Undesirable properties of the dimensionless normalisation for spatio-temporal variables

Abstract

We used theory and empirical data to demonstrate three undesirable properties of the dimensionless normalisation technique for gait spatio-temporal parameters. Firstly, it may not fully remove the correlation between leg length and spatio-temporal parameters. Secondly, it induces spurious correlation among spatio-temporal parameters, which might obscure their true correlation structure. Thirdly, it induces spurious correlation with external covariates, which complicates further statistical modelling. Therefore, depending on the objectives, we propose alternatives. If the objective is to compare datasets but remove the confounding effect of leg length, residualisation may be an alternative, although the generalisability of the residualisation is less well established than dimensionless normalisation. If the objective is to build a regression model, the raw spatio-temporal parameters could be used with leg length, or a function of leg length, as an explicit regressor to avoid spurious correlation. If correlation is the objective, partial correlation can be used instead.