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Predictive Accuracy of Fitted Logistic Regression Model Using Ranked Set Samples
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*Kevin Carl Pena Santos, University of the Philippines School of Statistics 
Erniel Bayhon Barrios, University of the Philippines School of Statistics 

Keywords: Logistic Regression Model, Ranked Set Sampling, Rare Characteristics, Separation of Likelihood

Separation of likelihood and rare events are two interrelated problems in fitting the logistic regression model. We propose to address these issues by drawing the sample using ranked set sampling. An extensive simulation study was conducted to assess the performance of a logistic regression model fitted from ranked set samples and compared to those estimates using simple random samples. RSS performs best in small populations regardless of the distribution of the binary response variable in the population. As the sample and population sizes increase, the predictive ability under RSS also improves but it stabilizes to become comparable to SRS. Furthermore, RSS mitigates the problem of separation of likelihood especially when the population size is relatively large. In addition, RSS can be an alternative sampling scheme to Inverse Sampling in obtaining samples involving rare characteristics without necessarily blowing up the sample size. RSS provides sample into the estimation of logistic regression models high predictive accuracy and keeps costs at low levels.

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