Incorporating Survey Weights into Binary and Multinomial Logistic Regression Models
Science Journal of Applied Mathematics and Statistics
Volume 3, Issue 6, December 2015, Pages: 243-249
Received: Jul. 29, 2015;
Accepted: Aug. 4, 2015;
Published: Nov. 19, 2015
Views 6095 Downloads 304
Kennedy Sakaya Barasa, Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Science and Technology, Nairobi, Kenya
Chris Muchwanju, Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Science and Technology, Nairobi, Kenya
Since sampling weights are not simply equal to the reciprocal of selection probabilities its always challenging to incorporate survey weights into likelihood-based analysis. These weights are always adjusted for various characteristics. In cases where logistic regression model is used to predict categorical outcomes with survey data, the sampling weights should be considered if the sampling design does not give each individual an equal chance of being selected in the sample. The weights are rescaled to sum to an equivalent sample size since original weights have small variances. The new weights are called the adjusted weights. Quasi-likelihood maximization is the method that is used to make estimation with the adjusted weights but the other new method that can be created is correct likelihood for logistic regression which included the adjusted weights. Adjusted weights are further used to adjust for both covariates and intercepts when the correct likelihood method was used. We also looked at the differences and similarities between the two methods. Analysis: Both binary logistic regression model and multinomial logistic regression model were used in parameter estimation and we applied the methods to body mass index data from Nairobi Hospital, which is in Nairobi County where a sample of 265 was used. R-software Version 3.0.2 was used in the analysis. Conclusion: The results from the study showed that there were some similarities and differences between the quasi-likelihood and correct likelihood methods in parameter estimates, standard errors and statistical p-values.
Kennedy Sakaya Barasa,
Incorporating Survey Weights into Binary and Multinomial Logistic Regression Models, Science Journal of Applied Mathematics and Statistics.
Vol. 3, No. 6,
2015, pp. 243-249.
Andersson J.C, Verkuilen, J., and Peyton, B. L. (2010).Modeling Polytomous Item Responses using Simultaneously Estimated Multinomial Logistic Regression Model. Journal of Educational and Behavioral Statistics, 422.
Balgobin Nandram and Jai Won Choi. (2010). A Bayesian Analysis of Body Mass Index Data from Small Domains Under Nonignorable Nonresponse and Selection. Journal of American Statistical Association, 105, 120-135.
Courvoisier, D.S., C. Combescure, T. Agoritsas, A. Gayet-Ageron and T.V. Perneger (2011) “Performance of logistic regression modeling: beyond the number of events per variable, the role of data structure.” Journal of Clinical Epidemiology 64: 993-1000.
Einicke, G.A.; Falco, G.; Dunn, M.T.; Reid, D.C. (May 2012). "Iterative Smoother-Based Variance Estimation". IEEE Signal Processing Letters 19 (5)
Gelman, Andrew. (2007) Struggles with Survey Weighting and Regression Modeling. Statistical Science, 22, 153-164.
Grilli, L., and Pratesi, M. (2004). Weighted Estimation in Multinomial Ordinal and Binary Models in the Presence of Informative Sampling Designs. Survey Methodology, 30, 93-103.
Hosmer D.W and Lemeshow S, (2000), Applied Logistic Regression 2nd Ed. John Wiley & Sons, Inc. Canada. PP1-17
Michael, H., Kutner, C J., and Nachtsheim, J. N. (2004).Applied Linear Regression Models. McGraw-Hill/Irwin
Nandram, B., and Choi, J. W. (2002), A Hierarchical Bayesian Nonresponse Model for Binary Data With Uncertainty About Ignorability, Journal of the American Statistical Association, 97, 381-388.
Pfeffermann, D., Skinner, C. J., Holmes, D. J., Goldstein, H., and Rasbash, J. (1998).Weighting for Unequal Selection Probabilities in Multinomial Models. Journal of the Royal Statistical Society, 60, 23-40.
Potthoff R, Woodbury, M. A., and Manton, K. G. (1992). Equivalent Sample Size and Equivalent Degrees of Freedom Refinements for Inference using Survey Weights under Super population Models. Journal of the American Statistical Association, 87, 383-396.
Swinburn BA, Sacks G, Hall KD, et al. The global obesity pandemic: shaped by global drivers and local environments. Lancet. 2011; 378(9793)
Wang YC, McPherson K, Marsh T, Gortmaker SL, Brown M. Health and economic burden of the projected obesity trends in the USA and the UK. Lancet. 2011; 378(9793).