denom_corr_cat {SimMultiCorrData}

Calculate Denominator Used in Intercorrelations Involving Ordinal Variables

Description

This function calculates part of the the denominator used to find intercorrelations involving ordinal variables or variables that are treated as ordinal (i.e. count variables in the method used in rcorrvar2). It uses the formula given by Olsson et al. (1982, doi: 10.1007/BF02294164) in describing polyserial and point-polyserial correlations. For an ordinal variable with r >= 2 categories, the value is given by:

\sum_{j = 1}^{r-1} \phi(\tau_{j})*(y_{j+1} - y_{j}),

where

\phi(\tau) = (2\pi)^{-1/2} * exp(-0.5 * \tau^2).

Here, y_{j} is the j-th support value and \tau_{j} is \Phi^{-1}(\sum_{i=1}^{j} Pr(Y = y_{i})). This function would not ordinarily be called directly by the user.

Usage

denom_corr_cat(marginal, support)

Arguments

marginal

a vector of cumulative probabilities defining the marginal distribution of the variable; if the variable can take r values, the vector will contain r - 1 probabilities (the r-th is assumed to be 1)

support

a vector of containing the ordered support values

Value

A scalar

References

Olsson U, Drasgow F, & Dorans NJ (1982). The Polyserial Correlation Coefficient. Psychometrika, 47(3): 337-47. doi: 10.1007/BF02294164.

See Also

ordnorm, rcorrvar, rcorrvar2, findintercorr_cont_cat, findintercorr_cont_pois2,
findintercorr_cont_nb2