BayesTools Contrast Matrices

BayesTools provides several contrast matrix functions for Bayesian factor analysis. These functions create different types of contrast matrices that can be used with factor variables in Bayesian models.

contr.orthonormal(n, contrasts = TRUE)

contr.meandif(n, contrasts = TRUE)

contr.independent(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

Details

The package includes the following contrast functions:

contr.orthonormal

Return a matrix of orthonormal contrasts. Code is based on stanova::contr.bayes and corresponding to description by Rouder et al. (2012) . Returns a matrix with n rows and k columns, with k = n - 1 if contrasts = TRUE and k = n if contrasts = FALSE.

contr.meandif

Return a matrix of mean difference contrasts. This is an adjustment to the contr.orthonormal that ascertains that the prior distributions on difference between the gran mean and factor level are identical independent of the number of factor levels (which does not hold for the orthonormal contrast). Furthermore, the contrast is re-scaled so the specified prior distribution exactly corresponds to the prior distribution on difference between each factor level and the grand mean – this is approximately twice the scale of contr.orthonormal. Returns a matrix with n rows and k columns, with k = n - 1 if contrasts = TRUE and k = n if contrasts = FALSE.

contr.independent

Return a matrix of independent contrasts – a level for each term. Returns a matrix with n rows and k columns, with k = n if contrasts = TRUE and k = n if contrasts = FALSE.

References

Rouder JN, Morey RD, Speckman PL, Province JM (2012). “Default Bayes factors for ANOVA designs.” Journal of Mathematical Psychology, 56(5), 356–374. doi:10.1016/j.jmp.2012.08.001 .

Examples

# Orthonormal contrasts
contr.orthonormal(c(1, 2))
#>            [,1]
#> [1,] -0.7071068
#> [2,]  0.7071068
contr.orthonormal(c(1, 2, 3))
#>            [,1]       [,2]
#> [1,]  0.0000000  0.8164966
#> [2,] -0.7071068 -0.4082483
#> [3,]  0.7071068 -0.4082483

# Mean difference contrasts
contr.meandif(c(1, 2))
#>      [,1]
#> [1,]   -1
#> [2,]    1
contr.meandif(c(1, 2, 3))
#>            [,1] [,2]
#> [1,]  0.0000000  1.0
#> [2,] -0.8660254 -0.5
#> [3,]  0.8660254 -0.5

# Independent contrasts
contr.independent(c(1, 2))
#>      [,1] [,2]
#> [1,]    1    0
#> [2,]    0    1
contr.independent(c(1, 2, 3))
#>      [,1] [,2] [,3]
#> [1,]    1    0    0
#> [2,]    0    1    0
#> [3,]    0    0    1