Heterogeneous Correlation Matrix

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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

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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 nearPD function in the Matrix package. Note that default arguments to nearPD are used (except corr=TRUE); for more control call nearPD 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.

See Also

polychor, polyserial, nearPD

Examples

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if(require(mvtnorm)){
    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
    }
if(require(mvtnorm)){
    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.
    }
if(require(mvtnorm)){
    hetcor(x1, x2, y1, y2, ML=TRUE) # Pearson, polychoric, polyserial correlations, ML est.
    }

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