Generalize the model considered in Example 4.11 to a marginal model for the longitudinal DOS data and compare the findings with that in Example4.11

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Example 4.11 For the models in Example 4.8 DOS, there are several independent variables. Since age, education, and CIRS are continuous covariates, we may use the Hosmer-Lemeshow test to assess goodness of fit of the model. To apply the Hosmer-Lemeshow test, we first divide the subjects into ten groups and then compute the XL statistic and compare it against a chi-square distribution with eight degrees of freedom to determine the p-value. Shown in the table below are the observed (O), expected (E), and related quantities needed to compute this statistic when the logit link function is applied. Dep=1 (O-E)/E 2.507502 Dep = 0 Group Total O E 0 E (O-E)/E 1 73 5 10.01 68 62.99 0.398478 2 73 13 14.39 0.134267 60 58.61 0.032965 134567819 74 21 18.06 0.478605 53 55.94 0.154516 73 25 20.68 0.902437 48 52.32 0.356697 73 26 23.60 0.244068 47 49.40 0.116599 73 73 33 29.43 28 26.47 0.088436 45 46.53 0.050309 0.433058 40 43.57 0.292515 73 28 32.73 0.683559 45 40.27 0.555572 73 34 37.49 0.324889 39 35.51 0.343005 10 73 47 47.15 0.000477 26 25.85 0.000870 0.4240. Thus, we will not The Hosmer Lemeshow statistic is 8.0974 with a p-value reject the good fit of the model. If the probit and complementary log-log link function are used, the Hosmer Lemeshow statistics are 7.0048 and 8.3057 with p-values 0.5361 and 0.4042, respectively. Thus, no issue of goodness of fit is detected by the Hosmer-Lemeshow test for the three link functions. I