| mentalHealth {gnm} | R Documentation |
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).
data(mentalHealth)
A data frame with 24 observations on the following 3 variables.
countSESA < B < C < D < E < FMHSwell < mild < moderate < impairedFrom Agresti (2002, p381); originally in Srole et al. (1978, p289).
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.
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(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))
rowScores <- coef(RC1model)[pickCoef(RC1model, "[.]SES")]
colScores <- coef(RC1model)[pickCoef(RC1model, "[.]MHS")]
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)