The Individual as Moderator of Variable Relations - A Configural Approach.

Moderators are variables that change the relations among other variables. Moderators are variables that are substantive just as the variables whose relations are moderated. In the present article, we propose using individuals as moderators. Specifically, we propose using Configural Frequency Analysis, that is, investigating moderators from a person-oriented perspective. The question asked is whether variable relations vary across individuals. Base models are specified for Configural Frequency Analysis that allow one to identify individuals that differ in variable relations. In a data example, it is shown that not a single individual in a sample of alcoholics shows the pattern of association between subjective stress and beer consumption that was found for the entire sample. Extensions of the configural moderator model are discussed.

Log-Linear and Configural Analysis of Intra-Individual Time Series under Consideration of Serial Dependence.

Serial dependence often prevents researchers from obtaining unbiased parameter estimates. In this article, we propose taking serial dependence into account, and exploiting the information that comes with serial dependence. This can be done in the form of shifted variables that are included in addition to the original variables, when models are specified. This way, models become more complex but relations can be considered that, otherwise, cannot be analyzed. Two fields of application are discussed. The first is log-linear modeling. This method is variable-oriented, but it has found applications in person-oriented research. The gain from including shifted variables in log-linear models is that new, specific variable relations can be analyzed. The second field is that of Configural Frequency Analysis. This method is person-oriented, and it allows researchers to detect local relations that, without consideration of shifted variables, cannot be detected. Application examples are given in the context of single-case analysis.

Latent Variables Analysis in Person-Oriented Research.

In this article, we demonstrate that latent variable analysis can be of great use in person-oriented research. Starting with exploratory factor analysis of metric variables, we present an example of the problems that come with generalization of aggregate-level results to subpopulations. Oftentimes, results that are valid for populations do not represent subpopulations at all. This applies to confirmatory factor analysis as well. When variables are categorical, latent class analysis can be used to create latent variables that explain the covariation of observed variables. In an example, we demonstrate that latent class analysis can be applied to data from individuals, when the number of observation points is sufficiently large. In each case of latent variables analysis, the latent variables can be considered moderators of the structure of covariation among observed variables.

Local Effects of Intervention: a Configural Analysis.

In standard statistical data analysis, the effects of intervention or prevention efforts are evaluated in terms of variable relations. Results from application of regression-type methods suggest whether, overall, intervention is successful. In this article, we propose using configural frequency analysis (CFA) either in tandem with regression-type methods or by itself. CFA allows one to adopt a person-oriented perspective in which individuals are targeted that can be characterized by particular profiles. The questions asked in CFA concern these individuals instead of variables. In prevention research, one can ask whether, for particular profiles, the preventive measures are successful. In three real-world data examples, CFA is applied and compared to standard log-linear modeling. Examples consider non-randomized (observational) and randomized intervention settings. The results of these analyses suggest that person-oriented CFA and standard variable-oriented methods of analysis respond to different questions. We show that integrating person- and variable-oriented perspectives can help researchers obtain a fuller picture of intervention effectiveness. Extensions of the CFA approach are discussed.

Distributional causal effects: Beyond an "averagarian" view of intervention effects.

The usefulness of mean aggregates in the analysis of intervention effectiveness is a matter of considerable debate in the psychological, educational, and social sciences. In addition to studying "average treatment effects," the evaluation of "distributional treatment effects," (i.e., effects that go beyond means), has been suggested to obtain a broader picture of how an intervention affects the study outcome. We continue this discussion by considering distributional causal effects. We present formal definitions of causal effects that go beyond means and utilize a distributional regression framework known as generalized additive models for location, scale, and shape (GAMLSS). GAMLSS allows one to characterize an intervention effect in its totality through simultaneously modeling means, variances, skewnesses, kurtoses, as well as ceiling and floor effects of outcome distributions. Based on data from a large-scale randomized controlled trial, we use GAMLSS to evaluate the impact of a teacher classroom management program on student academic performance. Results suggest the teacher classroom management training increased mean academic competence as well as the chance to obtain the maximum score on the academic competence scale. These effects would have been completely overlooked in a traditional evaluation of mean aggregates. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Configural Analysis in Component Space.

Unless very large samples are available, the number of variables and variable categories that can be simultaneously used in categorical data analysis is small when models are estimated. In this article, an approach is proposed that can help remedy this problem. Specifically, it is proposed to perform, in a first step, principal component analysis or factor analysis. These methods help reduce the dimensionality of the data space without loss of important information. In a second step, sectors are created in the component or factor space. These sectors can, in a third step, be subjected to Configural Frequency analysis (CFA). CFA identifies those sectors that contradict a priori-specified hypotheses. It is also proposed to take into account the ordinal nature of the sectors. In addition, distributional assumptions can be considered. This is illustrated in data examples. Possible extensions of the proposed approach are discussed.

Base Models for Configural Frequency Analysis - Data Generation Processes.

In Configural Frequency Analysis (CFA), model-data discrepancies are interpreted with reference to CFA base models. Thus far, CFA base models are defined as probability models that differ in the constraints they place on variable relations. In this article, it is proposed extending the scope of CFA base models. Specifically, it is proposed that the specification of base models is conducted with reference to data generation processes (DGPs). These processes result in uni- or multivariate distributions that reflect variable relations, probability distributions, or processes that result in change in series of observations. The new, DGP-based definition of CFA base models retains the concept of unique interpretability of CFA results, but it opens the doors to many more forms of base models than considered before. Four classes of base models are defined. Data examples illustrate various CFA base models.

Configural frequency trees.

Although variable-oriented analyses are dominant in developmental psychopathology, researchers have championed a person-oriented approach that focuses on the individual as a totality. This view has methodological implications and various person-oriented methods have been developed to test person-oriented hypotheses. Configural frequency analysis (CFA) has been identified as a prime method for a person-oriented analysis of categorical data. CFA searches for configurations in cross-classifications and asks whether the number of observed cases is larger (CFA type) or smaller (CFA antitype) than expected under a probability model. The present study introduces a combination of CFA and model-based recursive partitioning (MOB) to test for type/antitype heterogeneity in the population. MOB CFA is well suited to detect complex moderation processes and can distinguish between subpopulation and population types/antitypes. Model specifications are discussed for first-order CFA and prediction CFA. Results from two simulation studies suggest that MOB CFA is able to detect moderation processes with high accuracy. Two empirical examples are given from school mental health research for illustrative purposes. The first example evaluates heterogeneity in student behavior types/antitypes, the second example focuses on the effect of a teacher classroom management intervention on student behavior. An implementation of the approach is provided in R.

Configural Analysis of Oscillating Progression.

Oscillating series of scores can be approximated with locally optimized smoothing functions. In this article, we describe how such series can be approximated with locally estimated (loess) smoothing, and how Configural Frequency Analysis (CFA) can be used to evaluate and interpret results. Loess functions are often hard to describe because they cannot be represented by just one function that has interpretable parameters. In this article, we suggest that specification of the CFA base model be based on the width of the window that is used for local curve optimization, the weight given to data points in the neighborhood of the approximated one, and by the function that is used to locally approximate observed data. CFA types indicate that more cases were found than expected from the local optimization model. CFA antitypes indicate that fewer cases were found. In a real-world data example, the development of Covid-19 diagnoses in France is analyzed for the beginning period of the pandemic.

A Simple Configural Approach for Testing Person-Oriented Mediation Hypotheses.

Statistical methods to test hypotheses about direct and indirect effects from a person-oriented research perspective are scarce. For categorical variables, previously suggested approaches use configural frequency analysis (CFA) to detect extreme patterns (CFA Types/Antitypes) that are responsible for the observed direct and indirect effects. Existing methods rest on complex (log-linear) model comparison strategies and may perform poorly with respect to Type I error protection and statistical power. We, therefore, propose a simplified configural approach to answer the question "What carries a mediation process?" This simplified approach is based on two log-linear models that are needed to estimate (variable-oriented) direct and indirect effects. The first model identifies extreme patterns for the predictor-mediator path, the second model searches for extreme cells in the mediator-outcome path. Joint significance testing can be used to test the presence of mediation. Definitions of Mediation Types/Antitypes are given based on possible Type/Antitype patterns for the binary simple mediation model. In two Monte-Carlo simulation experiments, we evaluate the performance of the simplified approach in a homogenous population (i.e., where all individuals develop homogenously along a variable-oriented mediation mechanism) and a heterogenous population (i.e., where specific configurations, instead of a variable-oriented effect, drive the mediation process). Results suggest that the presented approach performs acceptably with respect to Type I error protection and statistical power. In general, larger sample sizes are preferable to reliably detect mediation-generating configurations. An empirical example is given for illustrative purposes and extensions and limitations of the proposed method are discussed.

Reciprocal relations in categorical variables.

The analysis of reciprocal relations in categorical variables poses methodological challenges. Effects that go in opposite causal directions must be integrated into the same model, and parameters must be interpretable. In this article, we propose taking an event-based perspective and present a new approach to the analysis of reciprocal relations in manifest categorical variables. Instead of asking questions about associations of categorical variables, the event-based perspective asks whether the occurrence of one event (the cause) leads to the occurrence of another event (the effect), and vice versa. Event-based reciprocal log-linear models are described. The presented approach enables one to estimate separate unidirectional causal effects in the same log-linear model. The Schuster transformation is applied to obtain interpretable parameter estimates when design matrices are nonorthogonal. A simulation study illustrates the viability and power of the proposed approach. Data examples illustrate the applicability of the proposed method, and that analysis of reciprocal relation hypotheses without Schuster transformation can lead to incorrect conclusions. Extensions of the proposed models are discussed. (PsycInfo Database Record (c) 2020 APA, all rights reserved).

Advances in Statistical Methods for Causal Inference in Prevention Science: Introduction to the Special Section.

The board of the Society for Prevention Research noted recently that extant methods for the analysis of causality mechanisms in prevention may still be too rudimentary for detailed and sophisticated analysis of causality hypotheses. This Special Section aims to fill some of the current voids, in particular in the domain of statistical methods of the analysis of causal inference. In the first article, Bray et al. propose a novel methodological approach in which they link propensity score techniques and Latent Class Analysis. In the second article, Kelcey et al. discuss power analysis tools for the study of causal mediation effects in cluster-randomized interventions. Wiedermann et al. present, in the third article, methods of Direction Dependence Analysis for the identification of confounders and for inference concerning the direction of causal effects in mediation models. A more general approach to the identification of causal structures in non-experimental data is presented by Shimizu in the fourth article. This approach is based on linear non-Gaussian acyclic models. Molenaar introduces vector-autoregressive methods for the optimal representation of Granger causality in time-dependent data. The Special Section concludes with a commentary by Musci and Stuart. In this commentary, the contributions of the articles in the Special Section are highlighted from the perspective of the experimental causal research tradition.

Testing the Causal Direction of Mediation Effects in Randomized Intervention Studies.

In a recent update of the standards for evidence in research on prevention interventions, the Society of Prevention Research emphasizes the importance of evaluating and testing the causal mechanism through which an intervention is expected to have an effect on an outcome. Mediation analysis is commonly applied to study such causal processes. However, these analytic tools are limited in their potential to fully understand the role of theorized mediators. For example, in a design where the treatment x is randomized and the mediator (m) and the outcome (y) are measured cross-sectionally, the causal direction of the hypothesized mediator-outcome relation is not uniquely identified. That is, both mediation models, x → m → y or x → y → m, may be plausible candidates to describe the underlying intervention theory. As a third explanation, unobserved confounders can still be responsible for the mediator-outcome association. The present study introduces principles of direction dependence which can be used to empirically evaluate these competing explanatory theories. We show that, under certain conditions, third higher moments of variables (i.e., skewness and co-skewness) can be used to uniquely identify the direction of a mediator-outcome relation. Significance procedures compatible with direction dependence are introduced and results of a simulation study are reported that demonstrate the performance of the tests. An empirical example is given for illustrative purposes and a software implementation of the proposed method is provided in SPSS.

A hybrid approach to regime shift detection.

In this article, we propose a method for the analysis of regime shifts in frequency data. This method identifies those points in the development of a process for which deviations are most extreme. Based on a statistical model, functions are estimated that describe the process. This description can represent either the entire series of scores or the series before and after a shift point. The shift point can be either given a priori or estimated from the data. The method is hybrid in that it first uses standard models for the estimation of parameters of the process that is examined and then, in a second step, elements of Configural Frequency Analysis. Uni- and multivariate versions of the method are proposed. In data examples, road traffic data from California and Germany are analyzed before and after particular shift points. Extensions of the proposed method are discussed.

Locating Event-Based Causal Effects: A Configural Perspective.

Statistical models for the analysis of hypotheses that are compatible with direction dependence were originally specified based on the linear model. In these models, relations among variables reflected directional or causal hypotheses. In a number of causal theories, however, effects are defined as resulting from causes that did versus did not occur. To accommodate this type of theory, the present article proposes analyzing directional or causal hypotheses at the level of configurations. Causes thus have the effect that, in a particular sector of the data space, the density of cases increases or decreases. With reference to log-linear models of direction dependence, this article specifies base models for the configural analysis of directional or causal hypotheses. In contrast to standard configural analysis, the models are applied in a confirmatory context. Specific direction dependence hypotheses are analyzed. In a simulation study, it is shown that the proposed methods have good power to identify the sectors in the data space in which density exceeds or falls below expectation. In a data example, it is shown that the evolutionary hypothesis that body size determines brain size is confirmed in particular for higher vertebrates.

Direction of dependence in measurement error models.

Methods to determine the direction of a regression line, that is, to determine the direction of dependence in reversible linear regression models (e.g., x→y vs. y→x), have experienced rapid development within the last decade. However, previous research largely rested on the assumption that the true predictor is measured without measurement error. The present paper extends the direction dependence principle to measurement error models. First, we discuss asymmetric representations of the reliability coefficient in terms of higher moments of variables and the attenuation of skewness and excess kurtosis due to measurement error. Second, we identify conditions where direction dependence decisions are biased due to measurement error and suggest method of moments (MOM) estimation as a remedy. Third, we address data situations in which the true outcome exhibits both regression and measurement error, and propose a sensitivity analysis approach to determining the robustness of direction dependence decisions against unreliably measured outcomes. Monte Carlo simulations were performed to assess the performance of MOM-based direction dependence measures and their robustness to violated measurement error assumptions (i.e., non-independence and non-normality). An empirical example from subjective well-being research is presented. The plausibility of model assumptions and links to modern causal inference methods for observational data are discussed.

Heteroscedasticity as a Basis of Direction Dependence in Reversible Linear Regression Models.

Heteroscedasticity is a well-known issue in linear regression modeling. When heteroscedasticity is observed, researchers are advised to remedy possible model misspecification of the explanatory part of the model (e.g., considering alternative functional forms and/or omitted variables). The present contribution discusses another source of heteroscedasticity in observational data: Directional model misspecifications in the case of nonnormal variables. Directional misspecification refers to situations where alternative models are equally likely to explain the data-generating process (e.g., x → y versus y → x). It is shown that the homoscedasticity assumption is likely to be violated in models that erroneously treat true nonnormal predictors as response variables. Recently, Direction Dependence Analysis (DDA) has been proposed as a framework to empirically evaluate the direction of effects in linear models. The present study links the phenomenon of heteroscedasticity with DDA and describes visual diagnostics and nine homoscedasticity tests that can be used to make decisions concerning the direction of effects in linear models. Results of a Monte Carlo simulation that demonstrate the adequacy of the approach are presented. An empirical example is provided, and applicability of the methodology in cases of violated assumptions is discussed.

Testing Event-Based Forms of Causality.

Three fundamental types of causal relations are those of necessity, sufficiency, and necessity and sufficiency. These types are defined in contexts of categorical variables or events. Using statement calculus or Boolean algebra, one can determine which patterns of events are in support of a particular form of causal relation. In this article, we approach the analysis of these forms of causality taking the perspective of the analyst of empirical data. It is proposed using Configural Frequency Analysis (CFA) to test hypotheses about type of causal relation. Models are proposed for two-variable and multi-variable cases. Two CFA approaches are proposed. In the first, individual patterns (configurations) are examined under the question whether they are in support of a particular type of causal relation. In the second, patterns that are in support are compared with corresponding patterns that are not in support. In an empirical example, hypotheses are tested on the prediction of sustainability of change in dietary fat intake habits.

Direction of effects in categorical variables: Looking inside the table.

In the variable-oriented domain, direction of dependence analysis of metric variables is defined in terms of changes that the independent (or causal) variable has on the univariate distribution of the dependent variable. In this article, we take a person-oriented perspective and extend this approach in two aspects, for categorical variables. First, instead of looking at univariate frequency distributions, direction dependence is defined in terms of special interactions. That is, direction dependence is defined as a process that can be detected "inside the table" instead of in its marginals. Second, the present approach takes an event-based perspective. That is, direction of effect is defined for individual categories of variables instead of the entire range of possible scores (or categories). Log-linear models are presented that allow researchers to test the corresponding hypotheses. Simulation studies illustrate characteristics and performance of these models. An empirical example investigates whether there is truth to the adage that money does not buy happiness. Extensions and limitations are discussed.