Journal of Mathematics and Statistics 5 (4): 387-394, 2009 ISSN 1549-3644 © 2009 Science Publications Corresponding Author: S.K. Sarkar, Laboratory of Applied and Computational Statistics, Institute for Mathematical Research, University Putra Malaysia, 43400 Serdang, Selangor, Malaysia 387 Optimization Techniques for Variable Selection in Binary Logistic Regression Model Applied to Desire for Children Data S.K. Sarkar and Habshah Midi Laboratory of Applied and Computational Statistics, Institute for Mathematical Research, University Putra Malaysia, 43400 Serdang, Selangor, Malaysia Abstract: Problem statement: The population problem is the biggest problem in the world. In the global and regional context, Bangladesh population has drawn considerable attention of the social scientists, policy makers and international organizations. Bangladesh is now world’s 10th populous country having about 140 million people. The recent experience of Bangladesh shows that fertility can sustain impressive declines even when women’s lives remain severely constrained. Recent statistics also suggest that, despite a continuing increase in contraceptive prevalence rate (56%), the expected fertility decline in Bangladesh has stalled. Approach: The purpose of this study was to explore the possibility of further fertility decline in Bangladesh with special attention to identify some social and demographic factors as predictors which are responsible to desire for more children using stepwise and best subsets logistic regression approaches. The study had compared two approaches to determine an optimum model for prediction of the outcome. Results: It had been found, excess desire for children is solely responsible for the stalled fertility. Conclusion: To overcome the situation, the policy makers of Bangladesh should pay their attention to eliminate the regional variations of desire for more children and introduce awareness programs among rural women about the positive impact of smaller family. Key words: Best subsets, stepwise logistic regression, design variables, Mallow’s C p , score test INTRODUCTION The population problem is the biggest problem in the world today. It makes every other problem worse and harder to solve. The world’s population is expected to grow by another 2.3 billion, from 6.8 billion in 2009 to 9.1 billion in 2050. Most of this growth will take place in the developing countries. In global and regional context, Bangladesh population has drawn considerable attention of the social scientists, policy makers and international organizations. Bangladesh is now world’s 10th populous country having about 140 million people. According to the United Nations and other agencies, the population growth rate of Bangladesh is still 1.65%. If this rate continues, the population of Bangladesh will double in 2050. Unless action is taken to accelerate the reductions in the rates of growth, the population of the world will not stabilize and certain region and countries like Bangladesh will go far beyond the limits consistent with political stability and acceptable social and economic conditions. However, recent statistics suggest that, despite a continuing increase in contraceptive prevalence rate (55.8%), the fertility decline in Bangladesh has stalled. The total fertility rate is still 3.1 and it is far beyond the replacement level fertility rate 2.1. Further fertility decline is required to achieve stable population in Bangladesh [14] . The purpose of this study is to explore the possibility of further fertility decline in Bangladesh with special attention to identify some crucial social and demographic factors as predictors which are responsible to desire for more children. The study provides a simple explanation and demonstration of how to obtain a best subsets solution in logistic regression and interpret the results. The criteria for including a variable in a model may vary from one problem to the next and from one scientific discipline to another. The traditional approach to statistical model building involves seeking the most parsimonious model that still explains the data. There are several steps one can follow to aid in the selection of variables for a logistic regression. The present study will discuss stepwise and best subset logistic regression for variable selection and compare them to determine a parsimonious model. Variables must be selected carefully so that the model makes accurate predictions, but without over fitting the data. Selecting variables by