Bayesian Analysis of Multi-Factorial Experimental Designs Using SEM.

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.

On the Relationship between ANOVA Main Effects and Average Treatment Effects.

We adopt a causal inference perspective to shed light into which ANOVA type of sums of squares (SS) should be used for testing main effects and whether main effects should be considered at all in the presence of interactions. We consider balanced, proportional and nonorthogonal designs, and models with and without interactions. When the design is balanced, we show that the average treatment effect is estimated by the main effects obtained by type I, II, and III sums of squares. In proportional designs, we show that the average treatment effect is estimated by the the type I and type II main effects, whereas type III SS yield biased estimates of the average treatment effect if there are interactions. When the design is nonorthogonal, ANOVA type I is always highly biased and ANOVA type II and III main effects are biased if there are interactions. We include a simulation study to illustrate the magnitude of the bias in estimating the average treatment effect across a variety of conditions, and provide recommendations for applied researchers.

A tutorial on using the paired t test for power calculations in repeated measures ANOVA with interactions.

The a priori calculation of statistical power has become common practice in behavioral and social sciences to calculate the necessary sample size for detecting an expected effect size with a certain probability (i.e., power). In multi-factorial repeated measures ANOVA, these calculations can sometimes be cumbersome, especially for higher-order interactions. For designs that only involve factors with two levels each, the paired t test can be used for power calculations, but some pitfalls need to be avoided. In this tutorial, we provide practical advice on how to express main and interaction effects in repeated measures ANOVA as single difference variables. In particular, we demonstrate how to calculate the effect size Cohen's d of this difference variable either based on means, variances, and covariances of conditions or by transforming [Formula: see text] or [Formula: see text] from the ANOVA framework into d. With the effect size correctly specified, we then show how to use the t test for sample size considerations by means of an empirical example. The relevant R code is provided in an online repository for all example calculations covered in this article.

The Jena Voice Learning and Memory Test (JVLMT): A standardized tool for assessing the ability to learn and recognize voices.

The ability to recognize someone's voice spans a broad spectrum with phonagnosia on the low end and super-recognition at the high end. Yet there is no standardized test to measure an individual's ability of learning and recognizing newly learned voices with samples of speech-like phonetic variability. We have developed the Jena Voice Learning and Memory Test (JVLMT), a 22-min test based on item response theory and applicable across languages. The JVLMT consists of three phases in which participants (1) become familiarized with eight speakers, (2) revise the learned voices, and (3) perform a 3AFC recognition task, using pseudo-sentences devoid of semantic content. Acoustic (dis)similarity analyses were used to create items with various levels of difficulty. Test scores are based on 22 items which had been selected and validated based on two online studies with 232 and 454 participants, respectively. Mean accuracy in the JVLMT is 0.51 (SD = .18) with an empirical (marginal) reliability of 0.66. Correlational analyses showed high and moderate convergent validity with the Bangor Voice Matching Test (BVMT) and Glasgow Voice Memory Test (GVMT), respectively, and high discriminant validity with a digit span test. Four participants with potential super recognition abilities and seven participants with potential phonagnosia were identified who performed at least 2 SDs above or below the mean, respectively. The JVLMT is a promising research and diagnostic screening tool to detect both impairments in voice recognition and super-recognition abilities.

Repeated Measures ANOVA with Latent Variables to Analyze Interindividual Differences in Contrasts.

Repeated measures analysis of variance (RM-ANOVA) is a broadly used statistical method to analyze data from experimental designs. RM-ANOVA aims at investigating effects of experimental conditions (i.e., factors) and predictors that affect the outcome of interest. It mainly considers contrasts that test standard main and interaction effects, even though more complex contrasts can in principle be used. Analyses, however, only focus on drawing conclusions about average effects and do not take into consideration interindividual differences in these effects. We propose an alternative approach to RM-ANOVA for analyzing repeated measures data, termed latent repeated measures analysis of variance (L-RM-ANOVA). The new approach is based on structural equation modeling and extends the latent growth components approach. L-RM-ANOVA enables the researcher to not only consider mean differences between different experimental conditions (i.e., average effects), but also to investigate interindividual differences in effects. Such interindividual differences are considered with regard to standard main and interactions effects and also with regard to customized contrasts that allow for testing specific hypotheses of interest. Furthermore, L-RM-ANOVA can include a measurement model for latent variables and can be used for the analysis of complex multi-factorial repeated measures designs. We conclude the presentation by demonstrating L-RM-ANOVA using a minimal repeated measures example.

Accounting for Latent Covariates in Average Effects from Count Regressions.

The effectiveness of a treatment on a count outcome can be assessed using a negative binomial regression, where treatment effects are defined as the difference between the expected outcome under treatment and under control. These treatment effects can to date only be estimated if all covariates are manifest (observed) variables. However, some covariates are latent variables that are measured by multiple fallible indicators. In such cases, it is important to control for measurement error of covariates in order to avoid attenuation bias and to get unbiased treatment effect estimates. In this paper, we propose a new approach to compute average and conditional treatment effects in regression models with a logarithmic link function involving multiple latent and manifest covariates. We extend the previously presented moment-based approach in several aspects: Building on a multigroup SEM framework for count variables instead of the generalized linear model, we allow for latent covariates and multiple covariates. We provide an illustrative example to explain the application and estimation in structural equation modeling software.

Analysis of Variance Models with Stochastic Group Weights.

The analysis of variance (ANOVA) is still one of the most widely used statistical methods in the social sciences. This article is about stochastic group weights in ANOVA models - a neglected aspect in the literature. Stochastic group weights are present whenever the experimenter does not determine the exact group sizes before conducting the experiment. We show that classic ANOVA tests based on estimated marginal means can have an inflated type I error rate when stochastic group weights are not taken into account, even in randomized experiments. We propose two new ways to incorporate stochastic group weights in the tests of average effects - one based on the general linear model and one based on multigroup structural equation models (SEMs). We show in simulation studies that our methods have nominal type I error rates in experiments with stochastic group weights while classic approaches show an inflated type I error rate. The SEM approach can additionally deal with heteroscedastic residual variances and latent variables. An easy-to-use software package with graphical user interface is provided.

Exploring the Link Between Daily Relationship Quality, Sexual Desire, and Sexual Activity in Couples.

Current models of sexual responding emphasize the role of contextual and relational factors in shaping sexual behavior. The present study used a prospective diary design to examine the temporal sequence and variability of the link between sexual and relationship variables in a sample of couples. Studying sexual responding in the everyday context of the relationship is necessary to get research more aligned with the complex reality of having sex in a relationship, thereby increasing ecological validity and taking into account the dyadic interplay between partners. Over the course of 21 days, 66 couples reported every day on their sexual desire, sexual activity (every morning), and relationship quality (every evening). In addition, we examined whether the link between these daily variables was moderated by relationship duration, having children, general relationship satisfaction, and sexual functioning. Results showed that the sexual responses of women depended on the relationship context, mainly when having children and being in a longer relationship. Male sexual responding depended less on contextual factors but did vary by level of sexual functioning. Several cross-partner effects were found as well. These results verify that relational and sexual variables feed forward into each other, indicating the need to incorporate interpersonal dynamics into current models of sexual responding and to take into account variability and dyadic influences between partners.

Cancer-related fatigue in patients with and survivors of Hodgkin's lymphoma: a longitudinal study of the German Hodgkin Study Group.

BACKGROUND: Patients with Hodgkin's lymphoma might have persistent fatigue even years after treatment. However, knowledge of the development of fatigue persisting long after completion of treatment is limited. Therefore, we did a detailed analysis of fatigue in our first-line clinical trials for early-stage favourable (HD13 trial), early-stage unfavourable (HD14 trial), and advanced-stage (HD15 trial) Hodgkin's lymphoma. Beyond the description of fatigue from diagnosis up to 5 years after treatment, we aimed to assess any effect of patient characteristics, disease characteristics, or treatment characteristics on persistent fatigue. METHODS: In this longitudinal study, we included patients with early-stage favourable, early-stage unfavourable, and advanced-stage Hodgkin's lymphoma from the HD13, HD14, and HD15 trials, respectively, aged between 18 and 60 years. Eligible patients for these trials had newly diagnosed, histologically proven Hodgkin's lymphoma, an Eastern Cooperative Oncology Group performance status of 2 or lower, HIV negativity, and absence of comorbidity disallowing protocol treatment. We used the fatigue scale of the European Organisation for Research and Treatment of Cancer (EORTC) QLQ-C30 questionnaire to assess fatigue from diagnosis up to 5 years after the end of treatment. The primary outcomes of interest in this study were fatigue scores in the second and fifth year after end of treatment. We estimated the effect of different disease, patient, and treatment characteristics on fatigue with multiple regression analyses and identified fatigue trajectories with growth mixture models. The regression analyses and growth mixture models used robust and full information maximum likelihood estimates to account for missing data. The HD13, HD14, and HD15 trials are registered as international standard randomised controlled trials, ISRCTN63474366, ISRCTN04761296, and ISRCTN32443041, respectively. FINDINGS: The HD13 trial enrolled patients with early-stage favourable disease from Jan 28, 2003, to Sept 30, 2009; the HD14 trial enrolled patients with early-stage unfavourable disease from Jan 28, 2003, to Dec 23, 2009; and the HD15 trial enrolled patients with advanced-stage disease from Jan 28, 2003, to April 18, 2008. 5306 patients were enrolled in these trials. We analysed 4215 patients with any valid fatigue assessment up to 5 years after the end of treatment. Patients with higher tumour burden at diagnosis had more fatigue at baseline (mean fatigue score in HD13: 30·8 [SD 28·0]; in HD14: 39·8 [29·4], and in HD15: 49·0 [30·2]). Fatigue scores (FA) in the second year after the end of treatment were 28·5 (24·7) in HD13, 28·8 (24·4) in HD14, and 30·7 (24·4) in HD15; in the fifth year after the end of treatment FA was 30·8 (26·0) in HD13, 27·1 (24·8) in HD14, and 28·2 (24·9) in HD15. Predictors of fatigue in the second and fifth year after end of treatment were baseline fatigue (p<0·0001) and age as a continuous variable (p<0·0001). In addition to preceding fatigue and age, patient sex and Hodgkin's lymphoma specific risk factors at baseline did not consistently and significantly improve the prognosis of fatigue in the first, second, and fifth year after end of treatment. There was no significant effect of treatment on fatigue scores in the second and fifth year after treatment. INTERPRETATION: Our findings show a high incidence of severe acute and persistent fatigue in Hodgkin's lymphoma survivors, which is largely independent of tumour stage and treatment. Our results contribute to a better understanding of fatigue in patients with Hodgkin's lymphoma and Hodgkin's lymphoma survivors and could inform development of urgently needed intervention strategies. FUNDING: Deutsche Krebshilfe.

The EffectLiteR Approach for Analyzing Average and Conditional Effects.

We present a framework for estimating average and conditional effects of a discrete treatment variable on a continuous outcome variable, conditioning on categorical and continuous covariates. Using the new approach, termed the EffectLiteR approach, researchers can consider conditional treatment effects given values of all covariates in the analysis and various aggregates of these conditional treatment effects such as average effects, effects on the treated, or aggregated conditional effects given values of a subset of covariates. Building on structural equation modeling, key advantages of the new approach are (1) It allows for latent covariates and outcome variables; (2) it permits (higher order) interactions between the treatment variable and categorical and (latent) continuous covariates; and (3) covariates can be treated as stochastic or fixed. The approach is illustrated by an example, and open source software EffectLiteR is provided, which makes a detailed analysis of effects conveniently accessible for applied researchers.

A theory of states and traits--revised.

We present a revision of latent state-trait (LST-R) theory with new definitions of states and traits. This theory applies whenever we study the consistency of behavior, its variability, and its change over time. States and traits are defined in terms of probability theory. This allows for a seamless transition from theory to statistical modeling of empirical data. LST-R theory not only gives insights into the nature of latent variables but it also takes into account four fundamental facts: Observations are fallible, they never happen in a situational vacuum, they are always made using a specific method of observations, and there is no person without a past. Although the first fact necessitates considering measurement error, the second fact requires allowances for situational fluctuations. The third fact implies that, in the first place, states and traits are method specific. Furthermore, compared to the previous version of LST theory (see, e.g., Steyer et al. 1992 , 1999 ), our revision is based on the notion of a person-at-time-t. The new definitions in LST-R theory have far-reaching implications that not only concern the properties of states, traits, and the associated concepts of measurement errors and state residuals, but also are related to the analysis of states and traits in longitudinal observational and intervention studies.

Theory and Analysis of Total, Direct, and Indirect Causal Effects.

Mediation analysis, or more generally models with direct and indirect effects, are commonly used in the behavioral sciences. As we show in our illustrative example, traditional methods of mediation analysis that omit confounding variables can lead to systematically biased direct and indirect effects, even in the context of a randomized experiment. Therefore, several definitions of causal effects in mediation models have been presented in the literature (Baron & Kenny, 1986 ; Imai, Keele, & Tingley, 2010 ; Pearl, 2012 ). We illustrate the stochastic theory of causal effects as an alternative foundation of causal mediation analysis based on probability theory. In this theory we define total, direct, and indirect effects and show how they can be identified in the context of our illustrative example. A particular strength of the stochastic theory of causal effects are the causality conditions that imply causal unbiasedness of effect estimates. The causality conditions have empirically testable implications and can be used for covariate selection. In the discussion, we highlight some similarities and differences of the stochastic theory of causal effects with other theories of causal effects.

Teaching happiness to students - implementation and evaluation of a program aiming at promoting wellbeing in elementary schools.

Since the beginning of the COVID-19 pandemic, the prevalence of mental disorders in children and adolescents has increased significantly. Evidence shows that childhood mental disorders can have serious consequences on psychosocial, cognitive, and physical development. Approaches from Positive Education go further than the urgently needed prevention of mental disorders by aiming directly at promoting subjective, psychological, and social wellbeing. The present study describes the implementation of a brief program to promote wellbeing in 15 elementary schools. For this purpose, in a regular university seminar, students of teaching and educational science were instructed to give 11 "happiness lessons" for fourth graders in a team of two and in the presence of the class teacher over the course of 3 months. Quantitative data were collected from children and parents in the treatment group classes and in the parallel classes serving as the waiting control group at four measurement points (pre, post, 1- and 2-month follow-up). We assessed psychological wellbeing, negative emotions and moods, parent support and home life, perception of the school environment, and self-esteem of the children with established instruments with versions for children and their parents and the frequency of positive and negative emotions of the children in self-report only. Additionally, we applied ad hoc items on subjective perception of the project and open questions in the treatment group. Data were analyzed with EffectLiteR using multigroup structural equation models. Results showed a small significant effect for negative emotions with the children's data and a medium effect for psychological wellbeing in the perception of the parents at the 1-month follow-up. Interaction effects suggest that lower baseline levels in parent support and home life and self-esteem would increase the treatment effect for these constructs. The need for more grounded framework in positive education and the inclusion of more qualitative methods as well as suggestions to improve the program in the sense of a whole school approach are discussed.

Average treatment effects on binary outcomes with stochastic covariates.

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.

Evaluation of frequentist test statistics using constrained statistical inference in the context of the generalized linear model.

When faced with a binary or count outcome, informative hypotheses can be tested in the generalized linear model using the distance statistic as well as modified versions of the Wald, the Score and the likelihood-ratio test (LRT). In contrast to classical null hypothesis testing, informative hypotheses allow to directly examine the direction or the order of the regression coefficients. Since knowledge about the practical performance of informative test statistics is missing in the theoretically oriented literature, we aim at closing this gap using simulation studies in the context of logistic and Poisson regression. We examine the effect of the number of constraints as well as the sample size on type I error rates when the hypothesis of interest can be expressed as a linear function of the regression parameters. The LRT shows the best performance in general, followed by the Score test. Furthermore, both the sample size and especially the number of constraints impact the type I error rates considerably more in logistic compared to Poisson regression. We provide an empirical data example together with R code that can be easily adapted by applied researchers. Moreover, we discuss informative hypothesis testing about effects of interest, which are a non-linear function of the regression parameters. We demonstrate this by means of a second empirical data example.

The Development of Predictive Gender Processing Strategies During Noun Phrase Decoding: An Eye-Tracking Study With German 5- to 10-Year-Old Children.

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.

Effects of adult inpatient group psychotherapy on attachment characteristics: an observational study comparing routine care to an untreated comparison group.

This study investigated the changes in attachment characteristics of patients undergoing inpatient group psychotherapy in routine care. We collected data from 265 consecutively recruited patients and 260 non-clinical control persons using self-report measures of attachment, depression, and socio-demographic characteristics. The effects of treatment on patients were analyzed using propensity score techniques (propensity strata and logit-transformed propensity scores) in combination with a generalized analysis of covariance. A moderate increase of attachment security was found which could be attributed to a decrease both in attachment anxiety and avoidance. Pre-post improvements in attachment with regard to romantic partnerships were stable after a 1-year follow-up. Furthermore, we found significant treatment-covariate interactions indicating that subjects with particularly high treatment propensities (propensities were highly correlated with depression and attachment anxiety) improved the most in terms of attachment security. Our results are encouraging for psychotherapeutic practice in that they provide evidence that long-term attachment improvements can be reached via psychotherapy. Our results will also provide a sound basis for future studies in the field of clinical attachment research, e.g., studies examining whether improved attachment security is correlated to symptom improvements in different psychological disorders.

Causal effect analysis in nonrandomized data with latent variables and categorical indicators: The implementation and benefits of EffectLiteR.

Instead of using manifest proxies for a latent outcome or latent covariates in a causal effect analysis, the R package EffectLiteR facilitates a direct integration of latent variables based on structural equation models (SEM). The corresponding framework considers latent interactions and provides various effect estimates for evaluating the differential effectiveness of treatments. In addition, a user-friendly graphical interface customizes the implementation of the complex models. We aim to enable applications of EffectLiteR in more contexts, and therefore generalize the framework for incorporating latent variables measured with categorical indicators. This refers, for instance, to achievement tests in educational large-scale assessments (LSAs), which are typically constructed in the tradition of item response theory (IRT). We review different modeling strategies for incorporating latent variables from IRT models in an effect analysis (i.e., individual score estimates, plausible values, SEM for categorical indicators). The strategies differ in the handling of measurement error and, thus, have different implications for the accuracy and efficiency of causal effect estimates. We describe our extensions of EffectLiteR based on SEM for categorical indicators and illustrate the model specification step-by-step. In addition, we present a hands-on example, where we apply EffectLiteR in LSA data. The practical benefit of using latent variables in comparison to proficiency scores is of special interest in the application and discussion. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Causal Mediation Analysis in Single Case Experimental Designs: Introduction to the Special Issue.

This special issue of Evaluation and the Health Professions is dedicated to methods for causal mediation analysis in Single Case Experimental Designs (SCEDs). Mediation analysis is used to identify intermediate variables that transmit the effect of the independent variable on the outcome. Until recently, mediation analysis was mostly confined to between-subjects designs and panel studies with few exceptions. Consequently, most of the developments in causal mediation analysis have also been restricted to such designs. In applied health research, SCEDs have been used to evaluate total effects of treatments on outcomes of interest. Providing researchers with the methods for evaluating causal indirect effects for individual participants can lead to important improvements in diagnosis, treatment, and prevention. This special issue includes articles that describe advanced quantitative methods for testing mediators in SCEDs, propose and test approaches that allow for relaxing statistical assumptions that may not hold in real data, and illustrate mediation analysis for a single participant in real and simulated SCEDs data.

Subgroup discovery in structural equation models.

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. (PsycInfo Database Record (c) 2022 APA, all rights reserved).