gnm (version 0.8-1)

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

data(mentalHealth)

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)
data(mentalHealth)

##  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(-1 + SES, -1 + MHS),
                family = poisson, data = mentalHealth)
## Row scores are parameters coef(RC1model)[10:15]
## Column scores are coef(RC1model)[16:19]
## -- 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))
rowScores <- coef(RC1model)[10:15]
colScores <- coef(RC1model)[16:19]
rowScores <- rowScores - sum(rowScores * rowProbs)
colScores <- colScores - sum(colScores * colProbs)
beta1 <- sqrt(sum(rowScores^2 * rowProbs))
beta2 <- sqrt(sum(colScores^2 * colProbs))
assoc <- list(beta = beta1 * beta2,
              mu = rowScores / beta1,
              nu = colScores / beta2)