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Last data update: 2014.03.03

R: Polyserial Correlation

polyserial

R Documentation

Polyserial Correlation

Description

Computes the polyserial correlation (and its standard error) between a quantitative variable and an ordinal variables, based on the assumption that the joint distribution of the quantitative variable and a latent continuous variable underlying the ordinal variable is bivariate normal. Either the maximum-likelihood estimator or a quicker “two-step” approximation is available. For the ML estimator the estimates of the thresholds and the covariance matrix of the estimates are also available.

Usage

polyserial(x, y, ML = FALSE, control = list(), std.err = FALSE, maxcor=.9999, bins=4)

Arguments

`x`	a numerical variable.
`y`	an ordered categorical variable; can be numeric, logical, a factor, or an ordered factor, but if a factor, its levels should be in proper order.
`ML`	if `TRUE`, compute the maximum-likelihood estimate; if `FALSE`, the default, compute a quicker “two-step” approximation.
`control`	optional arguments to be passed to the `optim` function.
`std.err`	if `TRUE`, return the estimated variance of the correlation (for the two-step estimator) or the estimated covariance matrix of the correlation and thresholds (for the ML estimator); the default is `FALSE`.
`maxcor`	maximum absolute correlation (to insure numerical stability).
`bins`	the number of bins into which to dissect `x` for a test of bivariate normality; the default is 4.

Value

If std.err is TRUE, returns an object of class "polycor" with the following components:

`type`	set to `"polyserial"`.
`rho`	the polyserial correlation.
`cuts`	estimated thresholds for the ordinal variable (`y`), for the ML estimator.
`var`	the estimated variance of the correlation, or, for the ML estimator, \the estimated covariance matrix of the correlation and thresholds.
`n`	the number of observations on which the correlation is based.
`chisq`	chi-square test for bivariate normality.
`df`	degrees of freedom for the test of bivariate normality.
`ML`	`TRUE` for the ML estimate, `FALSE` for the two-step estimate.

Othewise, returns the polyserial correlation.

Author(s)

John Fox jfox@mcmaster.ca

References

Drasgow, F. (1986) Polychoric and polyserial correlations. Pp. 68–74 in S. Kotz and N. Johnson, eds., The Encyclopedia of Statistics, Volume 7. Wiley.

Examples

set.seed(12345)
data <- rmvnorm(1000, c(0, 0), matrix(c(1, .5, .5, 1), 2, 2))
x <- data[,1]
y <- data[,2]
cor(x, y)  # sample correlation
y <- cut(y, c(-Inf, -1, .5, 1.5, Inf))
polyserial(x, y)  # 2-step estimate
polyserial(x, y, ML=TRUE, std.err=TRUE) # ML estimate