Computational problems in variable selection for multilevel models using stepwise regression

Multilevel modelling is a methodology that allows the consideration of variability in the level of the studied variables and the nature of the relationships between them, depending on the affiliation of study units to higher-level units (groups). Additionally, by dividing the studied population into groups, it is possible to explain part of the variability of the estimated characteristic using higher-level characteristics. The usefulness of multilevel modelling in estimating socioeconomic characteristics was investigated in the author's previous works. However, with large populations characterised by a multilevel structure, a significant drawback of this approach is its high computational complexity, often resulting in unacceptably long computation times. The main objective of the article is to propose a simplification in the algorithm of forward stepwise multilevel regression, allowing a significant reduction in the time required for variable selection in the model. The considerations will be illustrated by constructing a multilevel model to examine the determinants of daily flows related to employment based on the matrix of employment-related population flows developed from the 2021 National Census of Population and Housing (NSP 2021).