National University of Singapore
Department of Statistics and Applied Probability
ST5213 Categorial Data Analysis II
Assignment 2
Important: This assignment accounts for 20% of your final grade. Your work for this
assignment must be uploaded onto the LumNUS submission folder by 7 pm 5 April 2021
(Monday). Any student failing to submit work by the deadline will receive a penalty
for late submission unless the lecturer is advised as soon as possible of any extenuating
circumstances. Please upload a single pdf file labeled using your student number, e.g.,
A0123456M.pdf.
Plagiarism: The work that you submit must be your sole effort (i.e. not copied from
anyone else). You may be severely penalized If found guilty of plagiarism.
The two assignment tasks involve the analysis of some data and you should submit a
formal report for each task.
Format: The report for each task should not exceed two pages of A4 paper in-
cluding any relevant figures or tables. The first 4 pages should consist of your reports for
the two tasks. R code and output should be attached as appendix after these four pages.
Please write down your name and student number at the top of the first page. Do not
include any cover page. Please use Times New Roman font (11-12 point). You may be
penalized for exceeding the page limit or if any of the above instructions are not followed.
The aim of the report is to convey the methodology and results of your data analysis
in a clear and concise manner with appropriate use of figures or tables for summarization.
Marks will be awarded for
• Exposition: your report should be well-organized. You should aim to write in a clear
and concise manner.
• Statistical content: marks will be awarded for the correct use of appropriate statis-
tical techniques, and for the correct interpretation of results from these techniques.
• Completeness: ensure that you have answered all the parts of each question.
Note: All results must be included in the report itself and not in the appendix. You
will be assessed based on the report alone. I will refer to your R code and output only if
I wish to locate any source of error.
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Task 1. A cohort study in South Africa is designed to follow children born between
April and June 1990 in hopes of identifying risk factors for cardiovascular disease. After
five years, the children were invited to participate in interviews. Many children did not
participate in these interviews, leaving open the possibility of biases if inferences were
made based on those who participated. Morrell (1999) gave data comparing the children
who participated to those who did not with respect to whether the mother had medical
aid at the time of birth.
(a) Based on the information in Table 1, use Pearson’s Chi-square test to determine if
there is evidence of a relationship between medical aid status and participation in
the interviews. Compute the marginal odds ratio between medical aid status and
participation in the interviews and interpret.
No interview Interview
Had medical aid 195 46
No medical aid 979 370
Table 1
(b) The study further classified children by their racial group, with the results given
in Tables 2 and 3. Use Fisher’s exact test to determine if there is evidence of a
relationship between medical aid status and participation in the interviews for (i)
white children and (ii) black children. Explain how the probabilities of the observed
tables and p-values are computed in Fisher’s exact test. Compute the conditional
odds ratios between medical aid status and participation in the interviews given race
and interpret.
White children
No interview Interview
Had medical aid 104 10
No medical aid 22 2
Table 2
Black children
No interview Interview
Had medical aid 91 36
No medical aid 957 368
Table 3
(c) Explain why the marginal association is so different from the conditional associations.
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Task 2. The following are data on smoking from a survey of seventh graders (age: 1 =
12 or younger, 2 =13 or older):
Smoking
Family structure Race Gender Age None Some
Both parents
Black Male 1 27 2
2 12 2
Female 1 23 4
2 7 1
White Male 1 394 32
2 142 19
Female 1 421 38
2 94 11
Mother only
Black Male 1 18 1
2 13 1
Female 1 24 0
2 4 3
White Male 1 48 6
2 25 4
Female 1 55 15
2 13 4
Search for the loglinear model that can best explain the association patterns in the
contingency table by treating
(a) smoking and family structure as response variables and the rest as explanatory vari-
ables.
(b) smoking as a response variable and the rest as explanatory variables.
In each case,
i. State the minimal model.
ii. Give the symbol for the loglinear model that best describes the data and explain how
it was built. Write down the coefficients of the fitted model.
iii. Represent the conditional independence structure in the loglinear model using an
association graph and explain whether it is a graphical model. Give the symbol of
another model that has the same association graph, but is not a graphical model.
iv. Interpret the associations in the loglinear model, taking into account conditional
independence, collapsibility and odds ratios.
v. Explain whether the zero cell in the contingency table affects your analysis.
vi. State the logit model equivalent to the selected loglinear model for (b).
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