Refer to Exercise 12 in Chapter 4. Plot standardized residuals vs. the 1-2-3-4-5 scores for political ideology. Which models examined in this previous exercise fit the data reasonably well?
Exercise 12
The purpose of this problem is to further investigate the political ideology data of Section 4.2.6.
(a) Refit the model in Equation 4.11 by trying different score sets for I in the P I interaction as suggested in the example (0-2-3-4-6 and 2-1-0-1-2). Do any of them fit as well as 1-2-3-4-5?
(b) Consider the ordinality of I in the GI interaction.
i. Starting from Equation 4.11 consider all three score sets for GI. Compare deviances for these models to the one for Equation
4.11 to see whether the reduced number of parameters in each still provides an adequate explanation for the association.
ii. Is the association significant in each case?
(c) Use the GI linear association model with the smallest residual deviance from part (b) as the final model.
i. Estimate the GI odds ratio for a 1-unit difference in scores. Interpret what this measures and find the Wald confidence interval for the estimate.
ii. Compare the results of the ordinally estimated odds ratio to the nominal estimates obtained in the example on p. 237. In particular, compare the confidence intervals for each odds ratio. Do they give similar interpretations?
(d) Write a brief conclusion for the results of this analysis. Explain the nature of any associations that were found. Do not use mathematical symbols in this discussion.
