A Modified Iterative Weighted Least Squares Method

Abstract

The Iterative Weighted Least Squares (IWLS) method is one of the estimation procedures in logistic regression modeling. In consideration of the strategic role played by this model, especially in biometrics, the need to source for alternative logistic regression estimators has continued to resurface in the literature. In this paper, a modified IWLS method is developed by exponentiating the response probability. As a consequence, both the weight function and the adjusted dependent variate are modified. The resulting estimator is compared with the existing IWLS estimator using variances of parameter estimates and confidence intervals of the estimates. Four subpopulations were used in three illustrative examples with gender, Fasting Blood Sugar and Body Mass Index as explanatory variables. It is shown in this paper that the new update is superior to the traditional IWLS update in terms of variance reduction of parameter estimates and for the fact that it provides a more strict confidence interval for the test of hypotheses. In the first example, the confidence intervals for the parameter estimates of the existing IWLS scheme are (0.2183, 1.7197), (-1.9993, -0.1687), (1.7993, 0.0313), while those of the proposed method are (-2.6588, -2.2240), (1.1228, 1.6826), (0.8552, 1.4150). The proposed estimator allows for improved goodness-of-fit. By a careful formulation of the model, the proposed estimator is made to behave like a survival function in the sense that it can be used to model the probability of extra survival time in survival analysis.