Maximum likelihood estimation in the logistic regression model with a cure fraction

In this paper, the non-parametric bootstrap and non-parametric Bayesian bootstrap methods are applied for parameter estimation in the binary logistic regression model. A real data study and a simulation study are conducted to compare the Nonparametric bootstrap, Non-parametric Bayesian bootstrap and the maximum likelihood methods. Study results shows that three methods are all effective ways for parameter estimation in the binary logistic regression model. In small sample case, the non-parametric Bayesian bootstrap method performs relatively better than the non-parametric bootstrap and the maximum likelihood method for parameter estimation in the binary logistic regression model.

Abstrak. Analisis regresi logistik digunakan untuk menentukan hubungan antara peubah respon bersifat kategori dengan satu atau lebih peubah penjelas dengan asumsi bahwa respon tidak dipengaruhi oleh lokasi geografis (data spasial). Salah satu metode analisis spasial adalah Model Regresi Logistik Terboboti Geografis (RLTG). Model RLTG adalah bentuk regresi logistik lokal di mana lokasi geografis diperhatikan dan diasumsikan memiliki distribusi Bernoulli. Pendugaan parameter model RLTG menggunakan metode Maximum Likelihood Estimation (MLE) dengan memberikan bobot yang berbeda pada lokasi yang berbeda. Data dalam penelitian ini diperoleh dari publikasi Badan Pusat Statistik, yaitu data dan Informasi Kemiskinan di Provinsi Sulawesi Selatan. Penelitian ini bertujuan untuk mengetahui faktor-faktor yang mempengaruhi status kemiskinan di Provinsi Sulawesi Selatan dengan menggunakan model regresi logistik terboboti geografis dengan fungsi pembobot Kernel bisquare. Hasil penelitian menunjukkan bahwa peubah penjelas yang mempengaruhi status kemiskinan di Provinsi Sulawesi Selatan adalah persentase penduduk tidak bekerja dan persentase rumah tangga pengguna jamban bersama.Abstract. Logistic regression a analysis is used to determine the relationship between categorical response variables with one or more predictor variable assuming that the response is not influenced by geographical location (spatial data). One method of spatial analysis is Geographically Weighted Logistic Regression (GWLR). The GWLR model is a local form of logistic regression where the geographical location is considered and assumed to have a Bernoulli distribution. Estimating parameters of the RLTG model uses the Maximum Likelihood Estimation (MLE) method by giving different weights to different locations. The data were obtained from BPS publications, namely Data and Information on Poverty in South Sulawesi Province. This study aims to determine the factors that influence poverty status in South Sulawesi Province using a geographically weighted logistic regression model with kernel bisquare weighting function. The results showed that the explanatory variables that influence the status of poverty in the province of South Sulawesi were the percentage of the population not working and the percentage of common household toilet users.Keywords: logistic regression, kernel bisquare, GWLR and poverty.

Abstract This study aims to compare the efficacy of logistic regression model for identifying the risk factors of low-birth-weight babies in Indonesia using the maximum likelihood estimation (MLE)and the Bayesian estimation methods. The data used in this study is secondary data derived from the 2017 Indonesian Demographic Health Survey with a total sample of 16,344 newborn babies. Selection of the best logistic regression model was based on the smaller Bayesian Schwartz Information Criterion (BIC) value. The logistic regression model with the Bayesian estimation method has a smaller BIC value than the MLE method. Twin births, baby girl, maternal age at risk, birth spacing that is too close, iron deficiency, low education, low economy, inadequate drinking water sources have provided a higher risk of low-birth-weight incidence.