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.
composite_u_scalar(mean_ri = NULL, mean_ra = NULL, mean_u, k_vars)The estimated u ratio of the composite variable.
The mean range-restricted correlation among variables in the composite.
The mean unrestricted correlation among variables in the composite.
The mean u ratio of variables in the composite.
The number of variables in the composite.
This is computed as:
u_composite=_iu^2k(k-1)+ku^2_ak(k-1)+ku_composite = sqrt((mean_ri * mean_u^2 * k * (k - 1) + k * mean_u^2) / (mean_ra * k_vars * (k - 1) + k))
where u_compositeu_composite is the composite u ratio, umean_u is the mean univariate u ratio, _imean_ri is the mean restricted correlation among variables, _amean_ra is the mean unrestricted correlation among variables, and k is the number of variables in the composite.
composite_u_scalar(mean_ri = .3, mean_ra = .4, mean_u = .8, k_vars = 2)
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