EVALUATING LIKELIHOOD ESTIMATION METHODS IN MULTILEVEL ANALYSIS OF MODERN CONTRACEPTIVE USE IN NIGERIA

Abstract

Likelihood plays an important role in parameter estimation. It is one of the tools used in estimating parameters of multilevel models, including multilevel binary logistic models. Cluster sampling scheme often introduces multilevel dependency among clustered observations whereby samples from same cluster tends to have related characteristics but different from samples from other clusters. This dependency may render single-level statistical models inefficient in the process parameter estimation. Despite the inadequacy of single-level estimates in the cluster data, public health researchers, lay little emphasis on estimation technique. This has hitherto led to improper inferences. The aim of this research is to evaluate different multilevel likelihood analysis estimation procedures including the traditional methods and to identify the best parameter estimation method in clustered data. This study utilized the 2012 National AIDS and Reproductive Health Survey (NARHS), a multistage stratified duster dataset. The nationally representative survey used semi structured questionnaire to obtain information on reproductive behavior of women aged 15-49 years, The use of modem contraceptive was used as dependent variable while ages of respondents, place of residence, wealth status, religion, education among others were the independent variables. The standard binary logistic regression was first compared with multilevel binary logistic regression to obtain the percentage relative bias, then comparison of the performance of Penalized Quasi-Likelihood (PQL), Non-Adaptive Gaussian Quadrature(NAGQ) and Adaptive Gaussian Quadrature (AGQ) using XTMELOGIT. and GLLAMM syntax in estimating parameters for multi-level logistic regression models were carried out. The comparisons were in terms of bias, numerical convergence, best fitted model and computational time. STATA version 12 and SPSS version 20 were used for data analysis at 5% significant level. Using -2logL, AIC and BIC, as yardstick to determine the fitness of the models from the different likelihood estimation method. AGQ had highest values and lowest standard error and was considered the best model for both two and three levels logistic regression. PQL was less biased compared to the other multilevel maximum likelihood methods, the conventional logistic model has overestimated the parameters by about 2%, 19% and 20% compared to multilevel model using by the corresponding methods PQL, NAGQ and AGQ respectively. AGQ using XTMELOGIT syntax gave the largest ICC result (ICC=0.201) which means 20% of the total variance is explained by the variance within the cluster. The PQL method generate the smallest intral cluster correlation coefficient(ICC=0.052). Also current age of the respondents, their wealth index, place of residence. Education , religion and their cluster have significant contribution to modern contraceptive use. The adaptive Gaussian quadrature (AGQ) performed better than the Laplacian approximation (NAGQ) and penalized quasi likelihood (PQL) when considering two and three levels but PQL, performed relatively well in term of unbias estimate. ln terms of computational time AGQ with XTMELOGIT syntax were adequate for two-level models while AGQ using GLLAMM syntax was adequate for three levels. Multilevel analysis should be encouraged in analyzing cluster data rather than the traditional individual level analysis.