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R代寫--MATH 5885

UNSW SCIENCE

School of Mathematics and Statistics

MATH5885 Longitudinal Data Analysis

Term 2 2021 Assignment 2

? Due Sunday, 23:59, 18th July (end of Week 7). The assignment should be submitted via the Assignment tool. This tool is accessible via a clearly indicated link in the Assessments subfolder on moodle. Please, add a cover page containing a copy of your ID card, and write with your own handwriting:

“I declare that this assignment is my own work, except where acknowledged and I have read and understood the University rules regarding Academic Misconduct”, and sign it.

? Question 2 is theoretical and prepares the way for Lectures in Week 7 onwards. It can be done using the hints provided and general concepts of distributions and expectations.

1. (FOUR PAGES MAX) Refer to the VV study, which we considered in Lecture 2 of Week 4. Provide a report in which you summarize your conclusions from the following analyses:

(d) Look at the estimate of the unstructured covariance matrix. A possible simplification is compound symmetry. Using the linear in time model for the fixed effects, compare these two covariance models using the likelihood ratio test (after fitting the models using REML). Report the p-value and your decision.

(e) Create a model with a change in trend at year = 3. This model should be specified so that the linear model of lectures is a special case (i.e., it is nested within this model). Fit this model and compare your results with part (b). Specify the likelihood ratio test of the null hypothesis that the change in trend is not required. Perform also the similar Wald test and compare the results. Are the change in trend terms required?

(g) For the choice of covariance model you selected in part (f), can you write down a mixed effects model of the type considered in Week 5, Lecture 2 that would give this covariance structure? Explain why or why not.

2. (THREE PAGES MAX) Recall that if X ～ N n (μ,Σ), then the moment generating function of X is  #### 在線客服  Essay_Cheery  