# FINAL EXAM ISyE6420 Time to Second Birth

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## 1. Time to Second Birth.

The Medical Birth Registry of Norway was established in
1967 and contains information on all births in Norway since that time.1
The data set (given in a starter odc file secondbirth0.odc) provides the time between
first and second births for a selection of 16,341 Norwegian women. This time could be
possibly influenced by the age of mother and the fact that the firstborn child died within
one year of its birth.

The data set contains the following variables (as columns)
mage age of mother at first birth (in years)
death first child died within one year (0 = no, 1 = yes)
time time from first birth to second birth (in days)

(a) Using WinBUGS establish a regression model with variables mage and death as
covariates. What is the 95% CS for the slope β2 corresponding to variable death? Is this
variable significant?
(b) By analyzing β1, the coefficient of covariate mage, argue that age of mother is not
significant factor in influencing the response time.

(c) Helga is a mother with two children. The children are healthy and growing. Helga was
24 when her first child was born. What is the predicted time between the births according
(d) Emma lost her firstborn child at its birth when she was 28. She gave a birth to the
second child. What is the 95% CS for the predicted time between the births according to

Hint: Be careful: mean time and predicted time are not identical. Since sample size is
large, limit your MCMC to 10,000 max after the burn in.
1The Medical Birth Registry of Norway is acknowledged for allowing the usage of the data and Dr. Stein
Emil Vollset for providing the data.

## 2 Tasmanian Clouds.

The data clouds.csv|dat|xlsx provided by OzDASL were collected
in a cloud-seeding experiment in Tasmania between mid-1964 and January 1971. Analysis
of these data is discussed in Miller et al. (1979).
Figure 1: T-Rex Cloud Stomping over Tasmania

The rainfalls for target and control areas are given in inches. Variables TE and TW are
the east and west target areas, respectively, while CN, CS, and CNW are the corresponding
rainfalls in the north, south, and northwest control areas, respectively. S stands for seeded
and U for unseeded. Variables C and T are averages of control and target rainfalls. Variable
DIFF is the difference T – C.

(a) Provide a comprehensive Bayesian additive two-way ANOVA analysis on the response
DIFF to estimate and test the effects of factors Season and Seeded.
(b) Repeat the analysis from (a) after adding the interaction term.
Hint: Consult the Simvastatin example. You will need only three variables form the
data: Season, Seeded, and DIFF.

Recode the factor levels in Season and Seeded as numbers.
3
Miller Lumber Company Customer Survey. Kutner et al. (2005)2
analyze a data
set from a survey of customers of the Miller Lumber Company.

The response is the total
number of customers (in a representative 2-week period) coming from a census tract of a
metropolitan area within 10 miles from the store.
Figure 2: Miller Lumber Company

The covariates include five variables concerning the census tracts: number of housing
units, average income in dollars, average housing unit age in years, distance to nearest
competitor in miles, and distance to store in miles. Fit and assess a Poisson regression
model for the number of customers as predicted by the covariates. The data are in odc starter
file lumber0.odc and the variable are customers, hunits, aveinc, aveage, distcomp, and
diststore.

(a) Propose Poisson model with customers as response variable and hunits, aveinc,
aveage, distcomp, and diststore, as covariates. Use noninformative priors on regression
coefficients.
(b) If you are to propose a Poisson model with only two covariates which two you will