Generalized Linear Mixed Model Analysis of Acute Respiratory Infection Data on Children

Abstract

Statistical modeling often involves data which has a distribution of the exponential family. Generalized Linear Model (GLM) was developed to model these data by using a link function between the mean of the response variable and the linear form of the predictor variable. If the data of the response variable comes from several census blocks that are taken randomly, then the diversity between census blocks should not be ignored because it can increase bias. The Generalized Linear Mixed Model (GLMM) is a method that can capture a variety of random effects. However, it does not rule out if there are many predictor variables involved in the model and we use GLMMLasso as a combination method of GLMM and Lasso to shrink the parameter coefficients to zero, it is used to reduce the variance. In this study, a simulation was conducted to GLMMLasso use different numbers of predictor variables and different values of shrinkage coefficients to determine which shrinkage coefficient values have a minimum bias on parameter prediction. Acute Respiratory Infection (API) data on children in Jakarta is used to know the factors that could cause increased cases. The simulation result is the shrinkage coefficient which produces a minimum bias is 30, and the R2 value of data analysis on the model is 99.24%