# composite_r_matrix: Matrix formula to estimate the correlation between two... In psychmeta: Psychometric Meta-Analysis Toolkit

## Description

This function computes the weighted (or unweighted, by default) composite correlation between a set of X variables and a set of Y variables.

## Usage

 1 2 3 4 5 6 7 composite_r_matrix( r_mat, x_col, y_col, wt_vec_x = rep(1, length(x_col)), wt_vec_y = rep(1, length(y_col)) ) 

## Arguments

 r_mat Correlation matrix from which composite correlations are to be computed. x_col Column indices of variables from 'r_mat' in the X composite (specify a single variable if Y is an observed variable rather than a composite). y_col Column indices of variables from 'r_mat' in the Y composite (specify a single variable if Y is an observed variable rather than a composite). wt_vec_x Weights to be used in forming the X composite (by default, all variables receive equal weight). wt_vec_y Weights to be used in forming the Y composite (by default, all variables receive equal weight).

## Details

This is computed as:

\mjdeqn\rho

_XY\frac\mathbfw_X^T\mathbfR_XY\mathbfw_Y\sqrt\left(\mathbfw_X^T\mathbfR_XX\mathbfw_X\right)\left(\mathbfw_Y^T\mathbfR_YY\mathbfw_Y\right)r_composite = (t(wt_x) Rxy wt_y) / (sqrt(t(wt_x) Rxx wt_x) * sqrt(t(wt_y) Ryy wt_y))

where \mjeqn\rho_XYr_composite is the composite correlation, \mjeqn\mathbfwwt is a vector of weights, and \mjeqn\mathbfRR is a correlation matrix. The subscripts of \mjeqn\mathbfwwt and \mjeqn\mathbfRR indicate the variables indexed within the vector or matrix.

## Value

A composite correlation

## References

Mulaik, S. A. (2010). Foundations of factor analysis. Boca Raton, FL: CRC Press. pp. 83–84.

## Examples

 1 2 3 4 composite_r_scalar(mean_rxy = .3, k_vars_x = 4, mean_intercor_x = .4) R <- reshape_vec2mat(.4, order = 5) R[-1,1] <- R[1,-1] <- .3 composite_r_matrix(r_mat = R, x_col = 2:5, y_col = 1) 

### Example output

-----------------------------------------------------  psychmeta version 2.3.3  --

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We work hard to produce these open-source tools for the R community,
Dahlke, J. A., & Wiernik, B. M. (2018). psychmeta: An R package for
psychometric meta-analysis. Applied Psychological Measurement.

Attaching package: 'psychmeta'

The following object is masked from 'package:stats':

filter

[1] 0.4045199
[1] 0.4045199


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