Homework 2, Mixed effects models Solution

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Description

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”)

1

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, con-clusions. 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)

prior

posterior

6

dens4

2

0

0.4

0.5

0.6

0.7

0.8

sd

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)]))

  1. = “^(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

4

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

5