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
)object of cobot class.
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.
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
## The code is commented out because it will give a Fortran 90 runtime
## error due to the outdated version of Fortran 90 on CRAN's Debian test
## environment (11/2025).
#data(PResidData)
#cobot(x|y~z, data=PResidData)
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