gnm: mentalHealth – R documentation

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mentalHealth

Data on Mental Health and Socioeconomic Status

Description

A 2-way contingency table from a sample of residents of Manhattan. Classifying variables are child's mental impairment (MHS) and parents' socioeconomic status (SES).

Usage

mentalHealth

Format

A data frame with 24 observations on the following 3 variables.

count: a numeric vector
SES: an ordered factor with levels A < B < C < D < E < F
MHS: an ordered factor with levels well < mild < moderate < impaired

Source

From Agresti (2002, p381); originally in Srole et al. (1978, p289).

References

Agresti, A. (2002). Categorical Data Analysis (2nd edn). New York: Wiley.

Srole, L, Langner, T. S., Michael, S. T., Opler, M. K. and Rennie, T. A. C. (1978), Mental Health in the Metropolis: The Midtown Manhattan Study. New York: NYU Press.

Examples

set.seed(1)

##  Goodman Row-Column association model fits well (deviance 3.57, df 8)
mentalHealth$MHS <- C(mentalHealth$MHS, treatment)
mentalHealth$SES <- C(mentalHealth$SES, treatment)
RC1model <- gnm(count ~ SES + MHS + Mult(SES, MHS),
                family = poisson, data = mentalHealth)
## Row scores and column scores are both unnormalized in this
## parameterization of the model 

## The scores can be normalized as in Agresti's eqn (9.15):
rowProbs <- with(mentalHealth, tapply(count, SES, sum) / sum(count))
colProbs <- with(mentalHealth, tapply(count, MHS, sum) / sum(count))
mu <- getContrasts(RC1model, pickCoef(RC1model, "[.]SES"),
                   ref = rowProbs, scaleRef = rowProbs,
                   scaleWeights = rowProbs)
nu <- getContrasts(RC1model, pickCoef(RC1model, "[.]MHS"),
                   ref = colProbs, scaleRef = colProbs,
                   scaleWeights = colProbs)
all.equal(sum(mu$qv[,1] * rowProbs), 0)
all.equal(sum(nu$qv[,1] * colProbs), 0)
all.equal(sum(mu$qv[,1]^2 * rowProbs), 1)
all.equal(sum(nu$qv[,1]^2 * colProbs), 1)

gnm

Generalized Nonlinear Models

v1.1-1

GPL-2 | GPL-3

Authors

Heather Turner [aut, cre] (<https://orcid.org/0000-0002-1256-3375>), David Firth [aut] (<https://orcid.org/0000-0003-0302-2312>), Brian Ripley [ctb], Bill Venables [ctb], Douglas M. Bates [ctb], Martin Maechler [ctb] (<https://orcid.org/0000-0002-8685-9910>)

Initial release