The Gaussian Graphical Model in Cross-Sectional and Time-Series Data

We discuss the Gaussian graphical model (GGM; an undirected network of partial correlation coefficients) and detail its utility as an exploratory data analysis tool. The GGM shows which variables predict one-another, allows for sparse modeling of covariance structures, and may highlight potential causal relationships between observed variables. We describe the utility in three kinds of psychological data sets: data sets in which consecutive cases are assumed independent (e.g., cross-sectional data), temporally ordered data sets (e.g., n = 1 time series), and a mixture of the 2 (e.g., n > 1 time series). In time-series analysis, the GGM can be used to model the residual structure of a vector-autoregression analysis (VAR), also termed graphical VAR. Two network models can then be obtained: a temporal network and a contemporaneous network. When analyzing data from multiple subjects, a GGM can also be formed on the covariance structure of stationary means—the between-subjects network. We discuss the interpretation of these models and propose estimation methods to obtain these networks, which we implement in the R packages graphicalVAR and mlVAR. The methods are showcased in two empirical examples, and simulation studies on these methods are included in the supplementary materials.     

A latent state-trait anxiety model and its application to determine consistency and specificity coefficients

Abstract

In the present study the consistency model (Steyer, 1987) was applied to data gathered with the German version of the State-Trait Anxiety Inventory (Laux, Glanzmann, Schaffner, and Spielberger, 1981). The questionnaire was presented twice to 64 university students with an interval of two months between first and second testing. The consistency and specificity coefficients, estimated by LISREL (Jöreskog and Sörbom, 1984), support the state-trait distinction. The state variables have high specificity and consistency coefficients; the trait variables, in contrast, have high consistency coefficients but low or even negligible specificity coefficients. The discussion points out the advantages of the consistency model over the stability model; the most important advantage is that the theoretical structure of the consistency model is more appropriate for the type of application considered. It contains a state factor for each occasion of measurement and a trait factor common to all occasions of measurement. In the stability model, only latent states, but no latent traits occur. Consistency, specificity, and reliability can be identified as proportions of variance determined by latent variables specified in the model. Therefore, data analysis provides statistics concerning the practical significance of the trait and of the effects of situations and/or interactions.     

On the Measurement of Stability in Over-Time Data

ABSTRACT In this article, autoregressive models and growth curve models are compared Autoregressive models are useful because they allow for random change, permit scores to increase or decrease, and do not require strong assumptions about the level of measurement Three previously presented designs for estimating stability are described (a) time-series, (b) simplex, and (c) two-wave, one-factor methods A two-wave, multiple-factor model also is presented, in which the variables are assumed to be caused by a set of latent variables The factor structure does not change over time and so the synchronous relationships are temporally invariant The factors do not cause each other and have the same stability The parameters of the model are the factor loading structure, each variable's reliability, and the stability of the factors We apply the model to two data sets For eight cognitive skill variables measured at four times, the 2-year stability is estimated to be 92 and the 6-year stability is 83 For nine personality variables, the 3-year stability is 68 We speculate that for many variables there are two components one component that changes very slowly (the trait component) and another that changes very rapidly (the state component), thus each variable is a mixture of trait and state Circumstantial evidence supporting this view is presented     

A Latent Block Distance-Association Model for Profile by Profile Cross-Classified Categorical Data

Abstract

Distance association models constitute a useful tool for the analysis and graphical representation of cross-classified data in which distances between points inversely describe the association between two categorical variables. When the number of cells is large and the data counts result in sparse tables, the combination of clustering and representation reduces the number of parameters to be estimated and facilitates interpretation. In this article, a latent block distance-association model is proposed to apply block clustering to the outcomes of two categorical variables while the cluster centers are represented in a low dimensional space in terms of a distance-association model. This model is particularly useful for contingency tables in which both the rows and the columns are characterized as profiles of sets of response variables. The parameters are estimated under a Poisson sampling scheme using a generalized EM algorithm. The performance of the model is tested in a Monte Carlo experiment, and an empirical data set is analyzed to illustrate the model.     

Back to the basics: Rethinking partial correlation network methodology

The Gaussian graphical model (GGM) is an increasingly popular technique used in psychology to characterize relationships among observed variables. These relationships are represented as elements in the precision matrix. Standardizing the precision matrix and reversing the sign yields corresponding partial correlations that imply pairwise dependencies in which the effects of all other variables have been controlled for. The graphical lasso (glasso) has emerged as the default estimation method, which uses ℓ₁-based regularization. The glasso was developed and optimized for high-dimensional settings where the number of variables (p) exceeds the number of observations (n), which is uncommon in psychological applications. Here we propose to go ‘back to the basics’, wherein the precision matrix is first estimated with non-regularized maximum likelihood and then Fisher Z transformed confidence intervals are used to determine non-zero relationships. We first show the exact correspondence between the confidence level and specificity, which is due to 1 minus specificity denoting the false positive rate (i.e., α). With simulations in low-dimensional settings (p ≪ n), we then demonstrate superior performance compared to the glasso for detecting the non-zero effects. Further, our results indicate that the glasso is inconsistent for the purpose of model selection and does not control the false discovery rate, whereas the proposed method converges on the true model and directly controls error rates. We end by discussing implications for estimating GGMs in psychology.     

Two-Step Estimation of Models Between Latent Classes and External Variables

We consider models which combine latent class measurement models for categorical latent variables with structural regression models for the relationships between the latent classes and observed explanatory and response variables. We propose a two-step method of estimating such models. In its first step, the measurement model is estimated alone, and in the second step the parameters of this measurement model are held fixed when the structural model is estimated. Simulation studies and applied examples suggest that the two-step method is an attractive alternative to existing one-step and three-step methods. We derive estimated standard errors for the two-step estimates of the structural model which account for the uncertainty from both steps of the estimation, and show how the method can be implemented in existing software for latent variable modelling.     

随机截距潜在转变分析(RI-LTA)——个案自我转变与个案间差异的分离

传统的潜在转变分析属于单水平分析, 但其同样也可以看作二水平分析。Muthén和Asparouhov就以二水平分析的视角在单水平分析框架内提出了随机截距潜在转变分析(RI-LTA), 其中跨时间点产生的自我转变可以看作在水平1进行分析, 跨时间点不变的个案间差异可以看作在水平2进行分析, 使个案的自我转变和个案间的初始差异分离, 避免了高估保留在初始类别的概率。某研究型大学2016级本科生的追踪调查数据被用于演示使用随机截距潜在转变分析的过程。该方法的最大优势是通过引入随机截距避免了高估保留在本类别的转变概率。未来研究可以运用蒙特卡洛模拟研究探究随机截距潜在转变分析模型的适用性, 也可以用多水平分析的思路为灵感, 探究多水平随机截距潜在转变分析在统计软件中的实现。     

Using confidence intervals for graphically based data interpretation.

As a potential alternative to standard null hypothesis significance testing, we describe methods for graphical presentation of data--particularly condition means and their corresponding confidence intervals--for a wide range of factorial designs used in experimental psychology. We describe and illustrate confidence intervals specifically appropriate for between-subject versus within-subject factors. For designs involving more than two levels of a factor, we describe the use of contrasts for graphical illustration of theoretically meaningful components of main effects and interactions. These graphical techniques lend themselves to a natural and straightforward assessment of statistical power.     

Cognitive Indicators of Social Anxiety in Youth: A Structural Equation Analysis

Previous studies have demonstrated significant relationships among various cognitive variables such as negative cognition, self-efficacy, and social anxiety. Unfortunately, few studies focus on the role of cognition among youth, and researchers often fail to use domain-specific measures when examining cognitive variables. Therefore, the purpose of the present study was to examine domain-specific cognitive variables (i.e., socially oriented negative self-referent cognition and social self-efficacy) and their relationships to social anxiety in children and adolescents using structural equation modeling techniques. A community sample of children and adolescents (n = 245; 55.9% female; 83.3% Caucasian, 9.4% African American, 2% Asian, 2% Hispanic, 2% “other,” and 1.2% not reported) completed questionnaires assessing social cognition and social anxiety symptomology. Three latent variables were created to examine the constructs of socially oriented negative self-referent cognition (as measured by the SONAS scale), social self-efficacy (as measured by the SEQSS-C), and social anxiety (as measured by the SPAI-C and the Brief SA). The resulting measurement model of latent variables fit the data well. Additionally, consistent with the study hypothesis, results indicated that social self-efficacy likely mediates the relationship between socially oriented negative self-referent cognition and social anxiety, and socially oriented negative self-referent cognition yields significant direct and indirect effects on social anxiety. These findings indicate that socially oriented negative cognitions are associated with youth's beliefs about social abilities and the experience of social anxiety. Future directions for research and study limitations, including use of cross-sectional data, are discussed.     

A generalized rasch model for manifest predictors

A logistic regression model is suggested for estimating the relation between a set of manifest predictors and a latent trait assumed to be measured by a set ofk dichotomous items. Usually the estimated subject parameters of latent trait models are biased, especially for short tests. Therefore, the relation between a latent trait and a set of predictors should not be estimated with a regression model in which the estimated subject parameters are used as a dependent variable. Direct estimation of the relation between the latent trait and one or more independent variables is suggested instead. Estimation methods and test statistics for the Rasch model are discussed and the model is illustrated with simulated and empirical data.     

The Nature of Psychological Reactance Revisited: A Meta‐Analytic Review

Psychological reactance ( Brehm, 1966 ; Brehm & Brehm, 1981 ) has been a long‐standing topic of interest among scholars studying the design and effects of persuasive messages and campaigns. Yet, until recently, reactance was considered to be a motivational state that could not be measured. Dillard and Shen (2005) argued that reactance can be conceptualized as cognition and affect and made amenable to direct measurement. This article revisits Dillard and Shen's (2005) questions about the nature of psychological reactance and reports a test designed to identify the best fitting model of reactance. A meta‐analytic review of reactance research was conducted (K = 20, N = 4,942) and the results were used to test path models representing competing conceptualizations of reactance. The results offer evidence that the intertwined model—in which reactance is modeled as a latent factor with anger and counterarguments serving as indicators—best fit the data.     

Will the real relationship between facial expression and affective experience please stand up: The case of exhilaration

Abstract

It is hypothesised that the empirical correlation between facial expression and affective experience varies as a function of the correlational design used to compute the coefficients. Predictions about the rank order of five designs were derived based on two assumptions. Female subjects were placed into one of three alcohol conditions (no ethanol, low dose, high dose) and were exposed to 30 slides containing jokes or cartoons. The degree of rated funniness and overt behaviour were intercorrelated using five different designs to analyse the same set of data. The results show that within-subject analyses yielded higher coefficients than between-subjects analyses. Aggregation of data increased the coefficients for within-subject analyses, but not for between-subject analyses. A cheerful mood was associated with hyper-expressiveness, i.e. the occurrence of smiling and laughter at relatively low levels of perceived funniness. It was demonstrated that low correlations between facial expression and affective experience may be based on several method artefacts.     

Cross-Sectional Analysis of Longitudinal Mediation Processes

Statistical mediation analysis can help to identify and explain the mechanisms behind psychological processes. Examining a set of variables for mediation effects is a ubiquitous process in the social sciences literature; however, despite evidence suggesting that cross-sectional data can misrepresent the mediation of longitudinal processes, cross-sectional analyses continue to be used in this manner. Alternative longitudinal mediation models, including those rooted in a structural equation modeling framework (cross-lagged panel, latent growth curve, and latent difference score models) are currently available and may provide a better representation of mediation processes for longitudinal data. The purpose of this paper is twofold: first, we provide a comparison of cross-sectional and longitudinal mediation models; second, we advocate using models to evaluate mediation effects that capture the temporal sequence of the process under study. Two separate empirical examples are presented to illustrate differences in the conclusions drawn from cross-sectional and longitudinal mediation analyses. Findings from these examples yielded substantial differences in interpretations between the cross-sectional and longitudinal mediation models considered here. Based on these observations, researchers should use caution when attempting to use cross-sectional data in place of longitudinal data for mediation analyses.     

Interpreting cross-sectional data on stages of change

Abstract

The vast majority of studies investigating stage theories of health behaviour such as the transtheoretical model have used a cross-sectional research design. Participants are classified into stages and compared on theoretically relevant variables. This paper discusses the proper interpretation of cross-sectional data on stages of change. Linear patterns are not consistent with the stage model assumption that different causal factors are important at different stages but discontinuity patterns (patterns that do not show consistent increments or decrements across stages) can be diagnostic of a stage model. Researchers who use cross-sectional designs should specify predictions concerning the patterns to be expected under a stage model and under possible rival models, and interpret their data accordingly. Wherever possible, they should conduct prospective longitudinal and experimental studies which enable stronger inferences to be drawn.     

A mechanism model of the effect of hedonic product consumption on well‐being

In response to recent calls for research into activities that may increase happiness, this study uses longitudinal data to investigate changes in within-subject, instead of between-subject, well-being. In the context of hedonic product consumption, this study reveals a mechanism by which consumption influences well-being through the mediating effect of satisfaction with associated life domains. Four years of data from a large national panel survey show that consuming hedonic products has indirect effects on well-being, by improving consumers' satisfaction within relevant life domains. High hedonic consumption improves satisfaction with relevant life domains, primarily through more frequent consumption of low-cost hedonic products rather than less frequent consumption of high-cost hedonic products.     

Using confidence intervals in within-subject designs

We argue that to best comprehend many data sets, plotting judiciously selected sample statistics with associated confidence intervals can usefully supplement, or even replace, standard hypothesis-testing procedures. We note that most social science statistics textbooks limit discussion of confidence intervals to their use in between-subject designs. Our central purpose in this article is to describe how to compute an analogous confidence interval that can be used in within-subject designs. This confidence interval rests on the reasoning that because between-subject variance typically plays no role in statistical analyses of within-subject designs, it can legitimately be ignored; hence, an appropriate confidence interval can be based on the standard within-subject error term—that is, on the variability due to the subject × condition interaction. Computation of such a confidence interval is simple and is embodied in Equation 2 on p. 482 of this article. This confidence interval has two useful properties. First, it is based on the same error term as is the corresponding analysis of variance, and hence leads to comparable conclusions. Second, it is related by a known factor (√2) to a confidence interval of the difference between sample means; accordingly, it can be used to infer the faith one can put in some pattern of sample means as a reflection of the underlying pattern of population means. These two properties correspond to analogous properties of the more widely used between-subject confidence interval.     

Implementing continuous non-normal skewed distributions in latent growth mixture modeling: An assessment of specification errors and class enumeration

Abstract

Recent advances have allowed for modeling mixture components within latent growth modeling using robust, skewed mixture distributions rather than normal distributions. This feature adds flexibility in handling non-normality in longitudinal data, through manifest or latent variables, by directly modeling skewed or heavy-tailed latent classes rather than assuming a mixture of normal distributions. The aim of this study was to assess through simulation the potential under- or over-extraction of latent classes in a growth mixture model when underlying data follow either normal, skewed-normal, or skewed-t distributions. In order to assess this, we implement skewed-t, skewed-normal, and conventional normal (i.e., not skewed) forms of the growth mixture model. The skewed-t and skewed-normal versions of this model have only recently been implemented, and relatively little is known about their performance. Model comparison, fit, and classification of correctly specified and mis-specified models were assessed through various indices. Findings suggest that the accuracy of model comparison and fit measures are dependent on the type of (mis)specification, as well as the amount of class separation between the latent classes. A secondary simulation exposed computation and accuracy difficulties under some skewed modeling contexts. Implications of findings, recommendations for applied researchers, and future directions are discussed; a motivating example is presented using education data.     

An Unscented Kalman Filter Approach to the Estimation of Nonlinear Dynamical Systems Models

In the past several decades, methodologies used to estimate nonlinear relationships among latent variables have been developed almost exclusively to fit cross-sectional models. We present a relatively new estimation approach, the unscented Kalman filter (UKF), and illustrate its potential as a tool for fitting nonlinear dynamic models in two ways: (1) as a building block for approximating the log–likelihood of nonlinear state–space models and (2) to fit time-varying dynamic models wherein parameters are represented and estimated online as other latent variables. Furthermore, the substantive utility of the UKF is demonstrated using simulated examples of (1) the classical predator-prey model with time series and multiple–subject data, (2) the chaotic Lorenz system and (3) an empirical example of dyadic interaction.     

Relationship Between Graphical Device Comprehension and Overall Text Comprehension for Third-Grade Children

This study examined relationships between reading comprehension, known predictors of reading comprehension (i.e., cognitive flexibility, fluency, reading motivation and attitude, vocabulary), and graphical device comprehension. One-hundred fifty-six third graders completed assessments of known predictor variables and an assessment tapping comprehension of graphical devices commonly found in age-appropriate informational texts: captioned pictures, insets, surface diagrams, cross-sectional diagrams, flow charts, timelines, and tables. Graphical device comprehension was strongly correlated with reading comprehension, r_s = 0.49, p (one-tailed) < 0.01. Regression analyses, including known and new variables, revealed that graphical device comprehension accounted for 12.81% of the resulting standardized model predicting general reading comprehension.     

Regression among factor scores

Structural equation models with latent variables are sometimes estimated using an intuitive three-step approach, here denoted factor score regression. Consider a structural equation model composed of an explanatory latent variable and a response latent variable related by a structural parameter of scientific interest. In this simple example estimation of the structural parameter proceeds as follows: First, common factor models areseparately estimated for each latent variable. Second, factor scores areseparately assigned to each latent variable, based on the estimates. Third, ordinary linear regression analysis is performed among the factor scores producing an estimate for the structural parameter. We investigate the asymptotic and finite sample performance of different factor score regression methods for structural equation models with latent variables. It is demonstrated that the conventional approach to factor score regression performs very badly. Revised factor score regression, using Regression factor scores for the explanatory latent variables and Bartlett scores for the response latent variables, produces consistent estimators for all parameters.