A 6 x 4 contingency table representing the cross-classification of mental
health status (mental) of 1660 young New York residents by their
parents' socioeconomic status (ses).
Format
A data frame frequency table with 24 observations on the following 3 variables.
sesan ordered factor with levels
1<2<3<4<5<6mentalan ordered factor with levels
Well<Mild<Moderate<ImpairedFreqcell frequency: a numeric vector
Source
Haberman, S. J. The Analysis of Qualitative Data: New Developments, Academic Press, 1979, Vol. II, p. 375.
Srole, L.; Langner, T. S.; Michael, S. T.; Kirkpatrick, P.; Opler, M. K. & Rennie, T. A. C. Mental Health in the Metropolis: The Midtown Manhattan Study, NYU Press, 1978, p. 289
Details
Both ses and mental can be treated as ordered factors or
integer scores. For ses, 1="High" and 6="Low".
Examples
data(Mental)
str(Mental)
#> 'data.frame': 24 obs. of 3 variables:
#> $ ses : Ord.factor w/ 6 levels "1"<"2"<"3"<"4"<..: 1 1 1 1 2 2 2 2 3 3 ...
#> $ mental: Ord.factor w/ 4 levels "Well"<"Mild"<..: 1 2 3 4 1 2 3 4 1 2 ...
#> $ Freq : int 64 94 58 46 57 94 54 40 57 105 ...
(Mental.tab <- xtabs(Freq ~ ses + mental, data=Mental))
#> mental
#> ses Well Mild Moderate Impaired
#> 1 64 94 58 46
#> 2 57 94 54 40
#> 3 57 105 65 60
#> 4 72 141 77 94
#> 5 36 97 54 78
#> 6 21 71 54 71
# mosaic and sieve plots
mosaic(Mental.tab, gp=shading_Friendly)
sieve(Mental.tab, gp=shading_Friendly)
if(require(ca)){
plot(ca(Mental.tab), main="Mental impairment & SES", lines=TRUE)
}
# fit linear x linear (uniform) association model, using integer scores
# for rows/cols
indep <- glm(Freq ~ mental + ses, family = poisson, data = Mental)
Cscore <- as.numeric(Mental$ses)
Rscore <- as.numeric(Mental$mental)
linlin <- glm(Freq ~ mental + ses + Rscore:Cscore,
family = poisson, data = Mental)
anova(linlin, test = "Chisq")
#> Analysis of Deviance Table
#>
#> Model: poisson, link: log
#>
#> Response: Freq
#>
#> Terms added sequentially (first to last)
#>
#>
#> Df Deviance Resid. Df Resid. Dev Pr(>Chi)
#> NULL 23 217.400
#> mental 3 113.525 20 103.875 < 2.2e-16 ***
#> ses 5 56.457 15 47.418 6.543e-11 ***
#> Rscore:Cscore 1 37.523 14 9.895 9.035e-10 ***
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
# use update.glm method to fit other models
linlin <- update(indep, . ~ . + Rscore:Cscore)
roweff <- update(indep, . ~ . + mental:Cscore)
coleff <- update(indep, . ~ . + Rscore:ses)
rowcol <- update(indep, . ~ . + Rscore:ses + mental:Cscore)
# compare models
LRstats(indep, linlin, roweff, coleff, rowcol)
#> Likelihood summary table:
#> AIC BIC LR Chisq Df Pr(>Chisq)
#> indep 209.59 220.19 47.418 15 3.155e-05 ***
#> linlin 174.07 185.85 9.895 14 0.7698
#> roweff 174.45 188.59 6.281 12 0.9013
#> coleff 179.00 195.50 6.829 10 0.7415
#> rowcol 179.22 198.07 3.045 8 0.9315
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
# tests of nested models
anova(indep, linlin, roweff, test = "Chisq")
#> Analysis of Deviance Table
#>
#> Model 1: Freq ~ mental + ses
#> Model 2: Freq ~ mental + ses + Rscore:Cscore
#> Model 3: Freq ~ mental + ses + mental:Cscore
#> Resid. Df Resid. Dev Df Deviance Pr(>Chi)
#> 1 15 47.418
#> 2 14 9.895 1 37.523 9.035e-10 ***
#> 3 12 6.281 2 3.614 0.1641
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1