关于算法:MAST30027现代应用统计

MAST30027: Modern Applied Statistics

Assignment 2, 2022.
Due: 11:59pm Sunday September 11th
This assignment is worth 7% of your total mark.
To get full marks, show your working including 1) R commands and outputs you use, 2)
mathematics derivation, and 3) rigorous explanation why you reach conclusions or answers.
If you just provide final answers, you will get zero mark.
The assignment you hand in must be typed (except for math formulas), and be submitted
using LMS as a single PDF document only (no other formats allowed). For math formulas,
you can take a picture of them. Your answers must be clearly numbered and in the same
order as the assignment questions.
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Note: There is no unique answer for this problem. The report for this problem
should be typed. Hand-written report or report including screen-captured R codes
or figures won’t be marked. An example report written by a student previous year
has been posted on LMS.
Data: The dataset comes from the Fiji Fertility Survey and shows data on the number of children
ever born to married women of the Indian race classified by duration since their first marriage
(grouped in six categories), type of place of residence (Suva, urban, and rural), and educational
level (classified in four categories: none, lower primary, upper primary, and secondary or higher).
The data can be found in the file assignment2 prob1.txt. The dataset has 70 rows representing
70 groups of families. Each row has entries for:
duration: marriage duration of mothers in each group (years),
residence: residence of families in each group (Suva, urban, rural),
education: education of mothers in each group (none, lower primary, upper primary, sec-
ondary+),
nChildren: number of children ever born in each group (e.g. 4), and
nMother: number of mothers in each group (e.g. 8).
1
We can summarise data as a table as follows.

data <- read.table(file =”assignment2_prob1.txt”, header=TRUE)
data$duration <- factor(data$duration, levels=c(“0-4″,”5-9″,”10-14″,”15-19″,”20-24″,”25-29”)
, ordered=TRUE)
data$residence <- factor(data$residence, levels=c(“Suva”, “urban”, “rural”))
data$education <- factor(data$education, levels=c(“none”, “lower”, “upper”, “sec+”))
ftable(xtabs(cbind(nChildren,nMother) ~ duration + residence + education, data))
nChildren nMother
duration residence education

Problem: We want to determine which factors (duration, residence, education) and two-way
interactions are related to the number of children per woman (fertility rate). The observed number
of children ever born in each group (nChildren) depends on the number of mothers (nMother) in
each group. We must take account of the difference in the number of mothers (hint: one of the lab
problems shows how to handle this issue). Write a report on the analysis that should summarie the
substantive conclusions and include the highlights of your analysis: for example, data visualisation,
choice of model (e.g., Poisson, binomial, gamma, etc), model fitting and model selection (e.g., using
AIC), diagnostic, check for overdispersion if necessary, and summary/interpretation of your final
model.
At each step of you analysis, you should write why you do that and your interpretation/conclusion.
For example,“I make an interaction plot to see whether there are interactions between X and Y”,
show a plot, and“It seems that there are some interaction between X and Y”.