BFpack

R-functions for Bayesian exploratory (equal vs negative vs postive) and confirmatory (equality and/or order constraints) hypothesis testing for commonly used statistical models, including (but not limited to) univariate/multivariate t testing, (M)AN(C)OVA, multivariate/univariate regression, random intercept models. The functions need fitted models (e.g., lm) as input as well as a string that specifies a set of order constraints on the regression coefficients.

Developers and collaborators: Joris Mulder, Caspar van Lissa, Donald R. Williams, Xin Gu, Anton Olsson-Collentine, Florian Böing-Messing, Andrew Tomarken, Marlyne Bosman-Meijerink, Eric-Jan Wagenmakers, Yves Rosseel, Jean-Paul Fox, Janosch Menke, and Herbert Hoijtink.

Licensed under the GNU General Public License version 2 (June, 1991)

Installation

You can install BFpack from GitHub with:

``` r

install.packages("devtools")

devtools::install_github("jomulder/BFpack")

Example analyses

Aapplication 1

load R package BFpack and bain

library(BFpack) library(bain)

Frequentist one sample t test at the null point mu=5 on the therapeutic data

ttest1 <- t_test(therapeutic,mu=5) print(ttest1)

confirmatory Bayesian one sample t test

BF1 <- BF(ttest1,"mu=5") summary(BF1)

Application 2

Fit an anova model on the tvprices data

aov1 <- aov(price ~ anchor*motivation,data=tvprices)

Perform exploratory Bayes factor tests for ANOVA design

BF(aov1)

Application 3

Perform classical Bartlett test for homogeneity of group varianceson the accuracy data

bartlett <- bartlett_test(x = attention$accuracy, g = attention$group)

Specify informative hypotheses on the group variances based on substantive expectations

hypothesis <- c("Controls=TS<ADHD; Controls<TS=ADHD; Controls=TS=ADHD") set.seed(358)

Perform the Bayesian hypothesis tests

BF_var <- BF(bartlett, hypothesis) summary(BF_var)

Application 4

Fit the multivariate regression model on the fmri data

fmri.lm <- lm(cbind(Superficial,Middle,Deep) ~ Face + Vehicle, data=fmri)

Specify informative hypotheses on the coefficients across predictor and dependent variables

based on substantive expectations

constraints.fmri <- "Face_on_Deep = Face_on_Superficial = Face_on_Middle < 0 < Vehicle_on_Deep = Vehicle_on_Superficial = Vehicle_on_Middle; Face_on_Deep < Face_on_Superficial = Face_on_Middle < 0 < Vehicle_on_Deep = Vehicle_on_Superficial = Vehicle_on_Middle"

Perform the Bayesian hypothesis tests

set.seed(123) BF_fmri <- BF(fmri.lm, hypothesis = constraints.fmri) summary(BF_fmri)

Application 4b

constraints.fmri2 <- "Face_on_Deep = Face_on_Superficial = Face_on_Middle < 0; Face_on_Deep < Face_on_Superficial = Face_on_Middle < 0" fmri.lm2 <- lm(cbind(Superficial,Middle,Deep) ~ Face + Vehicle, data=fmri) BF.fmri2 <- BF(fmri.lm2, hypothesis=constraints.fmri2)

#Application 5

Fit logistic regression model

fit <- glm(sent ~ ztrust + zfWHR + zAfro + glasses + attract + maturity + tattoos, family = binomial(), data = wilson)

Perform the Bayesian hypothesis tests

set.seed(123) BF_glm <- BF(fit, hypothesis="ztrust > (zfWHR, zAfro) > 0; ztrust > (zfWHR, zAfro) = 0") summary(BF_glm)

Application 6: Correlation analysis

#Fit multivariate normal model lm6 <- lm(cbind(Im,Del,Wmn,Cat,Fas,Rat) ~ -1 + Group, data=memory) set.seed(123)

#Perform Bayes factor test of the order hypothesis against its compleplement BF6_cor <- BF(lm6,parameter="correlation", hypothesis= "Del_with_Im_in_GroupHC > Del_with_Im_in_GroupSZ & Del_with_Wmn_in_GroupHC > Del_with_Wmn_in_GroupSZ & Del_with_Cat_in_GroupHC > Del_with_Cat_in_GroupSZ & Del_with_Fas_in_GroupHC > Del_with_Fas_in_GroupSZ & Del_with_Rat_in_GroupHC > Del_with_Rat_in_GroupSZ & Im_with_Wmn_in_GroupHC > Im_with_Wmn_in_GroupSZ & Im_with_Cat_in_GroupHC > Im_with_Cat_in_GroupSZ & Im_with_Fas_in_GroupHC > Im_with_Fas_in_GroupSZ & Im_with_Rat_in_GroupHC > Im_with_Rat_in_GroupSZ & Wmn_with_Cat_in_GroupHC > Wmn_with_Cat_in_GroupSZ & Wmn_with_Fas_in_GroupHC > Wmn_with_Fas_in_GroupSZ & Wmn_with_Rat_in_GroupHC > Wmn_with_Rat_in_GroupSZ & Cat_with_Fas_in_GroupHC > Cat_with_Fas_in_GroupSZ & Cat_with_Rat_in_GroupHC > Cat_with_Rat_in_GroupSZ & Fas_with_Rat_in_GroupHC > Fas_with_Rat_in_GroupSZ") summary(BF6_cor)

Application 7. Testing intraclas correlations

library(lme4)

#Only consider the timssICC data for the measurements of the four counteries in 2011 timssICC_subset <- timssICC[(timssICC$groupNL11==1)+(timssICC$groupHR11==1)+ (timssICC$groupDE11==1)+(timssICC$groupDK11==1)>0,]

#Fit a random intercept model with country specific random effect variances across schools outlme1 <- lmer(math ~ -1 + gender + weight + lln + groupNL11 + (0+groupNL11 | schoolID) + groupHR11 + (0+groupHR11 | schoolID) + groupDE11 + (0+groupDE11 | schoolID) + groupDK11 + (0+groupDK11 | schoolID), data=timssICC_subset)

#Perform Bayes factor test on intraclass correlations across countries in 2011 set.seed(123) BFout <- BF(outlme1,hypothesis= "groupNL11<groupHR11<groupDE11<groupDK11; groupNL11=groupHR11=groupDE11=groupDK11") summary(BFout)