REGRESSION DIAGNOSTICS: MECHANICAL AND STRUCTURAL ASPECTS OF COLLINEARITY (COX REGRESSION, PROPORTIONAL HAZARDS MODEL, BUCKLEY-JAMES MODEL

One of the problems that can undermine the estimation of parameters for a statistical model is when two or more of the explanatory variables are correlated. The presence of this collinearity causes an instability in the estimation of the parameters in the model and may even cause a change in the sign of the estimate. Another important consideration when building a statistical model, is the assessment of the individual effect of each observation on the final parameter estimate.;In order to assess the potential effect of collinearity on the parameter estimates, the data matrix (X) is evaluated. When the X-matrix is ill-conditioned, it is computationally more difficult to estimate the model parameters. Assessing the severity of the computational problems gives a measure of the collinearity in the data.;In this dissertation, methods used to measure the computational effects of collinearity in statistical models for survival data are discussed. Collinearity measures which are analogous to those for the ordinary least squares model, are developed for logistic regression, Cox regression, and the Buckley-James model. For evaluation of these measures of collinearity, these models are separated into two groups, those models most appropriate for a censored response variable and those most appropriate for an uncensored response variable. Cox regression and the Buckley-James models are used for censored data, and the ordinary least squares and logistic models are used for uncensored data.;Also, the relative effects of collinearity in each of these statistical models are assessed. This is achieved by using the same data sets as examples for each of these models. For each example, a range of collinearities is used to demonstrate the relative effects of dependencies between explanatory variables. In this way, the effects of the same degree of collinearity in the data can be compared for all the models. The relative sensitivity of a model when collinearity is present can be compared to other types of survival models.;In addition, the measures of the computational effects of collinearity for each of the models are evaluated to determine how closely they identify the structural effects of collinearity. For each data set used in the examples, varying degrees of collinearity, from nearly orthogonal explanatory variables to highly correlated explanatory variables, are used.