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Last data update: 2014.03.03

R: Heterogeneous Correlation Matrix

hetcor

R Documentation

Heterogeneous Correlation Matrix

Description

Computes a heterogenous correlation matrix, consisting of Pearson product-moment correlations between numeric variables, polyserial correlations between numeric and ordinal variables, and polychoric correlations between ordinal variables.

Usage

hetcor(data, ..., ML = FALSE, std.err = TRUE, bins=4, pd=TRUE)
## S3 method for class 'data.frame'
hetcor(data, ML = FALSE, std.err = TRUE, 
  use = c("complete.obs", "pairwise.complete.obs"), bins=4, pd=TRUE, ...)
## Default S3 method:
hetcor(data, ..., ML = FALSE, std.err = TRUE, bins=4, pd=TRUE)
## S3 method for class 'hetcor'
print(x, digits = max(3, getOption("digits") - 3), ...)
## S3 method for class 'hetcor'
as.matrix(x, ...)

Arguments

`data`	a data frame consisting of factors, ordered factors, logical variables, and/or numeric variables, or the first of several variables.
`...`	variables and/or arguments to be passed down.
`ML`	if `TRUE`, compute maximum-likelihood estimates; if `FALSE`, compute quick two-step estimates.
`std.err`	if `TRUE`, compute standard errors.
`bins`	number of bins to use for continuous variables in testing bivariate normality; the default is 4.
`pd`	if `TRUE` and if the correlation matrix is not positive-definite, an attempt will be made to adjust it to a positive-definite matrix, using the `nearcor` function in the `sfsmisc` package. Note that default arguments to `nearcor` are used; for more control call `nearcor` directly.
`use`	if `"complete.obs"`, remove observations with any missing data; if `"pairwise.complete.obs"`, compute each correlation using all observations with valid data for that pair of variables.
`x`	an object of class `"hetcor"` to be printed, or from which to extract the correlation matrix.
`digits`	number of significant digits.

Value

Returns an object of class "hetcor" with the following components:

`correlations`	the correlation matrix.
`type`	the type of each correlation: `"Pearson"`, `"Polychoric"`, or `"Polyserial"`.
`std.errors`	the standard errors of the correlations, if requested.
`n`	the number (or numbers) of observations on which the correlations are based.
`tests`	p-values for tests of bivariate normality for each pair of variables.
`NA.method`	the method by which any missing data were handled: `"complete.obs"` or `"pairwise.complete.obs"`.
`ML`	`TRUE` for ML estimates, `FALSE` for two-step estimates.

Note

Although the function reports standard errors for product-moment correlations, transformations (the most well known is Fisher's z-transformation) are available that make the approach to asymptotic normality much more rapid.

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.

Olsson, U. (1979) Maximum likelihood estimation of the polychoric correlation coefficient. Psychometrika 44, 443-460.

Rodriguez, R.N. (1982) Correlation. Pp. 193-204 in S. Kotz and N. Johnson, eds., The Encyclopedia of Statistics, Volume 2. Wiley.

Ghosh, B.K. (1966) Asymptotic expansion for the moments of the distribution of correlation coefficient. Biometrika 53, 258-262.

Olkin, I., and Pratt, J.W. (1958) Unbiased estimation of certain correlation coefficients. Annals of Mathematical Statistics 29, 201-211.

Examples

set.seed(12345)
R <- matrix(0, 4, 4)
R[upper.tri(R)] <- runif(6)
diag(R) <- 1
R <- cov2cor(t(R) %*% R)
round(R, 4)  # population correlations
data <- rmvnorm(1000, rep(0, 4), R)
round(cor(data), 4)   # sample correlations
x1 <- data[,1]
x2 <- data[,2]
y1 <- cut(data[,3], c(-Inf, .75, Inf))
y2 <- cut(data[,4], c(-Inf, -1, .5, 1.5, Inf))
data <- data.frame(x1, x2, y1, y2)
hetcor(data)  # Pearson, polychoric, and polyserial correlations, 2-step est.
hetcor(x1, x2, y1, y2, ML=TRUE) # Pearson, polychoric, polyserial correlations, ML est.