BFpack: Flexible Bayes Factor Testing of Scientific Theories in R

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 constraints on the parameters of interest, and the interpretability of the outcome as the weight of evidence provided by the data in support of competing scientific theories. The available software tools for Bayesian hypothesis testing are still limited however. In this paper we present a new R package called BFpack that contains functions for Bayes factor hypothesis testing for the many common testing problems. The software includes novel tools for (i) Bayesian exploratory testing (e.g., zero vs positive vs negative effects), (ii) Bayesian confirmatory testing (competing hypotheses with equality and/or order constraints), (iii) common statistical analyses, such as linear regression, generalized linear models, (multivariate) analysis of (co)variance, correlation analysis, and random intercept models, (iv) using default priors, and (v) while allowing data to contain missing observations that are missing at random

Parental Age in Relation to Offspring's Neurodevelopment

Objective: Advanced parenthood increases the risk of severe neurodevelopmental disorders like autism, Down syndrome and schizophrenia. Does advanced parenthood also negatively impact offspring’s general neurodevelopment? Method: We analyzed child-, father-, mother- and teacher-rated attention-problems (N = 38,024), and standardized measures of intelligence (N = 10,273) and educational achievement (N = 17,522) of children from four Dutch population-based cohorts. The mean age over cohorts varied from 9.73–13.03. Most participants were of Dutch origin, ranging from 58.7%-96.7% over cohorts. We analyzed 50% of the data to generate hypotheses and the other 50% to evaluate support for these hypotheses. We aggregated the results over cohorts with Bayesian research synthesis. Results: We mostly found negative linear relations between parental age and attention-problems, meaning that offspring of younger parents tended to have more attention problems. Maternal age was positively and linearly related to offspring’s IQ and educational achievement. Paternal age showed an attenuating positive relation with educational achievement and an inverted U-shape relation with IQ, with offspring of younger and older fathers at a disadvantage. Only the associations with maternal age remained after including SES. The inclusion of child gender in the model did not affect the relation between parental age and the study outcomes. Conclusions: Effects were small but significant, with better outcomes for children born to older parents. Older parents tended to be of higher SES. Indeed, the positive relation between parenta

IsoGeneGUI: Multiple Approaches for Dose-Response Analysis of Microarray Data Using R

The analysis of transcriptomic experiments with ordered covariates, such as dose-response data, has become a central topic in bioinformatics, in particular in omics studies. Consequently, multiple R packages on CRAN and Bioconductor are designed to analyse microarray data from various perspectives under the assumption of order restriction. We introduce the new R package IsoGene Graphical User Interface (IsoGeneGUI), an extension of the original IsoGene package that includes methods from most of available R packages designed for the analysis of order restricted microarray data, namely orQA, ORIClust, goric and ORCME. The methods included in the new IsoGeneGUI range from inference and estimation to model selection and clustering tools. The IsoGeneGUI is not only the most complete tool for the analysis of order restricted microarray experiments available in R but also it can be used to analyse other types of dose-response data. The package provides all the methods in a user friendly fashion, so analyses can be implemented by users with limited knowledge of R programming

The latest update on Bayesian informative hypothesis testing

With the increased use of Bayesian informative hypothesis testing, practical, philosophical and methodological questions arise. This dissertation addresses a few of these questions. One step in the research cycle is to collect data for hypothesis testing. The amount of data required to answer a research question depends on the value of making wrong conclusions. The link between sample size, power and error probabilities is well-researched in the NHST framework. In Bayesian statistics research this relationship is less discussed and the value of power and unconditional error probabilities are debated. Chapter 2 presents four sample size determination methods for informative hypothesis testing by means of Bayes factors. The value of power and (un)conditional error probabilities and their link with sample size for Bayesian hypothesis tests are discussed. Another step in the research cycle is to translate the results from a statistical analysis into a conclusion. The analysis should match the research question to provide a sensible conclusion. Many hypothesis tests concern the presence and direction of *population* effects. However, in practice the conclusions from these hypothesis tests often are at the *individual* level. For example, after analyzing the effectiveness of a medication in the population, it is prescribed to individuals. The average effect does not imply the medicine works for all individuals. In many situations the main interest is in the individual effects rather than population effects. Chapters 3 and 4 describe how Bayesian hypothesis testing can be used to synthesize the results from multiple individual analyses. Bayesian statistics can be used to continuously add data and sequentially update knowledge about population effects. This process is called updating. Alternatively, data from multiple individuals can be analyzed separately and combined to learn about how the homogeneity (similarity) of individual effects. Chapter 3 presents the methodology and Chapter 4 is a hands-on description for how to execute such an analysis. For Chapter 2 an R package has been developed, and for Chapter 3 an R Shiny application has been developed. Both pieces of software are presented in Chapter 6. Chapter 5 discusses the updating cycle in Bayesian statistics and focuses on the starting point of an updating cycle. The information in a Bayes factor is useful to describe how we can update our knowledge. However, knowing the rate with which the relative belief for two hypotheses changes is meaningless if the starting point is unknown. Chapter 5 therefore discusses the importance of prior probabilities and how to specify these for a set of hypotheses. Chapters 7 and 8 present applied research where informative hypotheses are tested with Bayes factors. These are examples of research that commonly are analyzed with NHST and are thus exemplary in what the possibilities with informative hypothesis testing are. In Chapter 7 informative hypotheses are formulated to analyze the data from a repeated measures experiment. Chapter 8 evaluates the presence of a mediated effect at the the individual level by means of Bayesian informative hypothess tests

Sample size determination for Bayesian ANOVAs with informative hypotheses

Researchers can express their expectations with respect to the group means in an ANOVA model through equality and order constrained hypotheses. This paper introduces the R package SSDbain, which can be used to calculate the sample size required to evaluate (informative) hypotheses using the Approximate Adjusted Fractional Bayes Factor (AAFBF) for one-way ANOVA models as implemented in the R package bain. The sample size is determined such that the probability that the Bayes factor is larger than a threshold value is at least η when either of the hypotheses under consideration is true. The Bayesian ANOVA, Bayesian Welch's ANOVA, and Bayesian robust ANOVA are available. Using the R package SSDbain and/or the tables provided in this paper, researchers in the social and behavioral sciences can easily plan the sample size if they intend to use a Bayesian ANOVA

Sample-size determination for the Bayesian t test and Welch's test using the approximate adjusted fractional Bayes factor

When two independent means μ1 and μ2 are compared, H0 : μ1 = μ2, H1 : μ1≠μ2, and H2 : μ1 > μ2 are the hypotheses of interest. This paper introduces the R package SSDbain, which can be used to determine the sample size needed to evaluate these hypotheses using the approximate adjusted fractional Bayes factor (AAFBF) implemented in the R package bain. Both the Bayesian t test and the Bayesian Welch's test are available in this R package. The sample size required will be calculated such that the probability that the Bayes factor is larger than a threshold value is at least η if either the null or alternative hypothesis is true. Using the R package SSDbain and/or the tables provided in this paper, psychological researchers can easily determine the required sample size for their experiments

Prior sensitivity of null hypothesis Bayesian testing

Researchers increasingly use Bayes factor for hypotheses evaluation. There are two main applications: null hypothesis Bayesian testing (NHBT) and informative hypothesis Bayesian testing (IHBT). As will be shown in this article, NHBT is sensitive to the specification of the scale parameter of the prior distribution, while IHBT is not. As will also be shown in this article, for NHBT using four different Bayes factors, use of the recommended default values for the scaling parameters results in unpredictable operating characteristics, that is, the Bayes factor will usually be biased against or in favor of the null hypothesis. As will furthermore be shown in this article, this problem can be addressed by choosing the scaling parameter such that the Bayes factor is 19 in favor of the null hypothesis over the alternative hypothesis if the observed effect size is equal to zero, because this renders a Bayes factor with clearly specified operating characteristics. However, this does not solve all problems regarding NHBT. The discussion of this article contains elaborations with respect to: the multiverse of Bayes factors; the choice of "19"; Bayes factor calibration outside the context of the univariate normal linear model; and, reporting the results of NHBT. (PsycInfo Database Record (c) 2022 APA, all rights reserved)

Perception of action-outcomes is shaped by life-long and contextual expectations

The way humans perceive the outcomes of their actions is strongly colored by their expectations. These expectations can develop over different timescales and are not always complementary. The present work examines how long-term (structural) expectations – developed over a lifetime - and short-term (contextual) expectations jointly affect perception. In two studies, including a pre-registered replication, participants initiated the movement of an ambiguously rotating sphere by operating a rotary switch. In the absence of any learning, participants predominantly perceived the sphere to rotate in the same direction as their rotary action. This bias toward structural expectations was abolished (but not reversed) when participants were exposed to incompatible action-effect contingencies (e.g., clockwise actions causing counterclockwise percepts) during a preceding learning phase. Exposure to compatible action-effect contingencies, however, did not add to the existing structural bias. Together, these findings reveal that perception of action-outcomes results from the combined influence of both long-term and immediate expectations

Evaluation of inequality constrained hypotheses using a generalization of the AIC.

In the social and behavioral sciences, it is often not interesting to evaluate the null hypothesis by means of a p-value. Researchers are often more interested in quantifying the evidence in the data (as opposed to using p-values) with respect to their own expectations represented by equality and/or inequality constrained hypotheses (as opposed to the null hypothesis). This article proposes an Akaike-type information criterion (AIC; Akaike, 1973, 1974) called the generalized order-restricted information criterion approximation (GORICA) that evaluates (in)equality constrained hypotheses under a very broad range of statistical models. The results of five simulation studies provide empirical evidence showing that the performance of the GORICA on selecting the best hypothesis out of a set of (in)equality constrained hypotheses is convincing. To illustrate the use of the GORICA, the expectations of researchers are investigated in a logistic regression, multilevel regression, and structural equation model. (PsycInfo Database Record (c) 2021 APA, all rights reserved

Evaluation of inequality constrained hypotheses using a generalization of the AIC.

In the social and behavioral sciences, it is often not interesting to evaluate the null hypothesis by means of a p-value. Researchers are often more interested in quantifying the evidence in the data (as opposed to using p-values) with respect to their own expectations represented by equality and/or inequality constrained hypotheses (as opposed to the null hypothesis). This article proposes an Akaike-type information criterion (AIC; Akaike, 1973, 1974) called the generalized order-restricted information criterion approximation (GORICA) that evaluates (in)equality constrained hypotheses under a very broad range of statistical models. The results of five simulation studies provide empirical evidence showing that the performance of the GORICA on selecting the best hypothesis out of a set of (in)equality constrained hypotheses is convincing. To illustrate the use of the GORICA, the expectations of researchers are investigated in a logistic regression, multilevel regression, and structural equation model. (PsycInfo Database Record (c) 2021 APA, all rights reserved