GV900: Political Explanation - Logit Model Of Passenger Survival - Statistics Assignment Help

Political  Logit Model Of Passenger Statistics Assignment Help

Assignment Task: (a) Estimate a logit model of passenger survival where survived is the dependent vari-able and fare, female, and child are the independent variables. [7 points] (b) The fare variable is highly right-skewed (you could see this if you draw a histogram of it). That is, more than 80% of the passengers have a ticket worth less than 50 pounds, and less than 10% of the passengers have a ticket worth more than 100 pounds. When an independent variable is right skewed, we should try including the log transformed variable instead of the original variable to construct a better-tting model. Estimate another logit model by including the natural log of the fare variable instead of the original fare variable. Hint 1: the range of the fare variable is between 0 and 512. Since log(0) is undened, use log(fare + 1) instead. Hint 2: you should use the I() function when including the logged fare variable in a regression model (i.e., rather than creating a logged variable manually before estimation). This is to make the graphical interpretation (which we will do later) easier. (c) Produce a stargazer table summarizing the results from the two models estimated above. (d) According to the model t statistics, which model performs the better? Provide your answer in your R le as a comment. It goes without saying that you need to tell me the basis of your judgement as well. Your explanation here could be very brief (one sentence will do). (e) Produce two effect graphs that show the substantive eect of fare on passenger survival, one based on the rst model and the other based on the second model, holding all the other independent variables constant at their median value. Hint: Make sure that the x-axis of the second graph ranges between 0 and 500 (covering the range of the original fare variable), not between 0 and 6 (covering the range of the log transformed fare variable). If you have correctly used the I() function in 1-(b), you don't need to do anything special here. However, if your x-axis ranges between 0 and 6, you may want to go back to 1-(b) and correct it. (f) Compare the two graphs. Both graphs are somewhat non-linear, but one graph is more linear than the other (i.e., one graph is more non-linear than the other). The two graphs thus tell us dierent stories about the marginal effect of fare on passenger survival. Discuss this dierence (provide your answer in your R le as a comment) in ve sentences (You will lose points if you have more than ve sentences or less than ve sentences). Your discussion should have the following structure. Say something along the lines of: \The graph with the original fare variable suggests that the effect of fare on survival is linear / non-linear (choose one). That is (explain what a linear or non-linear relationship means in this context). On the other hand, the graph with the logged fare variable suggests that the effect of fare is linear / non- linear (choose one). That is (explain what a linear / non-linear relationship means in this context). Based on the model t statistics, we should believe the rst / second (choose one) story to be more plausible." (g) One way to understand the substantive importance of the fare variable would be to see how much this variable improves predictive abilities of the models. We can do so by comparing ROC curves with and without the logged fare variable. To do so, let's rst estimate a logit model that does not include the logged fare variable while retaining the female and child variables. Hint: You need to use a subset of the data where there is no missing value forthe fare variable. This is because we would like to ensure our comparison below is going to be based on the same set of observations. (h) Produce a stargazer table that contrasts the models you estimated in 1-(g) and another model that includes logged fare, female, and child that you estimated in 1-(b) Hint: Check if the two models have the same number of observations. If not, you probably did not use a subset of the data properly in 1-(g). Go back and correct it. (i) Produce a graph for ROC curves for these two models (i.e., the model that includes logged fare and the model that does not include fare). [7 points] Hint 1: Try to produce one graph that shows two ROC curves in one graph. (j) Report AUC scores for the two models. That is, write a command that gives us AUC scores for the two models. Hint 1: AUC = Area under the ROC curve, which is dierent from AIC = Akaike information criteria. (k) Based on the ROC curves and AUC scores you produced in 1-(i) and 1-(j), which model performs better? Your answer must be based on your interpretation of the ROC curves and/or the AUC scores (both will lead you to the same conclusion). Provide your answer in your R le as a comment. This could be very brief (two or three sentences will do). Read the following article and complete the following two tasks: Michael W. Doyle and Nicholas Sambanis. \International Peacebuilding: A Theo- retical and Quantitative Analysis." American Political Science Review, Vol. 94, No. 4 (Dec., 2000), pp. 779{801. The replication dataset for this article (peacebuilding.dta), the accompanying codebook (datanotes finalv2.pdf), as well as the article are available on Moodle. The data set contains numerous variables. To identify which variables are necessary for this assignment, you must refer to the codebook. (a) Replicate Table 2 on page 788 [10 points] The resulting regression table you produce should look like Table 1 in the Appendix of this document. That is, you need to do at least the following.  Run six logit models (Models A, B, C, D, E, F).  Produce a stargazer output that summarizes the estimated coecients, the number of observations, log likelihood, and AIC scores from the six models in a single table.

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