COVARIATES AND SAMPLE SIZE EFFECTS ON PARAMETER ESTIMATION FOR BINARY LOGISTIC REGRESSION MODEL
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Abstract
The types of covariate and sample size may influence many statistical methods. This study involves a rigorous Monte Carlo simulation to illustrate the effect of different types of covariate and sample size on parameter estimation for binary logistic regression model. The simulation study covers different sample sizes and types of covariate (continuous, count, categorical). This study shows how the MLE parameter estimates are affected by different types of covariate. The simulation results confirm that the parameter estimates improves as sample size increases. Results for single normal, two normal, categorical and count covariate show that sample size below 50 produced highly biased estimates. For model with skewed covariate, sample size of 150 and below produced biased estimates. The variability of parameter estimate increases when ï¬ of the Poisson distribution increases. An application to a real data set confirms the results of the simulation study. ABSTRAK Jenis pembolehubah tidak bersandar dan saiz sampel boleh mempengaruhi pelbagai kaedah berstatistik. Kajian ini mengkaji secara teliti menggunakan simulasi Monte Carlo dan seterusnya memperlihatkan kesan perbezaan pembolehubah tidak bersandar dan saiz sampel terhadap penganggaran parameter bagi model regresi logistik binari. Kajian simulasi dengan perbezaan saiz sampel dan jenis pembolehubah tidak bersandar (selanjar, kiraan, berkategori) telah dijalankan. Kajian ini menunjukkan bagaimana penganggaran kemungkinan maksima dipengaruhi oleh jenis pembolehubah tidak bersandar. Kajian simulasi menunjukkan penganggaran parameter semakin baik sejajar dengan peningkatan saiz sampel. Keputusan bagi model yang mempunyai satu dan dua pembolehubah tidak bersandar normal, satu pembolehubah berkategori dan kiraan menunjukkan saiz sampel kurang dari 50 menghasilkan penganggaran parameter yang sangat tidak tepat. Bagi model dengan pembolehubah tidak bersandar yang bertaburan tidak normal, saiz sampel 150 dan kurang menghasilkan penganggaran parameter yang tidak tepat. Variasi anggaran parameter meningkat apabila ï¬ bagi taburan Poisson meningkat. Suatu aplikasi terhadap data sebenar mengesahkan dapatan kajian simulasi.
Keywords: Parameter estimation, simulation, binary logistic regression, MLE
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