Re-examining the lower speed boundary of preferred coordination ratio constancy: estimator dependence and competing breakpoint regions

Abstract

BackgroundThe preferred coordination ratio (PCR), defined as step length divided by cadence, is approximately constant across a broad range of walking speeds in healthy adults, except at the slowest speeds. A previous study reported its lower boundary at approximately 62 m{middle dot}min-{superscript 1} from K-means clustering of speed and PCR. However, K-means partitions observations rather than formally estimating a changepoint, so it is unclear how well this value identifies where PCR changes. AimTo re-examine the location and identifiability of this boundary using published data. MethodCoordinates were independently recovered from the published figure, yielding speed and PCR for 95 markers. The reported K-means-derived boundary was reproduced and compared with changepoint and segmented-model estimates. Sensitivity analyses examined digitisation and model specification. ResultsFor the reference robust heteroscedastic segmented model, the profile likelihood was multimodal, with a global maximum at 50 m{middle dot}min-{superscript 1} and a competing mode at 62 m{middle dot}min-{superscript 1}; the twice-log-likelihood difference was 0.82. The support set was disconnected: 43-52 and 56-66 m{middle dot}min-{superscript 1}. Across eight segmented-model specifications the maximising breakpoint ranged from 45 to 62 m{middle dot}min-{superscript 1}, while a Gaussian mean-and-variance changepoint estimator yielded 38 m{middle dot}min-{superscript 1}. The reference segmented estimate remained at 50 m{middle dot}min-{superscript 1} in all coordinate-recovery analyses. The published K-means-derived boundary was reproduced at 62.4 m{middle dot}min-{superscript 1}. InterpretationThe reanalysis found competing breakpoint regions rather than a single dominant boundary. Alternative formulations indicated that the boundary may lie below approximately 62 m{middle dot}min-{superscript 1}, warranting direct testing with new data. HighlightsO_LIFormal analyses found competing regions rather than one dominant breakpoint C_LIO_LIThe reference profile peaked at 50 m/min; a competing mode occurred at 62 m/min C_LIO_LISeveral analyses indicated that the transition may occur below 62 m/min C_LI