countbot {PResiduals}

Conditional count by ordinal tests for association.

Description

countbot tests for independence between an ordered categorical variable, X, and a count variable, Y, conditional on other variables, Z. The basic approach involves fitting an ordinal model of X on Z, a Poisson or Negative Binomial 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 Pearson residual for the count outcome model and a latent variable residual for the ordinal model (Li C and Shepherd BE, 2012).

Usage

countbot(
  formula,
  data,
  link.x = c("logit", "probit", "loglog", "cloglog", "cauchit"),
  fit.y = c("poisson", "negative binomial"),
  subset,
  na.action = getOption("na.action"),
  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 countbot is called.

link.x

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’.

fit.y

The error distribution for the count model of Y on Z. Defaults to ‘⁠poisson⁠’. The other option is ‘⁠negative binomial⁠’. If ‘⁠negative binomial⁠’ is specified, glm.nb is called to fit the count model.

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.

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 hypothesis to be tested is H_0 : X independent of Y conditional on Z. The ordinal variable, X, must precede the | and be a factor variable, and Y must be an integer.

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)
countbot(x|c ~z, fit.y="poisson",data=PResidData)
countbot(x|c ~z, fit.y="negative binomial",data=PResidData)