Evaluating the properties of the coefficient of multiple correlation (CMC) for kinematic gait data

When assessing reliability of three dimensional gait analysis, the coefficient of multiple correlation (CMC), a measure of similarity of waveforms, is frequently used. Several shortcomings of the method have been reported. It is strongly related to the range of motion (ROM); it is supposed to take values from 0 to 1, but is known to obtain complex values and break down. Removing offset before calculations appears to make it insensitive to apparent differences in gait. In the present work we use stochastic simulations to demonstrate why all of this happens, and the consequences thereof. We also demonstrate other, lesser-known, issues with the method, such as the strong dependency on number of subjects and test situations. The results are demonstrated on real data from an inter-rater repeatability study. We conclude that the CMC in its current form is generally unsuitable as a tool for assessing reliability in kinematic gait data.