Homework 2, Mixed effects models Solution

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)]))

= "^(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




















































































































































































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