Computes the polychoric correlation (and its standard error)
between two ordinal variables or from their contingency table, under the
assumption that the ordinal variables dissect continuous latent variables that are bivariate normal. Either
the maximum-likelihood estimator or a (possibly much) 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
polychor(x, y, ML = FALSE, control = list(), std.err = FALSE, maxcor=.9999)
Arguments
x
a contingency table of counts or an ordered categorical variable; the latter can be numeric, logical, a factor,
or an ordered factor, but if a factor, its levels should be in proper order.
y
if x is a variable, a second ordered categorical variable.
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 (for the ML estimator) of the correlation and thresholds; the default is FALSE.
maxcor
maximum absolute correlation (to insure numerical stability).
Value
If std.err is TRUE,
returns an object of class "polycor" with the following components:
type
set to "polychoric".
rho
the polychoric correlation.
row.cuts
estimated thresholds for the row variable (x), for the ML estimate.
col.cuts
estimated thresholds for the column variable (y), for the ML estimate.
var
the estimated variance of the correlation, or, for the ML estimate,
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.