Anticipation of wheelchair and rollerblade actions in spinal cord injured people, rollerbladers, and physiotherapists

Embodied Cognition Theories (ECT) postulate that higher-order cognition is heavily influenced by sensorimotor signals. We explored the active role of somatosensory afferents and motor efferents in modulating the perception of actions in people who have suffered a massive body-brain disconnection because of spinal cord injury (SCI), which leads to sensory-motor loss below the lesion. We assessed whether the habitual use of a wheelchair enhances the capacity to anticipate the endings of tool-related actions, with respect to actions that have become impossible. In a Temporal Occlusion task, three groups of participants (paraplegics, rollerbladers and physiotherapists) observed two sets of videos depicting an actor who attempted to climb onto a platform using a wheelchair or rollerblades. Three different outcomes were possible, namely: a) success (the actor went up the step); b) fail (the actor stopped before the step without going up) and c) fall (the actor fell without going up). Each video set comprised 5 different durations increasing in complexity: in the shortest (600ms) only preparatory body movements were shown and in the longest (3000ms) the complete action was shown. The participants were requested to anticipate the outcome (success, fail, fall). The main result showed that the SCI group performed better with the wheelchair videos and poorer with rollerblade videos than both groups, even if the physiotherapists group never used rollerblades. In line with the ECT, this suggests that the action anticipation skills are not only influenced by motor expertise, but also by motor connection.

The direct contrasts between posterior distributions are reported in each row. A contrast is the difference between two posterior distributions. For example, the "Rollerblade v Wheelchair" contrast is the posterior distribution of the difference between "Rollerblade" and "Wheelchair".
Results are described by means of the Mode, the 89%HPDI, the ESS and the R value. Contrasts whose HPDIs are completely greater than the ROPE are marked with "+" (i.e., the first term of the contrast is larger than the second term), conversely, they are marked with "-" (i.e., the second term of the contrast is larger than the first term). These are considered credible differences/contrasts. Contrasts that are not marked with a "+" or a "-" are considered non-credible.
In the table it is observable that only contrasts within main effects and the Emotion:Ending interaction are giving credible results.
As reported in the main text, these analyses show that Fall and Safe endings elicit more negative emotions (anxiety and unpleasantness) than Success endings, while neutral emotions (arousal and unexpectedness) are elicited more by Success endings than Safe and Fall endings. In addition, Wheelchair videos were related to higher negative evaluations than Rollerblades videos.

B. Analysis of Kinematics
In order to test the kinematic differences between the different Endings (Success, Safe Fail, Fall) and Tools (Wheelchair, Rollerblades), and whether or not the six versions of the videos for each Ending and Tool where kinematically different, we calculated the angles formed by the actors' right elbow and left knee with respect to the floor, and the distance covered by the video actor in the four earlier frames: at the starting position (0 ms), and during the actions after 600 ms, 1200 ms and 1800 ms. We chose these information because they are representative of the whole action in both rollerblade and wheelchair videos: the right elbow angle is important for wheelchair users to push their wheelchair and for rollerblade users to maintain balance; the left knee angle in respect to the floor shows the preparation for the jumps in rollerblades, and is an indirect measure of the degree of the wheelchair tilt necessary in order to climb the platform; finally, the distance covered is an index of velocity (see Fig. B.1).

Figure B.1: Graphical representation of angles used for kinematic analyses.
In red the left knee angle with respect to the floor, in blue the right elbow angle. a = rollerblades video; b= wheelchair video.

Data handling and Statistical Analyses
The kinematic information was obtained from the 36 videos used in the Action Anticipation paradigm (see the main text) in the frames at 0 ms, 600 ms, 1200 ms and 1800 ms.
First, for each combination of Ending and Tool, we tested if there were differences between the six videos. Three separated analyses were conducted with the distance covered (in pixels), the right elbow angle (in radians), the left knee angle (in radians) as dependent variables (d.v.). The ID of the Video and the Frame (0, 600, 1200, 1800 ms) were the independent variables.
As a second step, we tested if there were kinematic differences between Tools and Endings. We tested all the above-mentioned d.v., with Ending (Success, Safe Fail, Fall), Tool (Wheelchair, Rollerblades) and Frame (0, 600, 1200, 1800 ms) as independent variables.
All the analyses were conducted following a Bayesian approach, similar to the one used for the Action Anticipation data (see below C). We computed the modes (Mo) and HPDIs for the µ parameters of the β coefficients.
The mathematical description of the Hierarchical Bayesian Linear Model is reported in Table B.1 (differences among videos) and Table B.2 (differences among tools and endings) and the corresponding JAGS codes (the script for the Bayesian analysis) are reported in Code B.1 and Code B.2, respectively.
The coefficients reported in Table B.3 and Table B.4 are the same as seen in Table A.2.
In Table B.3 we can observe that there are no differences between the six versions of the same video, both for the main effects and the covariation with Frame (0, 600, 1200 and 1800 ms).
The contrasts concern the comparisons between the main effects of the videos, and then their covariation with the Frame.
In all cases, the different six version of videos were not different in kinematics.
In Table B.4 we report the overall analyses of video kinematics, with Frame (0, 600, 1200 and 1800 ms), Ending (Safe Fail, Success, Fall) and Tool (Wheelchair, Rollerblades) as independent variables. As described in the main text, the left knee angle is only able to discriminate between Wheelchair and Rollerblade Videos, as expected. In fact, while in Rollerblades Videos the left knee has a great modulation, the left knee in Wheelchair Videos is only able to detect the tilt of the Wheelchair, which occurs in later frames. Furthermore, the direction of the angle in Wheelchair and Rollerblades Videos is opposite (as seen in Fig. B.1).   C. Action Anticipation Model

Estimation of the Coefficients via Hierarchical Bayesian Logit Model with non-informative prior
The estimation of coefficients is done through a standard Hierarchical Bayesian Logit Model (Gelman & Hill, 2006;Kruschke, 2011Kruschke, , 2014. This model allows us to relate binomial dependent variables (accuracies, frequencies, etc...) to linear coefficients.This is possible by assuming a normal latent variable)(an unobserved continuous variable underlying the non-parametric dependent variable, Agresti, 2012, p. 4). Therefore, it is possible to estimate coefficients for the independent variables from a conventional linear regression and transform itsresult (the normally distributed latent variables) into a binomial dependent variable (the data) via a "link-function", that in this case is the Logit function.
The Logit function in its canonical form is The inverse of the Logit function transforms the [0÷1] probability of getting correct responses into a continuous variable, that is the latent variable, which is then used to estimate the coefficients βs.
As to the Bayesian Logit Model, we are interested in the posterior distributions of the µ parameter of the β coefficients, i.e. the parameter of central tendency for each independent variable. These posterior distributions are then used to compute the contrasts of interest that are reported in the paper in terms of Mode and 89% HPDI.
The mathematical description of the Hierarchical Bayesian Logit Model is reported in Table A.1, and the corresponding JAGS code (the script for the Bayesian analysis) is reported in Code A.1. In the first column the formula for each term of the model. In the second column, the corresponding row in the JAGS code (see below). In the third column a short description for each term.
is the dependent variable (i.e. the number of correct responses in the i th case).
is the number of trials in the i th case.
ℎ is the covariate in the i th case: the duration of the video centred and re-scaled in the [-1; 1] range.

Formula
Rows in the JAGS code Description yi~Binomial (µi,Ni)

D. Posterior distributions
In this section we report the mode, 89% HPDI, ESS and R for the coefficients from all the posterior distributions.