Axel Mayer’s research while affiliated with Bielefeld University and other places

In psychology, researchers have to choice between different kinds of effect measures. For example, when evaluation whether a new treatment works or not, the effectiveness might be expressed as a difference between the treatment and control group (e.g., four points less in a test) or as a ratio (e.g., twice as many points in a test). It is unclear, however, how ratio-based effect measures might be interpreted from a causal perspective. It has often been shown that ratio-based effect measures are not easy to identify in randomized experiments, a phenomenon called collapsibility. In addition, different ratio-based effect measures (e.g., simple ratio and odds ratio) might yield very different implications on the effectiveness of a treatment. While causality theories do in principle allow for ratio-based effect measures, the literature lacks a comprehensive definition and examination of ratio-based effect measures. In this article, we show how both simple ratios and odds ratios can be defined based on the stochastic theory of causal effects. Then, we examine if and how expectations (i.e., true means) of these effect measures can be identified under four causality conditions. Finally, we discuss an alternative computation of ratio-based effect measures as ratios of causally unbiased expectations instead of expectations of individual ratios, which is identifiable under all causality conditions and consistent with difference-based effect measures.

In psychology and the social sciences, researchers often model count outcome variables accounting for latent predictors and their interactions. Even though neglecting measurement error in such count regression models (e.g., Poisson or negative binomial regression) can have unfavorable consequences like attenuation bias, such analyses are often carried out in the generalized linear model (GLM) framework using fallible covariates such as sum scores. An alternative is count regression models based on structural equation modeling, which allow to specify latent covariates and thereby account for measurement error. However, the issue of how and when to include interactions between latent covariates or between latent and manifest covariates is rarely discussed for count regression models. In this paper, we present a latent variable count regression model (LV-CRM) allowing for latent covariates as well as interactions among both latent and manifest covariates. We conducted three simulation studies, investigating the estimation accuracy of the LV-CRM and comparing it to GLM-based count regression models. Interestingly, we found that even in scenarios with high reliabilities, the regression coefficients from a GLM-based model can be severely biased. In contrast, even for moderate sample sizes, the LV-CRM provided virtually unbiased regression coefficients. Additionally, statistical inferences yielded mixed results for the GLM-based models (i.e., low coverage rates, but acceptable empirical detection rates), but were generally acceptable using the LV-CRM. We provide an applied example from clinical psychology illustrating how the LV-CRM framework can be used to model count regressions with latent interactions.

Zusammenfassung: Vorgestellt wird die bisher erste Skala zur Erfassung subjektiver Überzeugungen bzgl. der (Un–)‌Veränderbarkeit der individuellen Fähigkeiten in Statistik. Das entwickelte Instrument besteht aus neun vierstufigen Likert-Items; vier Items repräsentieren eine statische, fünf eine flexible Fähigkeitsüberzeugung. Zur Prüfung der faktoriellen Struktur und der psychometrischen Güte werden Fragebogendaten von Studierenden aus einer Explorations- und einer Validierungsstichprobe ( N 1 = 150, N 2 = 749) herangezogen. Zur Bestimmung der faktoriellen Struktur werden fünf Messmodelle an beiden Datensätzen getestet: Bifaktor-(S-1)-Modelle sowie zweifaktorielle Modelle mit und ohne korrelierte Residuen. Die Ergebnisse sprechen für eine zweidimensionale Struktur der Skala. Für Gesamt- und Subskalen ergaben sich sehr zufriedenstellende interne Konsistenzen. Die divergente Validität der Skala konnte für beide Faktoren bestätigt werden. Die Bestätigung der konvergenten Validität bleibt zunächst auf den Faktor für die statische Überzeugung beschränkt. Neben der ausführlichen Diskussion der Befunde werden abschließend auch Empfehlungen zur Anwendung und weiteren Validierung der Skala formuliert.

When evaluating the effect of psychological treatments on a dichotomous outcome variable in a randomized controlled trial (RCT), covariate adjustment using logistic regression models is often applied. In the presence of covariates, average marginal effects (AMEs) are often preferred over odds ratios, as AMEs yield a clearer substantive and causal interpretation. However, standard error computation of AMEs neglects sampling‐based uncertainty (i.e., covariate values are assumed to be fixed over repeated sampling), which leads to underestimation of AME standard errors in other generalized linear models (e.g., Poisson regression). In this paper, we present and compare approaches allowing for stochastic (i.e., randomly sampled) covariates in models for binary outcomes. In a simulation study, we investigated the quality of the AME and stochastic‐covariate approaches focusing on statistical inference in finite samples. Our results indicate that the fixed‐covariate approach provides reliable results only if there is no heterogeneity in interindividual treatment effects (i.e., presence of treatment–covariate interactions), while the stochastic‐covariate approaches are preferable in all other simulated conditions. We provide an illustrative example from clinical psychology investigating the effect of a cognitive bias modification training on post‐traumatic stress disorder while accounting for patients' anxiety using an RCT.

Latent repeated measures ANOVA (L-RM-ANOVA) has recently been proposed as an alternative to traditional repeated measures ANOVA. L-RM-ANOVA builds upon structural equation modeling and enables researchers to investigate interindividual differences in main/interaction effects, examine custom contrasts, incorporate a measurement model, and account for missing data. However, L-RM-ANOVA uses maximum likelihood and thus cannot incorporate prior information and can have poor statistical properties in small samples. We show how L-RM-ANOVA can be used with Bayesian estimation to resolve the aforementioned issues. We demonstrate how to place informative priors on model parameters that constitute main and interaction effects. We further show how to place weakly informative priors on standardized parameters which can be used when no prior information is available. We conclude that Bayesian estimation can lower Type 1 error and bias, and increase power and efficiency when priors are chosen adequately. We demonstrate the approach using a real empirical example and guide the readers through specification of the model. We argue that ANOVA tables and incomplete descriptive statistics are not sufficient information to specify informative priors, and we identify which parameter estimates should be reported in future research; thereby promoting cumulative research.

In non-linear regression models, the effect of a treatment or intervention is often expressed as a ratio (e.g., risk ratio, odds ratio). There is discussion about when ratio-based effect measures can be interpreted in a causal way. For example, it is well-known that ratio-based effect measures suffer from non-collapsibility, that is, the average over individual ratio effects is not equivalent to the ratio of group means in a randomized experiment. Even more, different ratio-based effect measures (e.g., simple ratio, odds ratio) can point into different directions regarding the effectiveness of the treatment making it difficult to decide which one is the causal effect of interest. While causality theories do in principle allow for ratio-based effect measures, the literature lacks a comprehensive derivation and definition of ratio-based effect measures and their possible identification from a causal perspective (including, but not restricted to randomized experiments). In this paper, we show how both simple ratios and odds ratios can be defined based on the stochastic theory of causal effects. Then, we examine if and how expectations of these effect measures can be identified under four causality conditions. Especially, we will show that ratio-based effect measures are collapsible under certain conditions. Finally, we discuss an alternative computation of ratio-based effect measures as ratios of causally unbiased expectations instead of expectations of individual ratios, which is identifiable under all causality conditions and consistent with difference-based effect measures.

Purpose Many models of language comprehension assume that listeners predict the continuation of an incoming linguistic stimulus immediately after its onset, based on only partial linguistic and contextual information. Their related developmental models try to determine which cues (e.g., semantic or morphosyntactic) trigger such prediction, and to which extent, during different periods of language acquisition. One morphosyntactic cue utilized predictively in many languages, inter alia German, is grammatical gender. However, studies of the developmental trajectories of the acquisition of predictive gender processing in German remain a few. Method This study attempts to shed light on such processing strategies used in noun phrase decoding among children acquiring German as their first language by examining their eye movements during a language–picture matching task (N = 78, 5–10 years old). Its aim was to confirm whether the eye movements indicated the presence of age-specific differences in the processing of a gender cue, provided either in isolation or in combination with a semantic cue. Results The results revealed that German children made use of predictive gender processing strategies from the age of 5 years onward; however, the pace of online gender processing, as well as confidence in the predicted continuation, increased up to the age of 10 years. Conclusion Predictive processing of gender cues plays a role in German language comprehension even in children younger than 8 years.

This article demonstrates how to perform univariate repeated measures ANOVA (U-RM-ANOVA) as a special case of structural equation models (SEMs). In the literature, sphericity is usually defined in terms of variances of pairwise differences of within-subject conditions. This article illustrates the original definition by Huynh and Feldt (1970) in terms of (co)variances of contrasts using SEM and demonstrates how to impose, test, and relax sphericity, and how to test main/interaction effects with and without the assumption of sphericity in SEM. We perform two simulation studies. The first study compares Mauchly’s sphericity test with an SEM based test and shows that the two approaches have a very similar Type 1 error and power. The second study compares U-RM-ANOVA with SEM for different degrees of departure from sphericity and shows that U-RM-ANOVA and SEM have similar statistical properties in terms of Type 1 error, power, as well as similar bias and efficiency of effect size estimates of main and interaction effects. We furthermore show how to implement sphericity in latent variable models and provide software to perform the proposed tests and analyses.

In psychology and the social sciences, it is often of interest how complex structural relations among variables are moderated by profiles or combinations of persons’ attributes. Some state-of-the-art methods, such as latent class analysis, are well-suited for this purpose. However, they can lead to methodological problems (e.g., convergence issues) or interpretative difficulties (e.g., due to nondistinctive profiles). For these cases, two other approaches combining structural equation modeling with machine learning have been proposed, namely structural equation model (SEM) trees and SubgroupSEM. These approaches allow for exploration of how parameters of a SEM differ depending on combinations of a person's attributes. This can be useful for generating hypotheses for future research. In this paper, we provide an empirical illustration of SubgroupSEM using an example from research on the development of commitment in interdisciplinary study programs in German higher education and identify combinations of vocational interests related to exceptional development.

Structural equation modeling is one of the most popular statistical frameworks in the social and behavioral sciences. Often, detection of groups with distinct sets of parameters in structural equation models (SEM) are of key importance for applied researchers, for example, when investigating differential item functioning for a mental ability test or examining children with exceptional educational trajectories. In the present article, we present a new approach combining subgroup discovery—a well-established toolkit of supervised learning algorithms and techniques from the field of computer science—with structural equation models termed SubgroupSEM. We provide an overview and comparison of three approaches to modeling and detecting heterogeneous groups in structural equation models, namely, finite mixture models, SEM trees, and SubgroupSEM. We provide a step-by-step guide to applying subgroup discovery techniques for structural equation models, followed by a detailed and illustrated presentation of pruning strategies and four subgroup discovery algorithms. Finally, the SubgroupSEM approach will be illustrated on two real data examples, examining measurement invariance of a mental ability test and investigating interesting subgroups for the mediated relationship between predictors of educational outcomes and the trajectories of math competencies in 5th grade children. The illustrative examples are accompanied by examples of the R package subgroupsem, which is a viable implementation of our approach for applied researchers.