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Homework 2, Mixed effects models
STA 442 Methods of Applied Statistics
Due 16 Oct 2019
Math (10 marks)
data("MathAchieve", package = "MEMSS")
head(MathAchieve)
School Minority Sex SES MathAch MEANSES
1 1224 No Female -1.528 5.876 -0.428
2 1224 No Female -0.588 19.708 -0.428
3 1224 No Male -0.528 20.349 -0.428
4 1224 No Male -0.668 8.781 -0.428
5 1224 No Male -0.158 17.898 -0.428
6 1224 No Male 0.022 4.583 -0.428
From Maindonald and Braun, ch 10 q 5. In the data set MathAchieve (MEMSS package),
the factors Minority (levels yes and no), and the variable SES (socio-economic status) are
clearly fixed effects. Carry out an analysis that treats School as a random effect. Does
it appear that there are substantial differences between schools, or are differences within
schools nearly as big as differences between students from different schools? Write a short
report ( a single page of text plus a few graphs).
Q3: Drugs (20 marks)
http://www.icpsr.umich.edu/icpsrweb/ICPSR/studies/35074
The Treatment Episode Data Set – Discharges (TEDS-D) is a national census data system of
annual discharges from substance abuse treatment facilities. TEDS-D provides annual data
on the number and characteristics of persons discharged from public and private substance
abuse treatment programs that receive public funding.
download.file("http://pbrown.ca/teaching/appliedstats/data/drugs.rds",
"drugs.rds")
xSub = readRDS("drugs.rds")
table(xSub$SUB1)
(4) MARIJUANA/HASHISH (2) ALCOHOL
188406 97013
(5) HEROIN (7) OTHER OPIATES AND SYNTHETICS
58511 45609
(10) METHAMPHETAMINE (3) COCAINE/CRACK
21606 11333
table(xSub$STFIPS)[1:5]
(1) ALABAMA (2) ALASKA (4) ARIZONA (5) ARKANSAS (6) CALIFORNIA
616 1360 4479 1508 48065
table(xSub$TOWN)[1:2]
ABILENE, TX AKRON, OH
42 1078
Each row of the dataset corresponds to an individual admitted to a drug or alcohol addiction
treatment facility. The variables above are:
• completed is TRUE if the individual in question completed their treatment and FALSE
otherwise.
• SUB1 is the substance which was the individual’s primary addiction.
• GENDER, AGE, raceEthnicity are the individuals age, gender and ethnicity, known to
be important confounders.
• STFIPS, TOWN, the US state and town in which the treatment was given.
Write a short report addressing the hypothesis that chance of a young person completing their
drug treatment depends on the substance the individual is addicted to, with ‘hard’ drugs
(Heroin, Opiates, Methamphetamine, Cocaine) being more difficult to treat than alcohol or
marijuana. A secondary hypothesis is that some American states have particularly effective
treatment programs whereas other states have programs which are highly problematic with
very low completion rates.
The report should be on the order of four paragraphs: introduction, methods, results, conclusions.
Not more than two pages of text, closer to one page is better.
Some code below may or may not be helpful.
forInla = na.omit(xSub)
forInla$y = as.numeric(forInla$completed)
library("INLA")
ires = inla(y ~ SUB1 + GENDER + raceEthnicity + homeless +
2
f(STFIPS, hyper=list(prec=list(
prior='pc.prec', param=c(0.1, 0.05)))) +
f(TOWN),
data=forInla, family='binomial',
control.inla = list(strategy='gaussian', int.strategy='eb'))
sdState = Pmisc::priorPostSd(ires)
do.call(matplot, sdState$STFIPS$matplot)
do.call(legend, sdState$legend)
0.4 0.5 0.6 0.7 0.8
0 2 4 6
sd
dens
prior
posterior
Figure 1: State-level standard deviation
toPrint = as.data.frame(rbind(exp(ires$summary.fixed[,
c(4, 3, 5)]), sdState$summary[, c(4, 3, 5)]))
sss = "^(raceEthnicity|SUB1|GENDER|homeless|SD)(.[[:digit:]]+.[[:space:]]+| for )?"
toPrint = cbind(variable = gsub(paste0(sss, ".*"),
"\\1", rownames(toPrint)), category = substr(gsub(sss,
"", rownames(toPrint)), 1, 25), toPrint)
Pmisc::mdTable(toPrint, digits = 3, mdToTex = TRUE,
guessGroup = TRUE, caption = "Posterior means and quantiles for model parameters.")
ires$summary.random$STFIPS$ID = gsub("[[:punct:]]|[[:digit:]]",
"", ires$summary.random$STFIPS$ID)
ires$summary.random$STFIPS$ID = gsub("DISTRICT OF COLUMBIA",
"WASHINGTON DC", ires$summary.random$STFIPS$ID)
toprint = cbind(ires$summary.random$STFIPS[1:26, c(1,
2, 4, 6)], ires$summary.random$STFIPS[-(1:26),
c(1, 2, 4, 6)])
colnames(toprint) = gsub("uant", "", colnames(toprint))
knitr::kable(toprint, digits = 1, format = "latex")
3
Table 1: Posterior means and quantiles for model parameters.
0.5quant 0.025quant 0.975quant
(Intercept)
(Intercept) 0.682 0.562 0.826
SUB1
ALCOHOL 1.642 1.608 1.677
HEROIN 0.898 0.875 0.921
OTHER OPIATES AND SYNTHET 0.924 0.898 0.952
METHAMPHETAMINE 0.982 0.944 1.022
COCAINE/CRACK 0.876 0.834 0.920
GENDER
FEMALE 0.895 0.880 0.910
raceEthnicity
Hispanic 0.829 0.810 0.849
BLACK OR AFRICAN AMERICAN 0.685 0.669 0.702
AMERICAN INDIAN (OTHER TH 0.730 0.680 0.782
OTHER SINGLE RACE 0.864 0.810 0.920
TWO OR MORE RACES 0.851 0.790 0.917
ASIAN 1.133 1.038 1.236
NATIVE HAWAIIAN OR OTHER 0.847 0.750 0.955
ASIAN OR PACIFIC ISLANDER 1.451 1.225 1.720
ALASKA NATIVE (ALEUT, ESK 0.844 0.623 1.143
homeless
TRUE 1.015 0.983 1.048
SD
STFIPS 0.581 0.482 0.698
TOWN 0.537 0.482 0.597
ID mean 0.025q 0.975q ID mean 0.025q 0.975q
ALABAMA 0.2 -0.3 0.7 MONTANA -0.2 -1.0 0.6
ALASKA 0.0 -0.8 0.8 NEBRASKA 0.8 0.4 1.2
ARIZONA 0.0 -1.1 1.1 NEVADA -0.1 -0.8 0.5

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