# correct_means_mvrr: Multivariate select/correction for vectors of means In psychmeta: Psychometric Meta-Analysis Toolkit

## Description

Correct (or select upon) a vector of means using principles from the Pearson-Aitken-Lawley multivariate selection theorem.

## Usage

 ```1 2 3 4 5 6 7 8``` ```correct_means_mvrr( Sigma, means_i = rep(0, ncol(Sigma)), means_x_a, x_col, y_col = NULL, var_names = NULL ) ```

## Arguments

 `Sigma` The complete covariance matrix to be used to manipulate means: This matrix may be entirely unrestricted or entirely range restricted, as the regression weights estimated from this matrix are expected to be invariant to the effects of selection. `means_i` The complete range-restricted (unrestricted) vector of means to be corrected (selected upon). `means_x_a` The vector of unrestricted (range-restricted) means of selection variables `x_col` The row/column indices of the variables in `Sigma` that correspond, in order, to the variables in means_x_a `y_col` Optional: The variables in `Sigma` not listed in `x_col` that are to be manipuated by the multivariate range-restriction formula. `var_names` Optional vector of names for the variables in `Sigma`, in order of appearance in the matrix.

## Value

A vector of means that has been manipulated by the multivariate range-restriction formula.

## References

Aitken, A. C. (1934). Note on selection from a multivariate normal population. Proceedings of the Edinburgh Mathematical Society (Series 2), 4(2), 106–110.

Lawley, D. N. (1943). A note on Karl Pearson’s selection formulae. Proceedings of the Royal Society of Edinburgh. Section A. Mathematical and Physical Sciences, 62(1), 28–30.

## Examples

 ```1 2 3 4 5 6``` ```Sigma <- diag(.5, 4) Sigma[lower.tri(Sigma)] <- c(.2, .3, .4, .3, .4, .4) Sigma <- Sigma + t(Sigma) diag(Sigma) <- 1 correct_means_mvrr(Sigma = Sigma, means_i = c(.3, .3, .1, .1), means_x_a = c(-.1, -.1), x_col = 1:2) ```

psychmeta documentation built on June 1, 2021, 9:13 a.m.