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.