cobot {PResiduals}

Conditional ordinal by ordinal tests for association.

Description

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.

Usage

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
)

Arguments

formula

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’.

link

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’.

link.x

The link function to be used for a model of the first ordered variable. Defaults to value of link.

link.y

The link function to be used for a model of the second variable. Defaults to value of link.

data

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.

subset

an optional vector specifying a subset of observations to be used in the fitting process.

na.action

how NAs are treated.

fisher

logical; if TRUE, Fisher transformation and delta method a used to compute p value for the test statistic based on correlation of residuals.

conf.int

numeric specifying confidence interval coverage.

Details

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)

Value

object of ‘⁠cobot⁠’ class.

References

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

See Also

Formula, as.data.frame

Examples

data(PResidData)
cobot(x|y~z, data=PResidData)