Consider data from the Low Birth Weight Study described in Section 1.6.2 and use as the outcome variable low birth weight (LOW) and race of the mother (RACE) as the covariate. (a) Prepare a table...

Consider data from the Low Birth Weight Study described in Section 1.6.2 and use as the outcome variable low birth weight (LOW) and race of the mother (RACE) as the covariate.

(a) Prepare a table showing the coding of the two design variables for RACE using the value RACE = 1, white, as the reference group. Show that the estimated log-odds ratios obtained from the cross-classification of LOW by RACE, using RACE = 1 as the reference group, are identical to estimated slope coefficients for the two design variables from the logistic regression of LOW on RACE. Verify that the estimated standard errors of the estimated slope coefficients for the two design variables for RACE are identical to the square root of the sum of the inverse of the cell frequencies from the cross-classification of LOW by RACE used to calculate the odds ratio. Use either set of computations to compute the 95% confidence interval for the odds ratios. Note that in this example the results are significant at the 10 but not 5% level of significance. Explain circumstances under which you would choose to keep RACE in a statistical model and ones when you might not keep it.

(b) Create design variables for RACE using the deviation from means coding typically employed in ANOVA. Perform the logistic regression of LOW on RACE. Use the four-step method to compute the estimate of the odds ratio RACE = 2 versus RACE = 1 and RACE = 3 versus RACE = 1. Are these estimates the same as those computed in 2(a)? Use the results of the logistic regression to obtain the 95% confidence interval for the odds ratios and verify that they are the same limits as obtained in 2(a). In this example you need the estimated covariance matrix for the estimated coefficients to obtain the estimated variances of the two log-odds ratios.