cobot tests for independence between two ordered categorical
variables, X and Y conditional on other variables,
Z. The basic approach involves fitting models of X on
Z and Y on Z and determining whether there is any
remaining information between X and Y. This is done by
computing one of 3 test statistics. T1 compares empirical
distribution of X and Y with the joint fitted
distribution of X and Y under independence conditional
on Z. T2 computes the correlation between ordinal
(probability-scale) residuals from both models and tests the null
of no residual correlation. T3 evaluates the
concordance--disconcordance of data drawn from the joint fitted
distribution of X and Y under conditional independence
with the empirical distribution. Details are given in Li C and
Shepherd BE, Test of association between two ordinal variables
while adjusting for covariates. Journal of the American Statistical
Association 2010, 105:612-620.
cobot(
formula,
link = c("logit", "probit", "cloglog", "loglog", "cauchit"),
link.x = link,
link.y = link,
data,
subset,
na.action = na.fail,
fisher = TRUE,
conf.int = 0.95
)an object of class Formula (or one
that can be coerced to that class): a symbolic description of the
model to be fitted. The details of model specification are given
under ‘Details’.
The link family to be used for ordinal models of both X and Y. Defaults to logit. Other options are probit, cloglog,loglog, and cauchit.
The link function to be used for a model of the first
ordered variable. Defaults to value of link.
The link function to be used for a model of the
second variable. Defaults to value of link.
an optional data frame, list or environment (or object
coercible by as.data.frame to a data frame)
containing the variables in the model. If not found in
data, the variables are taken from
environment(formula), typically the environment from which
cobot is called.
an optional vector specifying a subset of observations to be used in the fitting process.
how NAs are treated.
logical; if TRUE, Fisher transformation and delta method a
used to compute p value for the test statistic based on correlation of
residuals.
numeric specifying confidence interval coverage.
object of cobot class.
formula is specified as X | Y ~ Z.
This indicates that models of X ~ Z and
Y ~ Z will be fit. The null hypothsis to be
tested is \(H_0 : X\) independant of Y conditional
on Z.
Note that T2 can be thought of as an adjusted rank
correlation.(Li C and Shepherd BE, A new residual for ordinal
outcomes. Biometrika 2012; 99:473-480)
Li C and Shepherd BE, Test of association between two ordinal variables while adjusting for covariates. Journal of the American Statistical Association 2010, 105:612-620.
Li C and Shepherd BE, A new residual for ordinal outcomes. Biometrika 2012; 99:473-480
# NOT RUN {
data(PResidData)
cobot(x|y~z, data=PResidData)
# }
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