to subsequent self-agency experiences. Therefore, we manipulated causal knowledge that was either relevant or irrelevant by varying the probability of co-occurrence (50% or 80%) of specific actions and outcomes. Afterwards, we measured self-agency experiences in an action–outcome task where outcomes were primed or not. Results showed that motor prediction only affected self-agency when relevant actions and outcomes were learned to be causally related. Interestingly, however, inference effects also occurred when no relevant causal knowledge was acquired.     

Why people underestimate y when extrapolating in linear functions

E. L. DeLosh, J. R. Busemeyer, and M. A. McDaniel (1997) found that when learning a positive, linear relationship between a continuous predictor (x) and a continuous criterion (y), trainees tend to underestimate y on items that ask the trainee to extrapolate. In 3 experiments, the authors examined the phenomenon and found that the tendency to underestimate y is reliable only in the so-called lower extrapolation region--that is, new values of x that lie between zero and the edge of the training region. Existing models of function learning, such as the extrapolation-association model (DeLosh et al., 1997) and the population of linear experts model (M. L. Kalish, S. Lewandowsky, & J. Kruschke, 2004), cannot account for these results. The authors show that with minor changes, both models can predict the correct pattern of results.     

Generalized latent variable models with non‐linear effects

Until recently, item response models such as the factor analysis model for metric responses, the two‐parameter logistic model for binary responses and the multinomial model for nominal responses considered only the main effects of latent variables without allowing for interaction or polynomial latent variable effects. However, non‐linear relationships among the latent variables might be necessary in real applications. Methods for fitting models with non‐linear latent terms have been developed mainly under the structural equation modelling approach. In this paper, we consider a latent variable model framework for mixed responses (metric and categorical) that allows inclusion of both non‐linear latent and covariate effects. The model parameters are estimated using full maximum likelihood based on a hybrid integration–maximization algorithm. Finally, a method for obtaining factor scores based on multiple imputation is proposed here for the non‐linear model.     

Bidimensional Emotional Health in College Students: a Comparison of Categorical and Continuous Analytic Approaches

This study reports on an investigation of the concurrent validity of the bidimensional model of emotional health, using two analytic approaches—one categorical and the other continuous—with two subsamples of college students. Results from the categorical approach, using analyses of variance with the first subsample (n = 461), indicated that, compared to isolated emotional wellbeing and distress models, the bidimensional model of emotional health had incremental validity in relation to social connectedness, life satisfaction, physical health, and academic achievement outcomes. Findings from the continuous approach, using latent-variables path analyses with the second subsample (n = 490), indicated that the isolated emotional wellbeing model was a better predictor of the aforementioned quality-of-life outcomes than were the bidimensional and isolated distress models. Taken together, findings from both sets of analyses suggest that emotional wellbeing is a distinguishing predictor of college student outcomes. Implications for the theory and practice of mental health work at the college level are discussed.     

The Long Arm of Mentoring: A Counterfactual Analysis of Natural Youth Mentoring and Employment Outcomes in Early Careers

Young people often develop natural mentoring relationships with nonparental adults during adolescence and young adulthood. While much has been learned about the benefits of natural mentoring for more proximate outcomes such as mental health and education, relatively little is known about the causal impact of youth mentoring relationships on career opportunities. This study uses data from the National Longitudinal Study of Adolescent Health (Add Health) survey to explore the effects of different kinds of natural mentoring relationships on employment outcomes during the early career years (when workers are in their late twenties and early thirties). Whereas traditional methods of causal conditioning show a broad range of employment benefits from being mentored, results from counterfactual analysis using propensity score matching reveal that the benefits of mentoring are confined to intrinsic job rewards. The findings imply that mentors help steer youth toward intrinsically rewarding careers.     

The linear mixed model and the hierarchical Ornstein–Uhlenbeck model: Some equivalences and differences

We focus on comparing different modelling approaches for intensive longitudinal designs. Two methods are scrutinized, namely the widely used linear mixed model (LMM) and the relatively unexplored Ornstein–Uhlenbeck (OU) process based state‐space model. On the one hand, we show that given certain conditions they result in equivalent outcomes. On the other hand, we consider it important to emphasize that their perspectives are different and that one framework might better address certain types of research questions than the other. We show that, compared to a LMM, an OU process based approach can cope with modelling inter‐individual differences in aspects that are more substantively interesting. However, the estimation of the LMM is faster and the model is more straightforward to implement. The models are illustrated through an experience sampling study.     

A Bayesian Modeling Approach for Generalized Semiparametric Structural Equation Models

In behavioral, biomedical, and psychological studies, structural equation models (SEMs) have been widely used for assessing relationships between latent variables. Regression-type structural models based on parametric functions are often used for such purposes. In many applications, however, parametric SEMs are not adequate to capture subtle patterns in the functions over the entire range of the predictor variable. A different but equally important limitation of traditional parametric SEMs is that they are not designed to handle mixed data types—continuous, count, ordered, and unordered categorical. This paper develops a generalized semiparametric SEM that is able to handle mixed data types and to simultaneously model different functional relationships among latent variables. A structural equation of the proposed SEM is formulated using a series of unspecified smooth functions. The Bayesian P-splines approach and Markov chain Monte Carlo methods are developed to estimate the smooth functions and the unknown parameters. Moreover, we examine the relative benefits of semiparametric modeling over parametric modeling using a Bayesian model-comparison statistic, called the complete deviance information criterion (DIC). The performance of the developed methodology is evaluated using a simulation study. To illustrate the method, we used a data set derived from the National Longitudinal Survey of Youth.     

The average rate of change for continuous time models

The average rate of change (ARC) is a concept that has been misunderstood in the applied longitudinal data analysis literature, where the slope from the straight-line change model is often thought of as though it were the ARC. The present article clarifies the concept of ARC and shows unequivocally the mathematical definition and meaning of ARC when measurement is continuous across time. It is shown that the slope from the straight-line change model generally is not equal to the ARC. General equations are presented for two measures of discrepancy when the slope from the straight-line change model is used to estimate the ARC in the case of continuous time for any model linear in its parameters, and for three useful models nonlinear in their parameters.     

A Note on Comparing the Estimates of Models for Cluster-Correlated or Longitudinal Data with Binary or Ordinal Outcomes

When using linear models for cluster-correlated or longitudinal data, a common modeling practice is to begin by fitting a relatively simple model and then to increase the model complexity in steps. New predictors might be added to the model, or a more complex covariance structure might be specified for the observations. When fitting models for binary or ordered-categorical outcomes, however, comparisons between such models are impeded by the implicit rescaling of the model estimates that takes place with the inclusion of new predictors and/or random effects. This paper presents an approach for putting the estimates on a common scale to facilitate relative comparisons between models fit to binary or ordinal outcomes. The approach is developed for both population-average and unit-specific models.