Selection of variables in logistic linear mixed model with L1-penalty (Case study: Low birth weight in Indonesia)

Abstract

The generalized Mixed Linear Model is applicable in Indonesia’s Low Birth Weight (LBW) case. During 2003-2028, this case happened 2.6% to 8.9% of total birth. The lowest low birth weight case was in Jambi province, and the highest was in Central Sulawesi. The forms of LBW models include census blocks as random influences, and the fixed effects used are parents’ background, household socio-economic conditions, maternal conditions. The link function used was logit because the response is binary. Therefore, this research aims to estimate the GLMM of each province and then do the selection using the glmmLasso model by L1-norm. The results indicate that the results of the selection method using the glmmLasso method are simpler than the GLMM for both Jambi and Central Sulawesi provinces. This result is supported by the goodness of fit (BIC and AIC), where the BIC for glmmLasso for Jambi and Central Sulawesi provinces are 135.488 and 214.783, respectively. Equivalent to the goodness of the model, estimation of the random effect influences for the glmmLasso model is also smaller than GLMM. The variable with a significant effect on LBW in Jambi province is the mother’s age, and two variables are shrunk toward zero. However, the glmmLasso LWB’s model of Central Sulawesi has four variables that have a significant effect. Those variables are the father’s occupation, mother’s education level, level of the wealth index, and multiple births, and just one variable is reduced.