Multilevel logistic regression analysis applied to binary contraceptive prevalence data

In public health, demography and sociology, large-scale surveys often follow a hierarchical data structure as the surveys are based on mul- tistage stratified cluster sampling. The appropriate approach to analyzing such survey data is therefore based on nested sources of variability which come from different levels of the hierarchy. When the variance of the resid- ual errors is correlated between individual observations as a result of these nested structures, traditional logistic regression is inappropriate. We use the 2004 Bangladesh Demographic and Health Survey (BDHS) contraceptive bi- nary data which is a multistage stratified cluster dataset. This dataset is used to exemplify all aspects of working with multilevel logistic regression models, including model conceptualization, model description, understand- ing of the structure of required multilevel data, estimation of the model via the statistical package MLwiN, comparison between different estimations, and investigation of the selected determinants of contraceptive use. Bangladesh is the most densely populated country in the world. The country has currently a population about 150 million, with a corresponding population density of 939 per square kilometer and growth rate of 1.42% (M. Anwarul Iqbal, 2008). In the second half of the last century, the population grew extraordinarily rapidly, tripling during the period, whereas during the entire first half of the century the population increased by only 45%. Family planning was introduced in Bangladesh in the early 1950s. The policy to reduce fertility rates has been repeatedly reaffirmed by the Government of Bangladesh since liberation in 1971. During the mid 1970s, the contraceptive prevalence rate (CPR) was less than 10% and the total fertility rate (TFR) was more than 6 births per women (Islam and Islam, 1993). The subsequent last two rounds of the BDHS, in 1999−2000