% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/contr.bayes.R
\name{contr.bayes}
\alias{contr.bayes}
\title{Orthonormal Contrast Matrices for Bayesian Estimation}
\usage{
contr.bayes(n, contrasts = TRUE)
}
\arguments{
\item{n}{a vector of levels for a factor, or the number of levels.}

\item{contrasts}{logical indicating whether contrasts should be computed.}
}
\value{
A \code{matrix} with n rows and k columns, with k=n-1 if contrasts is
  \code{TRUE} and k=n if contrasts is \code{FALSE}.
}
\description{
Returns a design or model matrix of orthonormal contrasts such that the
marginal prior on all effects is identical. Implementation from Singmann
\& Gronau's \href{https://github.com/bayesstuff/bfrms/}{\code{bfrms}},
following the description in Rouder, Morey, Speckman, \& Province (2012, p. 363).
}
\details{
Though using this factor coding scheme might obscure the interpretation of
parameters, it is essential for correct estimation of Bayes factors for
contrasts and multi-level order restrictions. See info on specifying correct
priors for factors with more than 2 levels in
\href{https://easystats.github.io/bayestestR/articles/bayes_factors.html}{the Bayes factors vignette}.
}
\examples{
\dontrun{
contr.bayes(2) # Q_2 in Rouder et al. (2012, p. 363)
#            [,1]
# [1,] -0.7071068
# [2,]  0.7071068

contr.bayes(5) # equivalent to Q_5 in Rouder et al. (2012, p. 363)
#            [,1]       [,2]       [,3]       [,4]
# [1,]  0.0000000  0.8944272  0.0000000  0.0000000
# [2,]  0.0000000 -0.2236068 -0.5000000  0.7071068
# [3,]  0.7071068 -0.2236068 -0.1666667 -0.4714045
# [4,] -0.7071068 -0.2236068 -0.1666667 -0.4714045
# [5,]  0.0000000 -0.2236068  0.8333333  0.2357023

## check decomposition
Q3 <- contr.bayes(3)
Q3 \%*\% t(Q3)
#            [,1]       [,2]       [,3]
# [1,]  0.6666667 -0.3333333 -0.3333333
# [2,] -0.3333333  0.6666667 -0.3333333
# [3,] -0.3333333 -0.3333333  0.6666667
## 2/3 on diagonal and -1/3 on off-diagonal elements
}
}
\references{
Rouder, J. N., Morey, R. D., Speckman, P. L., \& Province, J. M.
  (2012). Default Bayes factors for ANOVA designs. *Journal of Mathematical
  Psychology*, 56(5), 356-374. https://doi.org/10.1016/j.jmp.2012.08.001
}