Refer to Problem 7.13 with Table 7.25.
a. Show that model (CE,CH,CL,EH,EL,HL) fits well. Show that model (CEH,CEL,CHL,EHL) also fits well but does not provide a significant improvement. Beginning with (CE,CH,CL,EH,EL,HL), show that backward elimination yields (CE,CL,EH,HL). Interpret its fit.
b. Based on the independence graph for (CE,CL,EH,HL), show that: (i) every path between C and H involves a variable in {E,L}; (ii) collapsing over H, one obtains the same associations between C and E and between C and L, and collapsing over C, one obtains the same associations between H and E and between H and L; (iii) the conditional independence patterns between C and H and between E and L are not collapsible.
Problem 7.13
Table 7.25 is from a General Social Survey. Subjects were asked about government spending on the environment (E), health (H), assistance to big cities (C), and law enforcement (L). The common response scale was (1 = too little,
2 = about right, 3 = too much).
a. Table 7.26 shows some results, including the two-factor estimates, for the homogeneous association model. All estimates at category 3 of each variable equal 0. Test the model goodness of fit, and interpret.
b. Explain why the estimated c nditional log odds ratio for the "too much" and "too little" categories of E and H equals which has estimated SE = 0.523. Show that a 95% confidence interval for the true odds ratio equals (3.1, 24.4). Interpret.
c. Estimate the conditional odds ratios using the "too much" and "too little" categories for each of the other pairs of variables. Summarize the associations. Based on these results, which term(s) might you consider dropping from the model? Why?
