MAST90139: Statistical Modelling for Data Science
Assignment 1
Due time: 5 pm Friday April 1, 2022.
Submit your assignment to Gradescope on the subject Canvas LMS.
In a study of the predictors of domestic violence, a survey was conducted among women, aged
18 and over, who attended a general practitioner in Metropolitan Melbourne between November
1993 and February 1994, and who had been in a relationship during the previous 12 months.
The “response” variable was whether or not the woman responded positively to questions about
physical domestic violence or mental abuse experienced during the previous 12 months. The
predictor variables considered included the following:
Age (in years) 0 = 18 – 29
1 = 30 – 49
2 = 50 – 64
3 = 65+
Current marital status 1 = married
2 = de Facto
3 = divorced
4 = separated
5 = widowed
6 = never married
Married/de Facto more than once 0 = yes
1 = no
Smoker 0 = yes
1 = no
Drinker (alcohol) 0 = < 8 drinks/week
1 = ≥ 8 drinks/week
Family member’s use of alcohol 0 = no
cause for concern when growing up 1 = yes
Number of years in formal education 0 = ≤ 6
1 = 7 – 11
2 = ≥ 12
Region 1 = north
2 = east
3 = south
4 = west
MAST90139 Semester 1, 2022 Assignment 1
The responses from 1316 women, for whom there were no missing values, have been stored in
file (domviolence.csv) which can be read into R using the command
domviolence <- read.csv(file="C:/subjects/MAST90139/data/domviolence.csv")
provided that domviolence.csv is on the path C:/subjects/MAST90139/data/. The file can be
found in the subject Canvas Module section.
The variable dv is the response variable: 0 = no; 1 = yes.
1. Carry out a series of data analysis using glm(), anova(), summary() and step() etc. to
argue that the “best” logistic model is of the form
logit(θ) = β0 + β1×ms.2+ β2×ms.3+ β3×ms.4+ β4×ms.5+ β5×ms.6
+β6×smok+ β7×falc+ β8×reg.2+ β9×reg.3+ β10×reg.4
+β11×age+ β12×educ+ β13×ms.2 : falc+ β14×ms.3 : falc
+β15×ms.4 : falc+ β16×ms.5 : falc+ β17×ms.6 : falc
where estimates of all βj in the above model can be obtained from the arguing process.
Present your work and results in no more than 300 words (excluding R outputs; the R outputs
should be presented as an appendix). [15]
Some suggestions:
(a) You can start the process by fitting a model0 that includes all predictor variables as
having main effects only. Then use anova(model0, test="Chi") alike commands re-
peatedly to remove any non-significant predictors. Note categorical predictors, e.g.
reg, should be treated as factors here and be included in the model in the form of e.g.
factor(reg). Denote as model1 after this process. Note model1 may also be obtained
by using commands model0.5 = step(model0) and anova(model0.5, test="Chi")
to remove any non-significant predictors.
(b) Even though age and education are observed as categorical variables, they are actually
numerical variables. Thus, replace factor(age) and factor(educ) with age and educ
in model1 to get model2. Then fit model2 to see whether it is significantly different from
model1 or not in terms of goodness of fit. Accept model2 if it is not significantly different
from model1, because model2 is simpler than model1 in terms of model complexity.
(c) Expand model2 to model3 that contains all predictors in model2 plus all their first-order
interaction terms. Perform model comparisons by anova(...) to simplify model3.
Alternatively, use step(model3) to select the stepwise “best” model. Denote the
resultant model as model4 and fit it. Then use anova(model4, test="Chi") and
summary(model4) to see whether it can be further simplified. You can use this eventu-
ally obtained model as the “best” model.
2. Suppose the “best” model is indeed the one shown above. Interpret this “best” model in
terms of odds ratios for each predictor in this mode. There will be many odds ratios to
be presented here. So it should be helpful to use tables or diagrams in your description.
Specifically, you can answer the question in following form: [15]
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MAST90139 Semester 1, 2022 Assignment 1
Marital status: Find the odds ratios involving ms by completing the following table
Odds ratios, at various levels of falc falc=0 falc=1
for ms=1 vs. ms=1
for ms=2 vs. ms=1
for ms=3 vs. ms=1
for ms=4 vs. ms=1
for ms=5 vs. ms=1
for ms=6 vs. ms=1
Then provide interpretations on two representative odds ratio values of your choice in the
above table.
Smoking: Find the odds ratio value in regard to smoking woman and interpret it.
Family alcohol: Find the odds ratios involving falc by completing the following table
Odds ratios, at various levels of ms ms=1 ms=2 ms=3 ms=4 ms=5 ms=6
for falc=0 vs. falc=0
for falc=1 vs. falc=0
Then interpret two representative odds ratio values of your choice in the above table.
Region: Find the odds ratios involving region by completing the following table
north east south west
Ratio of odds (OR) for each region vs. north
Then interpret two representative odds ratio values of your choice in the above table.
Age: Find the odds ratio associated with age and interpret it.
Education: Find the odds ratio associated with education and interpret it.
Total marks = 30
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