Description
Logistic Regression (* A type of Generalized Linear Model) with the bwt Data
The bwt data is a built in R dataset containing 9 variables and 189 cases – please see the following link for detailed description:
http://garthtarr.github.io/mplot/articles/birthweight.html
Your task is to use the other 8 variables to predict the binary dependent variable ‘low’ that indicates whether a given infant was born with low birth weight or not.
You can follow the detailed description of related methods in the following paper:
http://atm.amegroups.com/article/view/9706/pdf
Please note that for the logistic regression model, one does not use the coefficient of determination for model selection, but rather, one should use the information criterion, typically either the AIC, or the BIC.
They are both functions of the likelihood albeit with the opposite signs from the likelihood:
https://en.wikipedia.org/wiki/Bayesian_information_criterion
https://en.wikipedia.org/wiki/Akaike_information_criterion
Since a larger likelihood corresponds to a better model, a smaller AIC or BIC will correspond to a better model. The BIC will usually results in a smaller model, hence more robust and preferred than the AIC.
- Please find a model that best predicts whether the infant would be born with low birth weight or not using the stepwise variable selection method and the BIC. Please only use the original variables and no need to include any other variables such as interactions. Please report the final model and the associated BIC value.
- Please find a model that best predicts whether the infant would be born with low birth weight or not using the stepwise variable selection method and the BIC. Please use the original variables plus all the two-way interactions. Please report the final model and the associated BIC value. (*Please always remember that if an interaction term is found significant, then one must include both original variables even if they are not significant.)
- Please find a model that best predicts whether the infant would be born with low birth weight or not using the best subset variable selection method and the BIC. Please only use the original variables and no need to include any other variables such as interactions. Please report the final model and the associated BIC value.
- Please find a model that best predicts whether the infant would be born with low birth weight or not using the best subset variable selection method and the BIC. Please use the original variables plus all the two-way interactions. Please report the final model and the associated BIC value. (*Please always remember that if an interaction term is found significant, then one must include both original variables even if one/both is/are not significant.)
- Among all the models selected in steps 1, 2, 3, 4 above, which one is the best and why?