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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
Authors
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
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Abstract
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.
Keywords
Binary Logistic Regression, Multinomial Logistic Regression, Adjusted Weights, Correct Likelihood, Quasi-Likelihood, Nairobi
Kennedy Sakaya Barasa, Chris Muchwanju, 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. doi: 10.11648/j.sjams.20150306.13
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