R: Test of Proportion Homogeneity using Rao and Scott's...
raoscott
R Documentation
Test of Proportion Homogeneity using Rao and Scott's Adjustment
Description
Tests the homogeneity of proportions between I groups (H0: p_1 = p_2 = ... = p_I ) from clustered binomial
data (n, y) using the adjusted chi-squared statistic proposed by Rao and Scott (1993).
Usage
raoscott(formula = NULL, response = NULL, weights = NULL,
group = NULL, data, pooled = FALSE, deff = NULL)
Arguments
formula
An optional formula where the left-hand side is either a matrix of the form cbind(y, n-y),
where the modelled probability is y/n, or a vector of proportions to be modelled (y/n).
In both cases, the right-hand side must specify a single grouping variable. When the left-hand side of the formula
is a vector of proportions, the argument weight must be used to indicate the denominators of the
proportions.
response
An optional argument: either a matrix of the form cbind(y, n-y), where the modelled probability
is y/n, or a vector of proportions to be modelled (y/n).
weights
An optional argument used when the left-hand side of formula or response is a vector
of proportions: weight is the denominator of the proportions.
group
An optional argument only used when response is used. In this case, this argument is a factor
indicating a grouping variable.
data
A data frame containing the response (n and y) and the grouping variable.
pooled
Logical indicating if a pooled design effect is estimated over the I groups.
deff
A numerical vector of I design effects.
Details
The method is based on the concepts of design effect and effective sample size.
The design effect in each group i is estimated by deff_i = vratio_i / vbin_i, where vratio_i is
the variance of the ratio estimate of the probability in group i (Cochran, 1999, p. 32 and p. 66)
and vbin_i is the standard binomial variance. A pooled design effect (i.e., over the I groups)
is estimated if argument pooled = TRUE (see Rao and Scott, 1993, Eq. 6). Fixed design effects can be specified
with the argument deff.
The deff_i are used to compute the effective sample sizes nadj_i = n_i / deff_i, the effective numbers
of successes yadj_i = y_i / deff_i in each group i, and the overall effective proportion
padj = sum(yadj_i) / sum(deff_i).
The test statistic is obtained by substituting these quantities in the usual chi-squared statistic,
yielding:
which is compared to a chi-squared distribution with I - 1 degrees of freedom.
Value
An object of formal class “drs”: see drs-class for details. The slot tab
provides the proportion of successes, the variances of the proportion and the design effect for each group.
Cochran, W.G., 1999, 2nd ed. Sampling techniques. John Wiley & Sons, New York.
Rao, J.N.K., Scott, A.J., 1992. A simple method for the analysis of clustered binary data.
Biometrics 48, 577-585.
See Also
chisq.test, donner, iccbin, drs-class
Examples
data(rats)
# deff by group
raoscott(cbind(y, n - y) ~ group, data = rats)
raoscott(y/n ~ group, weights = n, data = rats)
raoscott(response = cbind(y, n - y), group = group, data = rats)
raoscott(response = y/n, weights = n, group = group, data = rats)
# pooled deff
raoscott(cbind(y, n - y) ~ group, data = rats, pooled = TRUE)
# standard test
raoscott(cbind(y, n - y) ~ group, data = rats, deff = c(1, 1))
data(antibio)
raoscott(cbind(y, n - y) ~ treatment, data = antibio)