Evaluating likelihood estimation methods in multilevel analysis of clustered survey data

Abstract

Introduction: Public health researchers often lay little or no emphasis on multilevel structure of clustered data and its likelihood estimation techniques. This has led to improper inferences. The aim of this research is to evaluate traditional methods and the different multilevel likelihood estimation procedures so as to compare their computational efficiencies. Methodology: We fitted mixed method effect regression model into data on use of modern contraceptive from the Nigeria 2012 National HIV/AIDS and Reproductive Health Survey (NARHS) PLUS II with respondent’s characteristics as the in dependent variables. Also, 600,000 observations was simulated to evaluate the performance of Penalized Quasi-Likelihood (PQL), Non-Adaptive Gaussian Quadrature (NAGQ) and Adaptive Gaussian Quadrature (AGQ) using syntax for Mixed Effects Logit Models (XTMELOGIT) and Generalized Linear Latent and Mixed Models (GLLAMM) in Stata and Generalized Linear Mixed Models (GENLINMIXED) in SPSS. Result: Full Maximum Likelihood (ML) methods had highest likelihood values with lowest standard error and was considered the best model for both two and three levels logistic regression in both the survey and simulated data. PQL procedure was least biased compared to the other multilevel full FL methods. The full likelihood method had the least −2logL, AIC and BIC for the two dataset. Which implies that full likelihood procedure had the best fitted model. Also, current age of the respondents, wealth index, residence, education and religion are significant predictors of modern contraceptive use. Conclusion: Full ML performed better than quasi likelihood method at both two and three levels for both simulated and survey data. However, PQL appeared to be the best considering whether the estimates were biased or not. In terms of computational time, NAGQ with XTMELOGIT syntax was the fastest for two-levels and three levels model. The cluster-level effect is more significant than zonal level effect on modern contraceptive use in Nigeria.