Joris Mulder

Joris Mulder
Tilburg University | UVT · Department of Methodology and Statistics

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93
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Publications

Publications (93)
Preprint
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The effects of a treatment may differ between patients with different characteristics. Addressing such treatment heterogeneity is crucial to identify which patients benefit from a treatment, but can be complex in the context of multiple correlated binary outcomes. The current paper presents a novel Bayesian method for estimation and inference for h...
Article
Real-life social interactions occur in continuous time and are driven by complex mechanisms. Each interaction is not only affected by the characteristics of individuals or the environmental context but also by the history of interactions. The relational event framework provides a flexible approach to studying the mechanisms that drive how a sequenc...
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Relational event or time-stamped social network data have become increasingly available over the years. Accordingly, statistical methods for such data have also surfaced. These techniques are based on log-linear models of the rates of interactions in a social network via actor covariates and network statistics. Particularly, the use of survival ana...
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In recent years there has been an increasing interest in the use of relational event models for dynamic social network analysis. The basis of these models is the concept of an "event", defined as a triplet of time, sender, and receiver of some social interaction. The key question that relational event models aim to answer is what drives social inte...
Article
The last 25 years have shown a steady increase in attention for the Bayes factor as a tool for hypothesis evaluation and model selection. The present review highlights the potential of the Bayes factor in psychological research. We discuss six types of applications: Bayesian evaluation of point null, interval, and informative hypotheses, Bayesian e...
Preprint
The Bayes factor is increasingly used for the evaluation of hypotheses. These may betraditional hypotheses specified using equality constraints among the parameters of thestatistical model of interest or informative hypotheses specified using equality andinequality constraints. So far no attention has been given to the computation of Bayesfactors f...
Article
Full-text available
Measures of association play a central role in the social sciences to quantify the strength of a linear relationship between the variables of interest. In many applications researchers can translate scientific expectations to hypotheses with equality and/or order constraints on these measures of association. In this paper a Bayes factor test is pro...
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A Bayes factor is proposed for testing whether the effect of a key predictor variable on the dependent variable is linear or nonlinear, possibly while controlling for certain covariates. The test can be used (i) when one is interested in quantifying the relative evidence in the data of a linear versus a nonlinear relationship and (ii) to quantify t...
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In relational event networks, the tendency for actors to interact with each other depends greatly on the past interactions between the actors in a social network. Both the quantity of past interactions and the time that elapsed since the past interactions occurred affect the actors' decision-making to interact with other actors in the network. Rece...
Article
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Meta-analysis methods are used to synthesize results of multiple studies on the same topic. The most frequently used statistical model in meta-analysis is the random-effects model containing parameters for the overall effect, between-study variance in primary study’s true effect size, and random effects for the study-specific effects. We propose Ba...
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Partial correlation networks have emerged as an increasingly popular model for studyingmental disorders. Although conditional independence is a fundamental concept in networkanalysis, which corresponds to the null hypothesis, the focus is typically to detect and thenvisualize non-zero partial correlations (i.e., the “edges” connecting nodes) in a g...
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The multivariate normal linear model is one of the most widely employed models for statistical inference in applied research. Special cases include (multivariate) t testing, (M)AN(C)OVA, (multivariate) multiple regression, and repeated measures analysis. Statistical criteria for a model selection problem where models may have equality as well as or...
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Directional relational event data, such as email data, often include multiple receivers for each event. Statistical methods for adequately modeling such data are limited however. In this article, a multiplicative latent factor model is proposed for relational event data with multiple receivers. For a given event (or message) all potential receiver...
Article
There have been considerable methodological developments of Bayes factors for hypothesis testing in the social and behavioral sciences, and related fields. This development is due to the flexibility of the Bayes factor for testing multiple hypotheses simultaneously, the ability to test complex hypotheses involving equality as well as order constrai...
Preprint
Meta-analysis methods are used to synthesize results of multiple studies on the same topic. The most frequently used statistical model in meta-analysis is the random-effects model containing parameters for the average effect, between-study variance in primary study's true effect size, and random effects for the study specific effects. We propose Ba...
Article
The aim of this work is to explore the construct of autistic traits through the lens of network analysis with recently introduced Bayesian methods. A conditional dependence network structure was estimated from a data set composed of 649 university students that completed an autistic traits questionnaire. The connectedness of the network is also exp...
Article
Gaussian graphical models (GGM; partial correlation networks) have become increasingly popular in the social and behavioral sciences for studying conditional (in)dependencies between variables. In this work, we introduce exploratory and confirmatory Bayesian tests for partial correlations. For the former, we first extend the customary GGM formulati...
Preprint
Full-text available
The aim of this work is to explore the construct of autistic traits through the lens of network analysis with recently introduced Bayesian methods. A conditional dependence network structure was estimated from a data set composed of 649 university students that completed an autistic traits questionnaire. The connectedness of the network is also exp...
Preprint
Full-text available
The last 25 years have shown a steady increase in attention for the Bayes factor as a tool for hypothesis evaluation and model selection. The present review highlights the potential of the Bayes factor in psychological research. We discuss six types of applications: Bayesian evaluation of point null, interval, and informative hypotheses, Bayesian e...
Article
Full-text available
This paper presents a novel Bayesian variable selection approach that accounts for the sign of the regression coefficients based on multivariate one-sided tests. We propose a truncated g prior to specify a prior distribution of coefficients with anticipated signs in a given model. Informative priors for the direction of the effects can be incorpora...
Article
Full-text available
The Savage-Dickey density ratio is a specific expression of the Bayes factor when testing a precise (equality constrained) hypothesis against an unrestricted alternative. The expression greatly simplifies the computation of the Bayes factor at the cost of assuming a specific form of the prior under the precise hypothesis as a function of the unrest...
Article
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Clinical trials often evaluate multiple outcome variables to form a comprehensive picture of the effects of a new treatment. The resulting multidimensional insight contributes to clinically relevant and efficient decision-making about treatment superiority. Common statistical procedures to make these superiority decisions with multiple outcomes hav...
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The network autocorrelation model has been the workhorse for estimating and testing the strength of theories of social influence in a network. In many network studies, different types of social influence are present simultaneously and can be modeled using various connectivity matrices. Often, researchers have expectations about the order of strengt...
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This Teacher’s Corner paper introduces Bayesian evaluation of informative hypotheses for structural equation models, using the free open-source R packages bain, for Bayesian informative hypothesis testing, and lavaan, a widely used SEM package. The introduction provides a brief non-technical explanation of informative hypotheses, the statistical un...
Article
Mixed-effects models are becoming common in psychological science. Although they have many desirable features, there is still untapped potential. It is customary to view homogeneous variance as an assumption to satisfy. We argue to move beyond that perspective, and to view modeling within-person variance as an opportunity to gain a richer understan...
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Network theory has emerged as a popular framework for conceptualizing psychological constructs and mental disorders. Initially, network analysis was motivated in part by the thought that it can be used for hypothesis generation. Although the customary approach for network modeling is inherently exploratory, we argue that there is untapped potential...
Preprint
The Savage-Dickey density ratio is a specific expression of the Bayes factor when testing a precise (equality constrained) hypothesis against an unrestricted alternative. The expression greatly simplifies the computation of the Bayes factor at the cost of assuming a specific form of the prior under the precise hypothesis as a function of the unrest...
Article
Full-text available
Informally, ‘information inconsistency’ is the property that has been observed in some Bayesian hypothesis testing and model selection scenarios whereby the Bayesian conclusion does not become definitive when the data seem to become definitive. An example is that, when performing a t test using standard conjugate priors, the Bayes factor of the alt...
Article
Full-text available
Gaussian graphical models are commonly used to characterize conditional (in)dependence structures (i.e., partial correlation networks) of psychological constructs. Recently attention has shifted from estimating single networks to those from various subpopulations. The focus is primarily to detect differences or demonstrate replicability. We introdu...
Article
Full-text available
In statistical practice, researchers commonly focus on patterns in the means of multiple dependent outcomes while treating variances as nuisance parameters. However, in fact, there are often substantive reasons to expect certain patterns in the variances of dependent outcomes as well. For example, in a repeated measures study, one may expect the va...
Preprint
BGGM is built around two approaches for Bayesian inference–estimation and hypothesistesting. This distinction is arbitrary (see Rouder, Haaf, & Vandekerckhove, 2018), but isused to organize this work. The former focuses on the posterior distribution and includesextensions to assess predictability (Haslbeck & Waldorp, 2018), as well as methodology t...
Article
Full-text available
The Schwarz or Bayesian information criterion (BIC) is one of the most widely used tools for model comparison in social science research. The BIC, however, is not suitable for evaluating models with order constraints on the parameters of interest. This article explores two extensions of the BIC for evaluating order-constrained models, one where a t...
Preprint
Full-text available
There has been a tremendous methodological development of Bayes factors for hypothesis testing in the social and behavioral sciences, and related fields. This development is due to the flexibility of the Bayes factor for testing multiple hypotheses simultaneously, the ability to test complex hypotheses involving equality as well as order constraint...
Article
This study aimed at developing and validating a new instrument to facilitate late adolescents and young adults to choose a higher education major. For the main study, the sample consisted of 6,215 late adolescents and young adults ( M age = 19.50, SD = 1.89, 42.3% female). After rational scale construction based on the RIASEC model of Holland (1997...
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Gaussian graphical models (GGM) allow for learning conditional independence structures that are encoded by partial correlations. Whereas there are several \proglang{R} packages for classical (i.e., frequentist) methods, there are only two that implement a Bayesian approach. These are exclusively focused on identifying the graphical structure; that...
Article
In linear regression problems with many predictors, penalized regression techniques are often used to guard against overfitting and to select variables relevant for predicting an outcome variable. Recently, Bayesian penalization is becoming increasingly popular in which the prior distribution performs a function similar to that of the penalty term...
Preprint
A default Bayes factor is proposed for evaluating multivariate normal linear models with competing sets of equality and order constraints on the parameters of interest. The default Bayes factor is based on generalized fractional Bayes methodology where different fractions are used for different observations and where the default prior is centered o...
Article
Full-text available
This paper presents a new statistical method and accompanying software for the evaluation of order constrained hypotheses in structural equation models (SEM). The method is based on a large sample approximation of the Bayes factor using a prior with a data-based correlational structure. An efficient algorithm is written into an R package to ensure...
Article
Full-text available
Scientific theories can often be formulated using equality and order constraints on the relative effects in a linear regression model. For example, it may be expected that the effect of the first predictor is larger than the effect of the second predictor, and the second predictor is expected to be larger than the third predictor. The goal is then...
Preprint
Full-text available
Gaussian graphical models are commonly used to characterize conditional independence structures (i.e., networks) of psychological constructs. Recently attention has shifted from estimating single networks to those from various sub-populations. The focus is primarily to detect differences or demonstrate replicability. We introduce two novel Bayesian...
Article
Full-text available
Learning about hypothesis evaluation using the Bayes factor could enhance psychological research. In contrast to null-hypothesis significance testing it renders the evidence in favor of each of the hypotheses under consideration (it can be used to quantify support for the null-hypothesis) instead of a dichotomous reject/do-not-reject decision; it c...
Preprint
Full-text available
Learning about hypothesis evaluation using the Bayes factor could enhance psychologicalresearch. In contrast to null-hypothesis significance testing: it renders the evidence in favorof each of the hypotheses under consideration (it can be used to quantify support for thenull-hypothesis) instead of a dichotomous reject/do-not-reject decision; it can...
Article
Full-text available
There has been an increasing interest in understanding how social networks evolve over time. The study of network dynamics is often based on modeling the transition of a (small) number of snapshots of the network observations. The approach however is not suitable for analyzing networks of event streams where edges are constantly changing in frequen...
Article
Full-text available
The effects of gender stereotype threat on mathematical test performance in the classroom have been extensively studied in several cultural contexts. Theory predicts that stereotype threat lowers girls’ performance on mathematics tests, while leaving boys’ math performance unaffected. We conducted a large-scale stereotype threat experiment in Dutch...
Preprint
We introduce methods for Bayesian hypothesis testing in Gaussian graphical models. Exploratory and confirmatory hypothesistesting with the Bayes factor are presented. The former uses the customary Wishart prior distribution, wherein a closed form expression for the Bayes factor is provided. There are extensions beyond the conditional (in)dependence...
Article
Full-text available
The matrix-F distribution is presented as prior for covariance matrices as an alternative to the conjugate inverted Wishart distribution. A special case of the univariate F distribution for a variance parameter is equivalent to a half-t distribution for a standard deviation, which is becoming increasingly popular in the Bayesian literature. The mat...
Article
Full-text available
The software package Bain can be used for the evaluation of informative hypotheses with respect to the parameters of a wide range of statistical models. For pairs of hypotheses the support in the data is quantified using the approximate adjusted fractional Bayes factor (BF). Currently, the data have to come from one population or have to consist of...
Article
Full-text available
The intraclass correlation plays a central role in modeling hierarchically structured data, such as educational data, panel data, or group-randomized trial data. It represents relevant information concerning the between-group and within-group variation. Methods for Bayesian hypothesis tests concerning the intraclass correlation are proposed to impr...
Preprint
Full-text available
Scientific theories can often be formulated using equality and order constraints on the relative effects in a linear regression model. For example, it may be expected that the effect of the first predictor is larger than the effect of the second predictor, and the second predictor is expected to be larger than the third predictor. The goal is then...
Preprint
Measures of association play a central role in the social sciences to quantify the degree of association between the variables of interest. In many applications researchers can translate scientific expectations to hypotheses with equality and/or order constraints on these measures of association. In this paper a Bayes factor test is proposed for te...
Article
Full-text available
The Bayes factor is increasingly used for the evaluation of hypotheses. These may be traditional hypotheses specified using equality constraints among the parameters of the statistical model of interest or informative hypotheses specified using equality and inequality constraints. Thus far, no attention has been given to the computation of Bayes fa...
Preprint
The Schwarz or Bayesian information criterion (BIC) is one of the most widely used tools for model comparison in social science research. The BIC however is not suitable for evaluating models with order constraints on the parameters of interest. This paper explores two extensions of the BIC for evaluating order constrained models, one where a trunc...
Article
In comparing characteristics of independent populations, researchers frequently expect a certain structure of the population variances. These expectations can be formulated as hypotheses with equality and/or inequality constraints on the variances. In this article, we consider the Bayes factor for testing such (in)equality-constrained hypotheses on...
Preprint
In linear regression problems with many predictors, penalized regression techniques are often used to guard against overfitting and to select variables relevant for predicting the outcome. Classical regression techniques find coefficients that minimize a squared residual; penalized regression adds a penalty term to this residual to limit the coeffi...
Preprint
Full-text available
The latent class model is a powerful unsupervised clustering algorithm for categorical data. Many statistics exist to test the fit of the latent class model. However, traditional methods to evaluate those fit statistics are not always useful. Asymptotic distributions are not always known, and empirical reference distributions can be very time consu...
Article
Bayesian structural equation modeling (BSEM) has recently gained popularity because it enables researchers to fit complex models and solve some of the issues often encountered in classical maximum likelihood estimation, such as nonconvergence and inadmissible solutions. An important component of any Bayesian analysis is the prior distribution of th...
Article
Informally, "Information Inconsistency" is the property that has been observed in many Bayesian hypothesis testing and model selection procedures whereby the Bayesian conclusion does not become definitive when the data seems to become definitive. An example is that, when performing a t-test using standard conjugate priors, the Bayes factor of the a...
Article
Full-text available
Currently available (classical) testing procedures for the network autocorrelation can only be used for falsifying a precise null hypothesis of no network effect. Classical methods can be neither used for quantifying evidence for the null nor for testing multiple hypotheses simultaneously. This article presents flexible Bayes factor testing procedu...
Article
Full-text available
Informative hypotheses are increasingly being used in psychological sciences because they adequately capture researchers’ theories and expectations. In the Bayesian framework, the evaluation of informative hypotheses often makes use of default Bayes factors such as the fractional Bayes factor. This paper approximates and adjusts the fractional Baye...
Article
Full-text available
Two marginal one-parameter item response theory models are introduced, by integrating out the latent variable or random item parameter. It is shown that both marginal response models are multivariate (probit) models with a compound symmetry covariance structure. Several common hypotheses concerning the underlying covariance structure are evaluated...
Article
Full-text available
Research has shown that independent groups often differ not only in their means, but also in their variances. Comparing and testing variances is therefore of crucial importance to understand the effect of a grouping variable on an outcome variable. Researchers may have specific expectations concerning the relations between the variances of multiple...
Article
Full-text available
In order to accurately control the Type I error rate (typically .05), a p value should be uniformly distributed under the null model. The posterior predictive p value (ppp), which is commonly used in Bayesian data analysis, generally does not satisfy this property. For example there have been reports where the sampling distribution of the ppp under...
Article
Full-text available
To date, the study of psychological contracts has primarily centred on the question how retrospective evaluations of the psychological contract impact employee attitudes and behaviours, and/or focus on individual coping processes in explaining responses to breached or overfulfilled obligations. In this study, we aim to assess the extent to which se...
Preprint
Bayesian structural equation modeling (BSEM) has recently gained popularity because it enables researchers to fit complex models while solving some of the issues often encountered in classical maximum likelihood (ML) estimation, such as nonconvergence and inadmissible solutions. An important component of any Bayesian analysis is the prior distribut...
Article
The network autocorrelation model has been extensively used by researchers interested modeling social influence effects in social networks. The most common inferential method in the model is classical maximum likelihood estimation. This approach, however, has known problems such as negative bias of the network autocorrelation parameter and poor cov...
Chapter
Statistical hypothesis testing plays a central role in applied research to determine whether theories or expectations are supported by the data or not. Such expectations are often formulated using order constraints. For example an executive board may expect that sales representatives who wear a smart watch will respond faster to their emails than s...
Article
In order to test their hypotheses, psychologists increasingly favor the Bayes factor, the standard Bayesian measure of relative evidence between two competing statistical models. The Bayes factor has an intuitive interpretation and allows a comparison between any two models, even models that are complex and nonnested. In this introduction to the sp...
Article
Full-text available
This paper investigates the classical type I and type II error probabilities of default Bayes factors for a Bayesian t test. Default Bayes factors quantify the relative evidence between the null hypothesis and the unrestricted alternative hypothesis without needing to specify prior distributions for the unknown parameters based on one's prior belie...
Article
Researchers are frequently interested in testing variances of two independent populations. We often would like to know whether the population variances are equal, whether population 1 has smaller variance than population 2, or whether population 1 has larger variance than population 2. In this article we consider the Bayes factor, a Bayesian model...
Article
Full-text available
The application of latent class (LC) analysis involves evaluating the LC model using goodness-of-fit statistics. To assess the misfit of a specified model, say with the Pearson chi-squared statistic, a p-value can be obtained using an asymptotic reference distribution. However, asymptotic p-values are not valid when the sample size is not large and...
Article
Full-text available
Bayesian item response theory models have been widely used in different research fields. They support measuring constructs and modeling relationships between constructs, while accounting for complex test situations (e.g., complex sampling designs, missing data, heterogenous population). Advantages of this flexible modeling framework together with p...
Article
Full-text available
Bayesian evaluation of inequality constrained hypotheses enables researchers to investigate their expectations with respect to the structure among model parameters. This article proposes an approximate Bayes procedure that can be used for the selection of the best of a set of inequality constrained hypotheses based on the Bayes factor in a very gen...
Article
A new method is proposed for testing multiple hypotheses with equality and inequality constraints on the parameters of interest. The method is based on the fractional Bayes factor with a modification that the updated prior is centered on the boundary of the constrained parameter space under investigation. The resulting prior adjusted default Bayes...
Article
Full-text available