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).
contr.bayes(n, contrasts = TRUE)
| n | a vector of levels for a factor, or the number of levels. |
|---|---|
| contrasts | logical indicating whether contrasts should be computed. |
A matrix with n rows and k columns, with k=n-1 if contrasts is
TRUE and k=n if contrasts is FALSE.
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.
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
if (FALSE) { 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 }