Binary logistic regression with random effects for productivity analysis in mining operations

Abstract

Binary logistic regression is a statistical method used to examine the relationship between a binary response variable and predictor variables, measured on a categorical or continuous scale. Binary logistic regression modeling is typically applied to cross-sectional data; however, this study extends its application to a binary logistic regression model for longitudinal data, which combines cross-sectional and time-series data. In longitudinal data, time and individual variables are critical components associated with random effects, as fixed predictor variables often do not fully explain temporal variations and inter-individual differences. Furthermore, the response variable is influenced by predictor variables (fixed effects) and random factors (random effects) such as sample selection, time, and area. A model that incorporates fixed and random effects components is called a mixed-effects model. This study develops a mixed-effects logistic regression model by considering the longitudinal data structure and predictor variables as random effects. The analysis is applied to loading equipment productivity data at PT Kaltim Prima Coal, with variables such as spotting time and loading time as fixed effects and environmental factors beyond control as random effects. This approach improves parameter estimation accuracy to 74.63% and provides a deeper interpretation of the factors affecting productivity.