bayestestR (version 0.8.0)

contr.bayes: Orthonormal Contrast Matrices for Bayesian Estimation

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 bfrms, following the description in Rouder, Morey, Speckman, \& Province (2012, p. 363).

Usage

contr.bayes(n, contrasts = TRUE)

Arguments

n

a vector of levels for a factor, or the number of levels.

contrasts

logical indicating whether contrasts should be computed.

Value

A matrix with n rows and k columns, with k=n-1 if contrasts is TRUE and k=n if contrasts is FALSE.

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 the Bayes factors vignette.

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

Examples

# NOT RUN {
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
# }