  A central task in the analysis of human movement behavior is to determine
systematic patterns and differences across experimental conditions,
participants and repetitions. This is possible because human movement is highly
regular, being constrained by invariance principles. Movement timing and
movement path, in particular, are linked through scaling laws. Separating
variations of movement timing from the spatial variations of movements is a
well-known challenge that is addressed in current approaches only through forms
of preprocessing that bias analysis. Here we propose a novel nonlinear
mixed-effects model for analyzing temporally continuous signals that contain
systematic effects in both timing and path. Identifiability issues of path
relative to timing are overcome by using maximum likelihood estimation in which
the most likely separation of space and time is chosen given the variation
found in data. The model is applied to analyze experimental data of human arm
movements in which participants move a hand-held object to a target location
while avoiding an obstacle. The model is used to classify movement data
according to participant. Comparison to alternative approaches establishes
nonlinear mixed-effects models as viable alternatives to conventional analysis
frameworks. The model is then combined with a novel factor-analysis model that
estimates the low-dimensional subspace within which movements vary when the
task demands vary. Our framework enables us to visualize different dimensions
of movement variation and to test hypotheses about the effect of obstacle
placement and height on the movement path. We demonstrate that the approach can
be used to uncover new properties of human movement.
