Multivariate approach for shoe size modelling of Malaysian Women

Abstract

The problem of finding the best fitting shoes among Malaysian women is due to the absence of a Malaysian women shoe sizing system. Currently, shoe manufacturers in Malaysia use United Kingdom (UK) and United States of America (USA) size which is based on the ISO 9407:2019 standard: Mondopoint shoe sizing system, which is basically developed based on foot length and foot breadth. The existing shoe sizes do not cover the width and girth part that is a unique foot shape for Malaysian women. Improper shoe sizing can interrupt the biomechanics of the foot and ankle causing pain and increasing the risk of falling to the wearer. This may create safety issues especially in the workplace like strained foot muscles, slips and falls, and body fatigue which gradually grow into severe musculoskeletal disorders or rheumatic diseases if they are unattended. These problems and related issues were addressed in this study using statistical modelling of foot measurements for the development of the Malaysian women shoe sizing system. The objectives of this study are to investigate the selection of foot measurements used in modelling foot measurements, to enhance existing clustering technique for modelling shoe size, to model foot size variation with multivariate normal model and piecewise regression, and to develop a process to determine shoe size. A set of foot measurement was measured by Infoot 3-dimensional foot scanner; foot length (FL), foot breadth (FB) and foot’s ball girth (BG) were used to represent shoe size. 252 women from University of Malaya (UM) volunteered to have their foot measurements taken using the Infoot 3D foot scanner. The data was then split into 161 training data and 91 testing data. The variations of size were investigated using an improved clustering analysis and the multivariate normal mixture probability distribution where a shoe size model is proposed. The process was repeated to five-foot measurements (FL, FB, BG, instep length (IL), and fibulare instep length (FIL)). As for three-foot measurements, FL is treated independently of FB and BG. Conditional on fixed FL value, subdivisions were identified for selected (FB, BG) combination. Taking advantage of the existence of normal probability distribution, univariate hypothesis testing was performed to test group separation and chi-square test to test goodness fit of subdivisions. An alternative approach called piecewise regression was used for five-foot measurements (FL, FB, BG, IL, FIL) to model shoe size as comparison. The study successfully attained the performance of aggregate loss which is less than benchmark value and coverage percentage of 71.25% for the training data. The proposed shoe size was then verified with testing data and showed high coverage percentage of 82.53%. This study concludes that a modest sample size of 252 women was sufficient to develop a prototype shoe sizing system using the proposed novel approach. In conclusion, this study provides a novel process to create a Malaysian women shoe sizing system that considers ball girth (BG), in which most Malaysian women have unique shape. The proposed system provides a significant improvement to the Mondopoint sizing system for Malaysian women. In addition, it also allows for a test of the significant separation of shoe sizes that is overlooked by most ergonomics by using a multivariate normal mixture model.