Can you please provide as much explanation as possible in every question within page limits. 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 (
View complete question Can you please provide as much explanation as possible in every question within page limits. 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: presi _ B(pi) independently, for i = 1, . . . , n where pi = E[presi = 1|prcpi ] = P[presi = 1|prcpi ] is link to prcpi through logit(pi) = _0 + _1 _prcpi 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? 1 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: Variable Description dp whether the dummy is in the driver or passenger seat weight weight of car (pounds) head_ic Head Injury Criterion In this question, we are interested in categorising the HIC into AIS codes2 , in increasing level of severity, as follows: HIC AIS code Description 135519 1 Headache or dizziness 520899 2 Unconscious less than 1 hour – linear fracture 9001254 3 Unconscious 1 – 6 hours – depressed fracture 12551574 4 Unconscious 6 – 24 hours- open fracture 15751859 5 Unconscious greater than 25 hours – large haematoma 1860 6 Non survivable 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. 1Consult http://en.wikipedia.org/wiki/Head_injury_criterion for the definition of the HIC. 2See http://www.eurailsafe.net/subsites/operas/HTML/Section3/Page220.127.116.11.htm 2 Write down the estimated model equation relating outcome AIS code = 2 to the reference outcome then interpret the parameters in the model equation. Question 3 We have data on the number of doctor visits for a sample of German male individuals in 1994. The data set is a subsample of the German Socioeconomic Panel (SOEP). The variable of interest is the number of doctor visits in the last three months. The data are available in file doc_visits.csv. For each observation, the following variables were recorded: Variable Description doc_visits number of doctor visits in last 3 months health health satisfaction score, 0 (low) – 10 (high) age50 TRUE if age is greater than 50 schooling years of schooling a) In a statistical model for the number of doctor visits, visualise the response variable and explain whether zero-inflated models should be considered. b) Model the number of doctor visits based on the ZINBI family with the gamlss package using the covariates as provided. What you have/dont have to do for the model building: Please provide the usual data visualisation and the corresponding comments. There is no need to consider transformation, higher-order (or smoothed) terms or interaction effects of them. You can also treat health as a continuous variable. There is no need to perform any single variable selection. You can leave the shape and the zero-inflation parameters as constants, i.e. you dont have to link them with any covariates. You may find functions such as drop1All() and stepGAIC() useful. For your final model: Write down the fitted model equation(s). Interpret the model parameter(s).
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