Specify based on the data set given:

1. livewred = 1 if livewith = 1 or 2
   2 if livewith = 3
   3 if livewith = 4, 5, 6, 7, 8 or 9
   99 if livewith = 99
2. agegrp = 1 if age < 18 (10-17)

2 if 17 < age < 99 (18-25)

99 if age = 99

Remove the cases with livewred = 99. (There are none with agegrp = 99.)

1. Using the software of your choice, with complex survey capabilities,

declare the two variables above to be categorical or class variables, and fit the model

logit(prob( everviol = 1)) = \[\alpha +{{\beta }_{1}}*livewre{{d}_{1}}+{{\beta }_{2}}*livewre{{d}_{2}}+{{\beta }_{3}}*agegr{{p}_{2}}\]

where \[livewre{{d}_{1}}=1\] if livewred =1 and 0 otherwise; similarly for the other two explanatory variables. (This means that the reference level for livewred is 3 and the reference level for agegrp is 1.) Declare the stratum variable to be \[stratum\] , the cluster variable to be \[cluster1\] , and the weight variable to be \[finalwt\] . Display the coefficient estimates and their estimated standard errors. For a youth in the population who lived with grandparents growing up and is 19 years old, what is the estimated probability from the model that everviol =1?

(b) In the model of (a), it can be said that \[{{\beta }_{2}}\] is a log (odds ratio). Explain what odds ratio is being referred to here.

(c) Using the bootstrap weight columns btwt1 to btwt10, but without using stratum and cluster information, fit the same model as in (a) 10 times. This will give you 10 estimates of \[{{\beta }_{3}}\] . Compute the sample standard error of these estimates. This estimates the standard error of \[{{\hat{\beta }}_{3}}\] from (a) in a different way. Compare the two estimated standard errors.

(d) The bootstrap weight columns btwt1 to btwt10 are computed according to the Rao- Wu formula; the bootstrap weight columns btwtc1 to btwtc10 are calibrated with respect to sex and agegrp . Using the second set of bootstrap weights, fit the same model as in (a) 10 times and compute the sample standard error of the estimates of \[{{\beta }_{3}}\] . Is there much of a change from the bootstrap standard error in (c)? Comment on the difference.

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