Polychotomous logistic regression via the Lasso

grantor: University of TorontoThe maximum likelihood method is traditionally used in estimating parameters in polychotomous logistic regression. The resulting estimates are known to have optimal theoretical properties in large samples but are prone to problems such as high variances in data multicollinearity, non-existence and small sample bias. In this thesis, alternative estimators for the polychotomous logistic regression are obtained via the Lasso. Lasso (Least Absolute Shrinkage Selection Operator) was invented by Tibshirani (1994) in the context of least squares regression. A defining characteristic of Lasso is its ability to produce parameter estimates which are identically equal to zero. A general Lasso model is proposed which involves shrinking all possible pairwise logits for each covariate in the model towards zero. Three realizations of the general model are considered, each motivated by a different data situation. Technical details necessary for the solving of the Lasso solutions and for fine-tuning the Lasso shrinkage are given. Approximate estimates of standard errors of the Lasso parameters are also proposed. An extensive simulation study is carried out to compare the performance of Lasso estimates to maximum likelihood estimates, as well as to Ridge estimates under a wide range of data situations. Finally, two Lasso polychotomous models are used to analyze two real life data sets.Ph.D