mentalHealth | 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`

).

mentalHealth

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`

From 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) ## 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)

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