STAT7111: Compute the AIS code - The Logistic Regression - Statistics Assignment Help

Assignment Task

Instructions 
• There is a limit of 15 pages for your submission. There will be a 10% penalty if your submission is 16 pages long and another 10% penalty if your submission is 17 pages long. After that, there will be 1% penalty for each CHARACTER (space included) from page 18 onwards. 
• All R related questions must be word-processed (preferably using R markdown & knitting directly into a pdf file; word-processed 6= Microsoft Word processed) and written in Times New Roman with font 12pt size (or equivalent default from markdwon). Pages should have a margin of at least 1cm in all sides. This is to discourage you from trying to squeeze as much content as possible within the page limit without thinking what should be included in your submission. 
• All pages should be numbered. 
• If possible, answer questions in the same order as they appear in the assignment sheet. If this is not possible, highlight (e.g., bold text) which question you are answering clearly to allow the assessor(s) to identify which question you are referring to. 
• When building a model, do not present interim models. Explain your model-building strategy and give a summary of your results in a table. While you should present only your final model in detail, make sure to provide enough information for the assessor(s) to evaluate the quality of all models. 
• You should include all important R output in your write up. Any R output provided in the appendix will not be marked. 
• Give your R code in an appendix. This is not counted in the page limit. However, keep in mind that the aim is to keep the assignment as short as it can be. 
• You should submit the assignment using the Turnitin tool on iLearn. 
Question 1 
Recall from Assignment 2 we started the analysis of some data_ecology data. Please refer back to Assignment 2 for the context and the dataset. One possible model you may have considered in Assignment 2 is the following logistic model: 
a) Plot the observed values versus the precipitation together with 
• fitted values of the logistic regression above; and 
• a spline or any appropriate non-parametric curve; 
and comment on the appropriateness of the logistic regression above. 
b) Fit two new models: a quadratic and a cubic model in precipitation and write down their fitted model equations. 
c) Compare the three models: linear, quadratic and cubic, using model selection criterion. Which one would you recommend? 
d) Comment the performance of your final model based on: 
• a classification table; 
• the corresponding sensitivity and specificity; and 
• a ROC curve. 
e) Conduct a likelihood ratio test to compare the quadratic and the cubic model. What would be the conclusion? 
f) Fit an appropriate generalized additive model and then compare to your chosen model in part c). 
Question 2 
As part of a road safety experiment, cars containing dummies in the driver or front passenger seat were crashed into a wall at 56 km per hour. National Transportation Safety Board officials collected information on how the crash affected the dummies. The relevant injury variable is the Head Injury Criterion (HIC)1. The data file, crash.csv, also contains information on the type and safety features of each crashed car: 
What you have to do: 
a) Compute the AIS code and give the corresponding frequency table. 
• Comment on how many missing values in the AIS code column. 
• Any category that has less than 20 observations should be combined with the neighbouring category in a sensible way. 
b) Using the covariates dp and weight only and as provided, i.e. no need to consider transformation, higher-order terms or interaction effects of them, fit an appropriate ordinal regression model for AIS code by assuming the proportional odds assumption is valid. 
• Write down one of the estimated model equations and interpret the parameters in the model equation. 
c) Using the covariates dp and weight only and as provided, i.e. no need to consider transformation, higher-order terms or interaction effects of them, fit an appropriate nominal regression model for AIS code. Use AIS code = 1 as your reference response category. 

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