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.
| Published in | Science Journal of Applied Mathematics and Statistics (Volume 3, Issue 6) |
| DOI | 10.11648/j.sjams.20150306.13 |
| Page(s) | 243-249 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
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Copyright © The Author(s), 2015. Published by Science Publishing Group |
Binary Logistic Regression, Multinomial Logistic Regression, Adjusted Weights, Correct Likelihood, Quasi-Likelihood, Nairobi
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APA Style
Kennedy Sakaya Barasa, Chris Muchwanju. (2015). Incorporating Survey Weights into Binary and Multinomial Logistic Regression Models. Science Journal of Applied Mathematics and Statistics, 3(6), 243-249. https://doi.org/10.11648/j.sjams.20150306.13
ACS Style
Kennedy Sakaya Barasa; Chris Muchwanju. Incorporating Survey Weights into Binary and Multinomial Logistic Regression Models. Sci. J. Appl. Math. Stat. 2015, 3(6), 243-249. doi: 10.11648/j.sjams.20150306.13
AMA Style
Kennedy Sakaya Barasa, Chris Muchwanju. Incorporating Survey Weights into Binary and Multinomial Logistic Regression Models. Sci J Appl Math Stat. 2015;3(6):243-249. doi: 10.11648/j.sjams.20150306.13
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Download@article{10.11648/j.sjams.20150306.13,
author = {Kennedy Sakaya Barasa and Chris Muchwanju},
title = {Incorporating Survey Weights into Binary and Multinomial Logistic Regression Models},
journal = {Science Journal of Applied Mathematics and Statistics},
volume = {3},
number = {6},
pages = {243-249},
doi = {10.11648/j.sjams.20150306.13},
url = {https://doi.org/10.11648/j.sjams.20150306.13},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20150306.13},
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.},
year = {2015}
}
TY - JOUR T1 - Incorporating Survey Weights into Binary and Multinomial Logistic Regression Models AU - Kennedy Sakaya Barasa AU - Chris Muchwanju Y1 - 2015/11/19 PY - 2015 N1 - https://doi.org/10.11648/j.sjams.20150306.13 DO - 10.11648/j.sjams.20150306.13 T2 - Science Journal of Applied Mathematics and Statistics JF - Science Journal of Applied Mathematics and Statistics JO - Science Journal of Applied Mathematics and Statistics SP - 243 EP - 249 PB - Science Publishing Group SN - 2376-9513 UR - https://doi.org/10.11648/j.sjams.20150306.13 AB - 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. VL - 3 IS - 6 ER -
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