npANCOVA (version 0.1.1)

Hettmansperger_McKean: Hettmansperger and McKean Method for ANCOVA

Description

Applies rank-based residual analysis for ANCOVA. This method involves fitting a model of the response on the covariate, calculating residuals, ranking them, and then performing an ANOVA on the (weighted) ranked residuals.

Usage

Hettmansperger_McKean(data, formula)

Value

A list containing the following components:

regression_equation_covariate

The summary of the initial model fitting response on covariates.

regression_equation_residuals

The summary of the model fitting weighted ranked residuals on the group.

anova

The ANOVA table for the model based on weighted ranked residuals.

group_means

A data frame of the mean of weighted ranked residuals for each group.

group_sds

A data frame of the standard deviation of weighted ranked residuals for each group.

data

The original data frame augmented with residuals, ranked residuals, and weighted ranked residuals.

Arguments

data

A data frame containing the variables specified in the formula.

formula

An object of class "formula": a symbolic description of the model to be fitted. The structure should be `response ~ covariate1 + ... + group`.

References

Hettmansperger TP, McKean JWJT. A robust alternative based on ranks to least squares in analyzing linear models. 1977;19(3):275-84.

Hettmansperger TP, McKean JWJJotASA. A geometric interpretation of inferences based on ranks in the linear model. 1983;78(384):885-93.

Examples

# 1. Create a sample data frame
data <- data.frame(
  group = c(1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3),
  response = c(16, 60, 82, 126, 137, 44, 67, 87, 100, 142, 17, 28, 105, 149, 160),
  covariate1 = c(26, 10, 42, 49, 55, 21, 28, 5, 12, 58, 1, 19, 41, 48, 35),
  covariate2 = c(12, 21, 24, 29, 34, 17, 2, 40, 38, 36, 8, 1, 9, 28, 16)
)

# 2. Run the Hettmansperger and McKean method
results <- Hettmansperger_McKean(
  formula = response ~ covariate1 + covariate2 + group,
  data = data
)

# 3. View the results
print(results)
print(results$anova)