A Simple Example
Let us assume we are conducting a simple experiment. In our setup, participants must respond by moving a mouse cursor from a starting position (bottom circle, coordinates (0,0)) to one of two end positions (top circles, coordinates (-1,1) and (1,1)):
dat stores simple toy data that may reflect our pilot
results. Let’s inspect the structure of the data:
head(dat)
#> # A tibble: 6 × 5
#> Trial Target Time x_coord y_coord
#> <int> <chr> <int> <dbl> <dbl>
#> 1 1 left 0 0 0
#> 2 1 left 1 -0.01 0.0140
#> 3 1 left 2 -0.02 0.0278
#> 4 1 left 3 -0.03 0.0416
#> 5 1 left 4 -0.04 0.0554
#> 6 1 left 5 -0.05 0.069
# gg_background has been created previously and is a ggplot object
gg_background + geom_path(aes(x_coord, y_coord, group = Trial), dat)
In this example, Time reflects the time passed since the
onset of the imperative stimulus and always increases by 1 arbitrary
unit. In a real experiment, a sensible first pre-processing step would
be to double-check the order of your data via
is_monotonic() applied to Time. Further, in a
real experiment you would likely group by not only by Time,
but also other variables like a subject or block identifier.
dat <- dat %>%
group_by(Trial) %>%
mutate(
# will throw a warning if times are not monotonically increasing
is_ok = is_monotonic(Time)
)As a next step, we will recode the coordinates so we can treat
movements to the left and to the right in the same way. This enables us
to restrict the trajectories to their relevant parts, i.e., after the
home was left and before the target has been reached. This also allows
us to extract our first dependent measures, InitiationTime
and MovementTime:
dat <- dat %>%
group_by(Trial) %>%
mutate(
x_coord = ifelse(Target == "left", -x_coord, x_coord),
InitiationTime = time_circle_left(
x_coord,
y_coord,
Time,
x_mid = 0,
y_mid = 0,
radius = 0.2
),
CompletionTime = time_circle_entered(
x_coord,
y_coord,
Time,
x_mid = 1,
y_mid = 1,
radius = 0.2
),
MovementTime = CompletionTime - InitiationTime
) %>%
filter(Time >= InitiationTime & Time < CompletionTime)
dat %>%
group_by(Trial, InitiationTime, CompletionTime, MovementTime) %>%
count()
#> # A tibble: 4 × 5
#> # Groups: Trial, InitiationTime, CompletionTime, MovementTime [4]
#> Trial InitiationTime CompletionTime MovementTime n
#> <int> <int> <int> <int> <int>
#> 1 1 12 84 72 72
#> 2 2 10 76 66 66
#> 3 3 10 79 69 69
#> 4 4 9 83 74 74
gg_background + geom_path(aes(x_coord, y_coord, group = Trial), dat)
Note that filtering the data to the relevant part leads to an unequal
amount of data points for each trajectory (column n). This
is bad news when you want to display average trajectories! One solution
for this problem is “time-normalization,” i.e., a separate linear
interpolation of the x and y coordinates at certain time points. It has
been proposed that this process should be done prior to the computation
of MAD, AUC, etc. So let’s do this via interp2(), a
convenient wrapper to signal::interp1():
dat_int <- dat %>%
group_by(Trial) %>%
reframe(
Time_new = 0:100,
x_new = interp2(Time, x_coord, 101),
y_new = interp2(Time, y_coord, 101),
)Now we are ready to compute dependent measures like AUC and MAD:
dat_int %>%
group_by(Trial) %>%
summarise(
MAD = max_ad(x_new, y_new),
AUC = auc(x_new, y_new),
CUR = curvature(x_new, y_new)
)
#> # A tibble: 4 × 4
#> Trial MAD AUC CUR
#> <int> <dbl> <dbl> <dbl>
#> 1 1 0.0353 0.0239 1.00
#> 2 2 -0.0274 -0.0183 1.00
#> 3 3 0.0462 0.0314 1.01
#> 4 4 0.126 0.0907 1.04As a last step, you may want to plot your average trajectory:
dat_avg <- dat_int %>%
group_by(Time_new) %>%
summarise(
x_avg = mean(x_new),
y_avg = mean(y_new)
)
gg_background +
geom_path(aes(x_avg, y_avg), dat_avg) +
geom_path(aes(c(0, 1), c(0, 1)), linetype = "dashed") # ideal trajectory
Congratulations, you worked trough your first mouse-tracking analysis!
As a final note: This package is currently under development. If you spot any bugs or have other improvement suggestions, please let us know by filing an issue at github.com/mc-schaaf/mousetRajectory/issues.