megabot {PResiduals}

Conditional tests for association.

Description

megabot tests for correlation between a variable, X, and another variable, Y, conditional on other variables, Z. The basic approach involves fitting an specified model of X on Z, a specified model of Y on Z, and then determining whether there is any remaining 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. The test statistic output is the correlation between probability-scale residuals. X and Y can be continous or ordered discrete variables. megabot replicates the functionality of cobot, cocobot, and countbot

Usage

megabot(
  formula,
  data,
  fit.x,
  fit.y,
  link.x = c("logit", "probit", "cloglog", "loglog", "cauchit", "logistic"),
  link.y = c("logit", "probit", "cloglog", "loglog", "cauchit", "logistic"),
  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 megabot is called.

fit.x, fit.y

The fitting function used for the model of X or Y on Z. Options are ‘⁠ordinal⁠’, ‘⁠lm⁠’, ‘⁠lm.emp⁠’, ‘⁠poisson⁠’, ‘⁠nb⁠’, and ‘⁠orm⁠’.

link.x, link.y

The link family to be used for the ordinal model of X on Z. Defaults to ‘⁠logit⁠’. Other options are ‘⁠probit⁠’, ‘⁠cloglog⁠’,‘⁠loglog⁠’, ‘⁠cauchit⁠’, and ‘⁠logistic⁠’(equivalent with ‘⁠logit⁠’). Used only when ‘⁠fit.x⁠’ is either ‘⁠ordinal⁠’ or ‘⁠orm⁠’.

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.

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)
megabot(y|w ~ z, fit.x="ordinal", fit.y="lm.emp", data=PResidData)