cocobot {PResiduals}

Conditional continuous by ordinal tests for association.

Description

cocobot tests for independence between an ordered categorical variable, X, and a continuous variable, Y, conditional on other variables, Z. The basic approach involves fitting an ordinal model of X on Z, a linear model of Y on Z, and then determining whether there is any residual information between X and Y. This is done by computing residuals for both models, calculating their correlation, and testing the null of no residual correlation. This procedure is analogous to test statistic T2 in cobot. Two test statistics (correlations) are currently output. The first is the correlation between probability-scale residuals. The second is the correlation between the observed-minus-expected residual for the continuous outcome model and a latent variable residual for the ordinal model (Li C and Shepherd BE, 2012).

Usage

cocobot(
  formula,
  data,
  link = c("logit", "probit", "cloglog", "loglog", "cauchit"),
  subset,
  na.action = getOption("na.action"),
  emp = TRUE,
  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’.

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 cocobot is called.

link

The link family to be used for the ordinal model of X on Z. Defaults to ‘⁠logit⁠’. Other options are ‘⁠probit⁠’, ‘⁠cloglog⁠’, ‘⁠loglog⁠’, and ‘⁠cauchit⁠’.

subset

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

na.action

action to take when NA present in data.

emp

logical indicating whether the residuals from the model of Y on Z are computed based on the assumption of normality (FALSE) or empirically (TRUE).

fisher

logical indicating whether to apply fisher transformation to compute confidence intervals and p-values for the correlation.

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. The ordinal variable, X, must precede the | and be a factor variable, and Y must be continuous.

Value

object of ‘⁠cocobot⁠’ class.

References

Li C and Shepherd BE (2012) A new residual for ordinal outcomes. Biometrika. 99: 473–480.

Shepherd BE, Li C, Liu Q (2016) Probability-scale residuals for continuous, discrete, and censored data. The Canadian Journal of Statistics. 44: 463–479.

Examples

data(PResidData)
cocobot(y|w ~ z, data=PResidData)