Miscellaneous Topics in Regression

This chapter discusses different regression methods in detail. Quantile regression is similar to piecewise regression because there is the capability of looking at different models for different ordered response values. In piecewise regression this is done by using intervals of the response variable, whereas in quantile regression it is done by using a specified quantile. Like logistic regression, Poisson regression is an iterative procedure, with the maximum likelihood estimates obtained using iteratively reweighted least squares. Negative binomial regression is used when the response values are counts but the variation in the data is greater than the variation for a Poisson random variable. Censored regression is similar to truncated regression, with the difference being that in censored regression no observations on the dependent variable are deleted; they are simply assigned the value at the censoring point. With multivariate regression, two or more dependent variables are jointly regressed against the same set of independent variables.