Dayton Student Survey on Substance Use
DaytonSurvey.RdThis data, from Agresti (2002), Table 9.1, gives the result of a 1992 survey in Dayton Ohio of 2276 high school seniors on whether they had ever used alcohol, cigarettes and marijuana.
Usage
data(DaytonSurvey)Format
A frequency data frame with 32 observations on the following 6 variables.
cigarettea factor with levels
YesNoalcohola factor with levels
YesNomarijuanaa factor with levels
YesNosexa factor with levels
femalemaleracea factor with levels
whiteotherFreqa numeric vector
Details
Agresti uses the letters G (sex), R (race),
A (alcohol), C (cigarette), M (marijuana) to refer to the table variables,
and this usage is followed in the examples below.
Background variables include sex and race of the
respondent (GR), typically treated as explanatory, so that any
model for the full table should include the term sex:race.
Models for the reduced table, collapsed over sex and race
are not entirely unreasonable, but don't permit the estimation
of the effects of these variables on the responses.
The full 5-way table contains a number of cells with counts of 0 or 1, as well as many cells with large counts, and even the ACM table collapsed over GR has some small cell counts. Consequently, residuals for these models in mosaic displays are best represented as standardized (adjusted) residuals.
Source
Agresti, A. (2002). Categorical Data Analysis, 2nd Ed., New York: Wiley-Interscience, Table 9.1, p. 362.
References
Thompson, L. (2009). R (and S-PLUS) Manual to Accompany Agresti's Categorical Data, http://www.stat.ufl.edu/~aa/cda/Thompson_manual.pdf
Examples
data(DaytonSurvey)
# mutual independence
mod.0 <- glm(Freq ~ ., data=DaytonSurvey, family=poisson)
# mutual independence + GR
mod.GR <- glm(Freq ~ . + sex*race, data=DaytonSurvey, family=poisson)
anova(mod.GR, 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 31 4818.1
#> cigarette 1 227.81 30 4590.2 < 2.2e-16 ***
#> alcohol 1 1281.71 29 3308.5 < 2.2e-16 ***
#> marijuana 1 55.91 28 3252.6 7.575e-14 ***
#> sex 1 0.57 27 3252.0 0.4505
#> race 1 1926.11 26 1325.9 < 2.2e-16 ***
#> sex:race 1 0.79 25 1325.1 0.3746
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# all two-way terms
mod.all2way <- glm(Freq ~ .^2, data=DaytonSurvey, family=poisson)
anova(mod.all2way, 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 31 4818.1
#> cigarette 1 227.81 30 4590.2 < 2.2e-16 ***
#> alcohol 1 1281.71 29 3308.5 < 2.2e-16 ***
#> marijuana 1 55.91 28 3252.6 7.575e-14 ***
#> sex 1 0.57 27 3252.0 0.450480
#> race 1 1926.11 26 1325.9 < 2.2e-16 ***
#> cigarette:alcohol 1 442.19 25 883.7 < 2.2e-16 ***
#> cigarette:marijuana 1 751.81 24 131.9 < 2.2e-16 ***
#> cigarette:sex 1 0.04 23 131.9 0.837426
#> cigarette:race 1 2.34 22 129.5 0.126405
#> alcohol:marijuana 1 91.64 21 37.9 < 2.2e-16 ***
#> alcohol:sex 1 2.22 20 35.7 0.136357
#> alcohol:race 1 6.50 19 29.2 0.010769 *
#> marijuana:sex 1 9.62 18 19.6 0.001926 **
#> marijuana:race 1 3.39 17 16.2 0.065758 .
#> sex:race 1 0.84 16 15.3 0.359722
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# compare models
LRstats(mod.0, mod.GR, mod.all2way)
#> Likelihood summary table:
#> AIC BIC LR Chisq Df Pr(>Chisq)
#> mod.0 1474.17 1482.96 1325.93 26 <2e-16 ***
#> mod.GR 1475.38 1485.64 1325.14 25 <2e-16 ***
#> mod.all2way 183.58 207.03 15.34 16 0.4999
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# collapse over sex and race
Dayton.ACM <- aggregate(Freq ~ cigarette+alcohol+marijuana,
data=DaytonSurvey,
FUN=sum)
Dayton.ACM
#> cigarette alcohol marijuana Freq
#> 1 Yes Yes Yes 911
#> 2 No Yes Yes 44
#> 3 Yes No Yes 3
#> 4 No No Yes 2
#> 5 Yes Yes No 538
#> 6 No Yes No 456
#> 7 Yes No No 43
#> 8 No No No 279