Olkin & Siotani variance-covariance matrix

Computational function to compute the Olkin & Siotani (1976) variance-covariance matrix for correlation matrices. It allows the user to specify three different computations.

Usage

olkin_siotani(data, n, type = c("average", "weighted", "simple"))

Arguments

data: A correlation matrix or a list of correlation matrices.
n: Sample size
type: The type of Olkin and Siotani correction to make.

Value

List of matrices, same length as the number of studies or number of correlation matrices.

Details

The three possible computations that can be specified are:

average: Average all the correlations element-wise to pool into a single correlation matrix. The variance-covariance is computed from the averaged correlation matrix, then divided by study specific sample sizes.
weighted: Same as the average process-wise, but uses a weighted average to pool into a single correlation matrix.
simple: Computes the variance-covariance for each individual correlation matrix, then divide these by the study specific sample sizes.

References

Becker, B. J. (1992). Using results from replicated studies to estimate linear models. Journal of Educational Statistics, 17(4), 341-362. Olkin, I. (1976). Asymptotic distribution of functions of a correlation matrix. Essays in provability and statistics: A volume in honor of Professor Junjiro Ogawa.

Examples

R1 <- matrix(c(1, .30, .20,
               .30, 1, .40,
               .20, .40, 1), 3, 3)
R2 <- matrix(c(1, .25, .10,
               .25, 1, .35,
               .10, .35, 1), 3, 3)
olkin_siotani(list(R1, R2), n = c(80, 100), type = "simple")
#> [[1]]
#>            [,1]       [,2]      [,3]
#> [1,] 0.01035125 0.00408375 0.0013425
#> [2,] 0.00408375 0.01152000 0.0026450
#> [3,] 0.00134250 0.00264500 0.0088200
#> 
#> [[2]]
#>              [,1]        [,2]         [,3]
#> [1,] 0.0087890625 0.003145625 0.0004628125
#> [2,] 0.0031456250 0.009801000 0.0020278750
#> [3,] 0.0004628125 0.002027875 0.0077000625
#>