residSVD: Multiplicative Approximation of Model Residuals

In gnm: Generalized Nonlinear Models

Multiplicative Approximation of Model Residuals

Description

This function uses the first d components of the singular value decomposition in order to approximate a vector of model residuals by a sum of d multiplicative terms, with the multiplicative structure determined by two specified factors.

Usage

residSVD(model, fac1, fac2, d = 1)

Arguments

model	a model object with na.action, residuals, and weights methods, e.g. objects inheriting from class "lm"
fac1	a factor
fac2	a factor
d	integer, the number of multiplicative terms to use in the approximation

Details

This function operates on the matrix of mean residuals, with rows indexed by fac1 and columns indexed by fac2. For glm and glm models, the matrix entries are weighted working residuals. The primary use of residSVD is to generate good starting values for the parameters in Mult terms in models to be fitted using gnm.

Value

If d = 1, a numeric vector; otherwise a numeric matrix with d columns.

Author(s)

David Firth and Heather Turner

See Also

gnm, Mult

Examples

set.seed(1)

##  Goodman RC1  association model fits well (deviance 3.57, df 8)
mentalHealth$MHS <- C(mentalHealth$MHS, treatment)
mentalHealth$SES <- C(mentalHealth$SES, treatment)
## independence model
indep <- gnm(count ~ SES + MHS, family = poisson, data = mentalHealth)
mult1 <- residSVD(indep, SES, MHS)
## Now use mult1 as starting values for the RC1 association parameters
RC1model <- update(indep, . ~ . + Mult(SES, MHS),
                   start = c(coef(indep), mult1), trace = TRUE)
##  Similarly for the RC2 model:
mult2 <- residSVD(indep, SES, MHS, d = 2)
RC2model <- update(indep, . ~ . + instances(Mult(SES, MHS), 2),
                   start = c(coef(indep), mult2), trace = TRUE)
##
## See also example(House2001), where good starting values matter much more!
##

gnm documentation built on Sept. 16, 2023, 5:06 p.m.