Assignment #6

PPol 604

Due: Thursday, 28 February 2013

Type up your answers. Give proper credit to those you work with and/or the text(s).

Solve the following problems. Show all of your work, but keep your answers concise. Highlight your (final) answer to distinguish it from your other numbers and text. Include a copy of your input (e.g. do file) or output (e.g. log file), when it is an appropriate way to show your work. However, do not include unnecessary output (i.e. no data dumps), and format any output so that it is easily readable. An appropriate time to include output is when you put your results in a table--if your results are wrong, then the grader has no idea how you came to your conclusions (i.e. give partial credit) unless you provide some output. Explanation includes statistical and substantive explanation (explain so that a statistical layperson can understand it, and so that a statistical analyst will see your erudition).

1. {5} Do Problem 2.4 in Rabe-Hesketh and Skrondal.
2. {15} Do Problem 2.5 in Rabe-Hesketh and Skrondal.
3. {45} Do Problem 3.3 in Rabe-Hesketh and Skrondal. Add the following within the problem parts:
   • After Part 1:
     • Plot the observed gpa trajectories: plot gpa against time
       • for the first 16 observations graphed separately [scatter y x if id <= n, by(id)]
       • for the first 16 observations on the same graph connecting successive observations on the same subject using connect(ascending) [scatter y x if id <= n, connect(ascending)]
       • for all observations on the same graph connecting successive observations on the same subject using connect(ascending)
       • What is the general pattern?
     • Fit a random-intercept model with gpa as the response variable and with no covariates. What are the estimated variance components between and within students? Obtain and explain the estimated intraclass correlation.
     • Include highgpa and a dummy variable for male. Discuss the changes in the estimated standard deviations of the random intercept and level-1 residual.
   • After Part 2:
     • Comment on how the estimated standard deviations have changed from the estimates after Part 1.
     • Obtain and explain the overall coefficient of determination R² for the model in Part 2.
     • Add the predicted mean trajectories to the graph of the observed gpa trajectories (after Part 1) using predict newvar, xb [scatter y newvar x]. How well does the model fit the data?
     • Add the predicted trajectories including the random effects to the graph of the observed gpa trajectories (after Part 1) using predict newvar, fitted. How well does the model fit the data? How does it compare to the model fit in the previous step? What is the difference?
   • After Part 5, obtain the histogram for the level-1 residuals [predict newvar, residuals] for the chosen model and assess their normality.
4. {15} Do Problem 3.7 in Rabe-Hesketh and Skrondal.
   • After Part 3, obtain the between and within estimates using xtreg with the be and fe options, respectively. Compare the estimates for the effect of education to the random-intercept model and regular regression model.
5. {20} Do Problem 3.8 in Rabe-Hesketh and Skrondal.
   • After Part 3, test the null hypothesis that the random-intercept variance is zero and explain the results.
   • After Part 4, explain why this test can be interpreted as an endogeneity test. Discuss what school-level omitted covariates might be responsible for the difference between the within-school and between-school effects.

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