gnm (version 1.0-7)

meanResiduals: Average Residuals within Factor Levels

Description

Computes the mean working residuals from a model fitted using Iterative Weighted Least Squares for each level of a factor or interaction of factors.

Usage

meanResiduals(object, by, standardized=TRUE, as.table=TRUE, ...)

Arguments

object

model object for which object$residuals gives the working residuals and object$weights gives the working weights.

by

either a formula specifying a factor or interaction of factors (recommended), or a list of factors (the elements of which must correspond exactly to observations in the model frame). When a list of factors is specified, their interaction is us

standardized

logical: if TRUE, the mean residuals are standardized to be approximately standard normal.

as.table

logical: logical: if TRUE and by specifies an interaction of factors, the result is returned as a table cross-classified by these factors.

...

currently ignored

Value

• An object of class "meanResiduals", for which print and summary methods are provided. A "meanResiduals" object is a list containing the following elements:
• call
  the call used to create the model object from which the mean residuals are derived.
• by
  a label for the grouping factor.
• residuals
  the mean residuals.
• df
  the degrees of freedom associated with the mean residuals.
• standardized
  the standardized argument.
• weights
  the weights corresponding to the mean residuals.

Details

For level $i$ of the grouping factor $A$ the mean working residual is defined as $$\frac{r_{ij} * w_{ij}}{\sum_{j = 1}^{n_i} w_{ij}}$$ where $r_{ij}$ is the $j$'th residual for level $i$, $w_{ij}$ is the corresponding working weight and $n_i$ is the number of observations for level $i$. The denominator gives the weight corresponding to mean residual.

For non-aggregated residuals, i.e. when the factor has one level per observation, the residuals are the same as Pearson residuals.

Examples

data(yaish)
## Fit a conditional independence model, leaving out
## the uninformative subtable for dest == 7:
CImodel <- gnm(Freq ~ educ*orig + educ*dest, family = poisson,
               data = yaish, subset = (dest != 7))

## compute mean residuals over origin and destination
meanRes <- meanResiduals(CImodel, ~ orig:dest)
meanRes
summary(meanRes)

## requires vcdExtra package
## display mean residuals for origin and destination
library(vcdExtra)
mosaic(CImodel, ~orig+dest)

## non-aggregated residuals
res1 <- meanResiduals(CImodel, ~ educ:orig:dest)
res2 <- residuals(CImodel, type = "pearson")
all.equal(as.numeric(res1), as.numeric(res2))