The timing of hand movement onsets were detected by using a velocity threshold of 25 visual degrees per second (see
Khan et al., 2011). Saccade onsets were detected with the default detection settings of the EyeLink 1000. We categorized the motor-target locations, probe locations, and effector type manipulations in three factors: (1)
motor-target match, that is the probe's location matched (one) or mismatched (zero) a movement's end-point location; (2)
motor task complexity, that is how many effectors (one, two, or three) moved towards a location(s); (3)
effector effectiveness, that is how many of the effectors (zero, one, two, or three) were planned to move to the location where the probe appeared. We also added session number (1 or 2) as a fourth factor to take into account learning effects across sessions and we added participant number as a random effect. We used these five factors as independent variables for a generalized linear mixed effects regression model predicting whether a probe was correctly recognized or not as the dependent variable. Our main goal was to scrutinize to what degree the first three factors affected performance while keeping the model parsimonious. Note that we could have also chosen to leave out the factor
motor-target match and regress the factor
effector effectiveness (0-3) with a quadratic term. The quadratic function would then capture the larger difference in percent correct between zero and one effector as com the probe's location (
Jonikaitis & Deubel, 2011). However, we chose to stick to a model with only linear parameters for the sake of simplicity. Also, different processes may be activated in motor-target mismatch trials than in motor-target match trials (e.g., a serial search through the fleeting image in working memory's visuospatial sketchpad), which can best be represented in the model as a separate, third factor (i.e., motor-target match probability). The predicted values for the Generalized Linear Mixed-Effects Model (GLME) consisted of a 1920 (trials) × 29 (number of participants) matrix with each value a correctly (1) or incorrectly (0) recognized probe. The GLME formula consisted of a logit function
\(\bar{y} = \frac{1}{{1 + {e^{ - y}}}}\) with
\( y = a_{intercept} + \beta_{match}* x_{match } + \beta_{motor}* x_{motor}+ \beta_{eff}* x_{eff} + \beta_{session} * x_{session} + b_{participant}\). A two-way repeated measures analysis of variance was performed to examine the difference in the effects of hands versus gaze on performance (i.e., the factor
effector type) in combination with either
motor task or
effector efficiency. Post-hoc statistical comparisons across conditions were performed with two-tailed, paired Student's
t-tests (alpha = 0.05). Correlations between the average percent correct of ground truth and the modeled predictions across conditions were computed with Spearman's rho (which is here most appropriate due to the skewed distribution of data caused by the deviant percent correct for mismatch trials).