MATH5945: Categorical Data Analysis
Term 3, 2023
Assignment 1 Submission deadline: Thursday 28 September, 4:05pm
Deliverables: 2 files uploaded to Moodle: (1) PDF file of your worked solutions, and (2) SAS file for ALL computations. Files names should be surname firstname z123456789 ASS1.
Assignment length: There is a 5 page limit and minimum 12pt font size. Any pages exceeding this limit or submissions with smaller font sizes will not be marked. Handwritten assignments will not be accepted. This does not include a SAS file of your code. Your document should begin with the Plagiarism Statement below (copy-and-paste it).
SAS code: All computations must be performed using SAS. Your SAS code must run as is and I should not need to modify your code in any way to make it work. You may create a library to import data, but any other code should only use the WORK library (you may assume data files of the same name are in my WORK library). SAS should be used for computing only and answers given only within SAS code will not be marked.
Penalties: Failure to adhere to instructions will result in a minimum 5% mark reduction.
Student Number:
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Code Help
1. In a study by Brown et al (2023) published in the journal Traffic Injury Prevention, data were collected on the proper use of a child restraint system in a motor vehicle. One outcome measure for this study was whether there were errors in the installation or use of a child restraint system. Data collection occurred both before and during the COVID-19 pandemic. Study participants were originally randomly selected from a target population; however, this changed to convenience sampling due to COVID-19 restrictions.
A 2 × 2 table for number of vehicles with any errors by the sampling method is given below.
Sampling Method Any Error Random Convenience Yes 123 115 No 12 26
(a) Create a SAS data set for the child restraint system data.
(b) Is there evidence that reported child restraint errors are associated with sampling method? Be sure to provide the results for the strength of association (and measure of uncertainty), and the results of an appropriate statistical test.
2. The probability mass function (pmf) for the non-central hypergeometric distribution is n1 n2ψa
P(a) = Pau n1 n2 ψx
x=al x m1−x
where al = max{0, n1 − m2}, au = min{n1, m1} and ψ is the odds ratio. This can be
considered a likelihood function for ψ.
(a) Write out the log-likelihood function for ψ.
(b) Derive the score function for ψ, U (ψ) = d log L(ψ)/dψ.
(c) Write out the observed score function using the AIDS/HIV data from the lecture notes.
(d) The MLE for ψ is the solution to U(ψˆ) = 0 which cannot be solved directly here. To find a solution, follow these steps:
i. Compute the odds ratio the usual way as a cross-product ratio.
ii. Create a SAS data file for values for ψ on either side of your estimate from part (i) with an appropriate resolution, and compute the score U(ψ) at each of those values given the observed table.
iii. Use SGPLOT to create a line graph of U(ψ) versus ψ.
iv. Print out values from your data set where U(ψ) is closest to 0. The value for
ψ is your estimated MLE of ψ. 2
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(e) Now, using a similar approach to (d) using the AIDS/HIV data, find the values ψl and ψu that satisfy the equations for a 95% confidence interval
X P(x; ψu) = 0.025
X P(a; ψl) = 0.025 x=a
(f) Use PROC FREQ to check your results for a 95% confidence interval for ψ (note that SAS will not compute the MLE ψˆ).
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