A Modified Iterative Weighted Least Squares Method

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.