composite_u_scalar {psychmeta}

Scalar formula to estimate the u ratio of a composite variable

Description

This function provides an approximation of the u ratio of a composite variable based on the u ratios of the component variables, the mean restricted intercorrelation among those variables, and the mean unrestricted correlation among those variables. If only one of the mean intercorrelations is known, the other will be estimated using the bivariate indirect range-restriction formula. This tends to compute a conservative estimate of the u ratio associated with a composite.

Usage

composite_u_scalar(mean_ri = NULL, mean_ra = NULL, mean_u, k_vars)

Arguments

mean_ri

The mean range-restricted correlation among variables in the composite.

mean_ra

The mean unrestricted correlation among variables in the composite.

mean_u

The mean u ratio of variables in the composite.

k_vars

The number of variables in the composite.

Details

This is computed as:

u_{composite}=\sqrt{\frac{\bar{\rho}_{i}\bar{u}^{2}k(k-1)+k\bar{u}^{2}}{\bar{\rho}_{a}k(k-1)+k}}

where u_{composite} is the composite u ratio, \bar{u} is the mean univariate u ratio, \bar{\rho}_{i} is the mean restricted correlation among variables, \bar{\rho}_{a} is the mean unrestricted correlation among variables, and k is the number of variables in the composite.

Value

The estimated u ratio of the composite variable.

Examples

composite_u_scalar(mean_ri = .3, mean_ra = .4, mean_u = .8, k_vars = 2)