Description Usage Arguments Details Value Author(s) References See Also Examples
Computes the polyserial correlation (and its standard error) between a quantitative variable and an ordinal variable, 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.
1 2 |
x |
a numerical variable. |
y |
an ordered categorical variable; can be numeric, logical, a factor, an ordered factor, or a character variables, but if a factor, its levels should be in proper order, and the values of a character variable are ordered alphabetically. |
ML |
if |
control |
optional arguments to be passed to the |
std.err |
if |
maxcor |
maximum absolute correlation (to insure numerical stability). |
bins |
the number of bins into which to dissect |
start |
optional start value(s): if a single number, start value for the correlation; if a list with the elements |
thresholds |
if |
The ML estimator is computed by maximizing the bivariate-normal likelihood with respect to the
thresholds for y (τ^y[j], j = 1,…, c - 1) and
the population correlation (ρ). The likelihood is maximized numerically using the optim
function,
and the covariance matrix of the estimated parameters is based on the numerical Hessian computed by optim
.
The two-step estimator is computed by first estimating the thresholds
(τ^y[j], j = 1,…, c - 1)
from the marginal distribution of y. Then if the standard error of ρ hat is requested, the
one-dimensional likelihood for ρ is maximized numerically, using optim
if standard errors are
requested; the standard error computed treats the thresholds as fixed. If the standard error isn't request,
ρ hat is computed directly.
If std.err
or thresholds
is TRUE
,
returns an object of class "polycor"
with the following components:
type |
set to |
rho |
the polyserial correlation. |
cuts |
estimated thresholds for the ordinal variable ( |
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 |
|
Othewise, returns the polyserial correlation.
John Fox jfox@mcmaster.ca
Drasgow, F. (1986) Polychoric and polyserial correlations. Pp. 68–74 in S. Kotz and N. Johnson, eds., The Encyclopedia of Statistics, Volume 7. Wiley.
hetcor
, polychor
, print.polycor
,
optim
1 2 3 4 5 6 7 8 9 10 11 12 13 14 | if(require(mvtnorm)){
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
}
if(require(mvtnorm)){
y <- cut(y, c(-Inf, -1, .5, 1.5, Inf))
polyserial(x, y) # 2-step estimate
}
if(require(mvtnorm)){
polyserial(x, y, ML=TRUE, std.err=TRUE) # ML estimate
}
|
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