Show all necessary Stata output and commands used in answering the questions. ? Answer the question asked and justify your answer. This will usually require reference to and interpretation of relevant parts of the Stata output you have provided. ? Occasional manual calculations may be required but only show these if specifically asked. ? Use Stata to create any graphs. Resize your graphs appropriately so that more than one will fit to a page. ? You need to effectively communicate the results of your analyses. Thus the presentation of your assignment, such as the formatting and how you express yourself, may affect your mark
Questiona. [2 marks] Using the mixed command with an unstructured residual covariance matrix, fit a linear model to model the change in the measured bmd with the visit number where visit is treated as a categorical variable. Your model should include group and a group x visit interaction term. Provide appropriate graphs (or graph) that show(s) the variation in individuals as well as the predicted means based on this model. (Hint: Although you are using the mixed command, none of your models should use random effects. The dependency between repeated measures is modelled by specifying a covariance structure for the model residuals.) b. [2 marks] The model in part a can be considered a “maximal” model for the mean in this study. Using the mixed command with this maximal model for the mean, fit additional models using the compound symmetry and first order autoregressive covariance structures. Use the estat wcorrelation command in Stata to ‘display model-implied within-cluster correlations and standard deviations’ for each of the three models fitted so far in this question. Comment on the similarities or differences between these. c. [1 mark] Which of these three covariance structures is ‘best’ for modeling the residuals from these models. (Hint: Your answer to part b may give some insight but appropriate hypothesis tests together with assessment of the Akaike Information Criterion (AIC) may also be useful for assessing which of the covariance structures tried is most appropriate.) d. [3 marks] Using the covariance structure you determined as “best” in part c, fit two additional models for the mean using a linear trend and a quadratic trend in visit number. Which of the three models for the mean is most appropriate? Why? (Hint: You should ‘center’ the visit variable before fitting the quadratic trend model. For example, create a new variable using gen visit3=visit-3. AIC, appropriate hypothesis tests and/or residual plots may be useful to justify your answer.) e. [2 mark] Does the way the measured bmd changes with visit differ with treatment group? Justify your answer using appropriate hypothesis tests based on the model you have assessed as “best” in part d. Also comment on the size of the effect. (Note: Although I expect they will give similar results, both Wald and likelihood ratio tests are required for full marks.) f. [1 mark] Compare the part d model using a linear trend to the linear trend model from Question 1 fitted using the regress command. Is there much difference in the parameters and their standard errors? Does this match your expectations? g. [1 mark] The calcium_Stata12.dta data set available on Blackboard is exactly the same data but is already in long form, some of the variables are expressed slightly differently, and it also contains the actual age of the girls at each visit. How might your analysis change if you were to use age rather than the visit number as your longitudinal variable? Which approach is more appropriate?