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MULTIPLE IMPUTATION FOR ORDINARY COUNT DATA BY NORMAL DISTRIBUTION APPROXIMATION

*Titin Siswantining orcid scopus  -  Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Indonesia, Indonesia
Muhammad Ihsan  -  Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Indonesia, Indonesia
Saskya Mary Soemartojo  -  Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Indonesia, Indonesia
Devvi Sarwinda  -  Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Indonesia, Indonesia
Herley Shaori Al-Ash  -  Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Indonesia, Indonesia
Ika Marta Sari  -  Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Indonesia, Indonesia
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Abstract
Missing values are a problem that is often encountered in various fields and must be addressed to obtain good statistical inference such as parameter estimation. Missing values can be found in any type of data, included count data that has Poisson distributed. One solution to overcome that problem is applying multiple imputation techniques. The multiple imputation technique for the case of count data consists of three main stages, namely the imputation, the analysis, and pooling parameter. The use of the normal distribution refers to the sampling distribution using the central limit theorem for discrete distributions. This study is also equipped with numerical simulations which aim to compare accuracy based on the resulting bias value. Based on the study, the solutions proposed to overcome the missing values in the count data yield satisfactory results. This is indicated by the size of the bias parameter estimate is small. But the bias value tends to increase with increasing percentage of observation of missing values and when the parameter values are small.
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Keywords: count data; generelized linear model; missing value; multiple imputation; poisson regression; rubin’s rule.
Funding: Universitas Indoesia

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