`../../Rtrack_website/vignettes/Rtrack_APA_metrics_description.Rmd`

`Rtrack_APA_metrics_description.Rmd`

At the heart of Rtrack is the processing of the raw paths to yield descriptive metrics. Some of these metrics, such as ‘path length’ and ‘time in wall zone’ are easily explained. Others are less clear, are named differently by different authors and/or depend on varying parameters.

This document describes each of the metrics calculated by
`calculate_metrics`

and the parameters used in their
definition.

A core functionality of the Rtrack package is the calculation of
metrics from the path coordinates. The `rtrack_metrics`

object that is returned by `calculate_metrics`

contains the
results of these calculations which are used for prediction by the
machine learning model. This section explains the information contained
in the `rtrack_metrics`

object and describes the individual
metrics in detail.

This section contains information that has been passed to the
`calculate_metrics`

function and is embedded in the
`rtrack_metrics`

object for convenience.

This is the track id supplied either to `read_path`

or
`read_experiment`

and should be a unique identifier for the
track. This will be used to name track analysis output and to title the
plots generated by `plot_path`

or
`plot_density`

.

The `rtrack_arena`

object associated with this track. See
the function `read_arena`

for details.

The active place avoidance arena is a circular space made up of several zones. The zones for this arena type are as follows:

- The
*arena*is defined as the circular arena in which the experiment was performed. The raw size, shape and centre point (to allow for path recording calibration) are set by the experimenter in the arena definition file/s (see the function`read_arena`

). The fraction of time spent in this zone should be 1 (excepting only small calibration errors). - The
*centre*is defined as a ring with a radius 20 % of the arena diameter, and which is centred on the centre of the arena. - The
*wall*is defined as a ring with the outer extent bounded by the pool/arena and the inner radius equal to 60 % of the arena radius (i.e. the wall zone width is 20 % of the pool/arena diameter). - The
*aversive.zone*is a sector of the arena that the subjects have been trained to avoid. The width of this sector is determined in the arena description file. - The
*old.aversive.zone*, if present, is a sector of the arena where the aversive zone was previously located. This is used for reversal trials. - The quadrants. The north quadrant is the quarter of the arena area
that is centred on the middle of the aversive zone. The other quadrants
are defined based on this.
*The quadrant definitions thus change when the aversive zone is moved (such as during a reversal).*

This section contains all the metrics, including those calculated for all time points (such as distance from goal and heading error).

The length of the path. This is in whatever units the path was measured in (millimetres, inches, pixels).

The *x* coordinates of all timepoints where the subject was
immobile. This is useful for plotting the spatial locations of periods
of immobility.

The *y* coordinates of all timepoints where the subject was
immobile. This is useful for plotting the spatial locations of periods
of immobility.

The angle, in the direction of rotation, separating the position of
the subject at each timepoint from the leading edge of the aversive
zone. If the subject is *in* the aversive zone, this angle is
0.

The number of times the path crossed (i.e. entered and exited once) the aversive.zone.

The fraction of the arena covered by the path. This is measured by calculating the area of the minimal polygon enclosing the path (i.e. the ‘silhouette’; actually the ‘convex hull’ in technical terms) as a fraction of the area of the arena.

This is an application of the Shannon entropy measure to spatial paths. In Rtrack, it is estimated by calculating a density map with a 50 \(\times\) 50 grid (and a bandwidth of 1/50) which is clipped to the bounds of the arena. This gives a computationally fast estimate of \(p\); the likelihood of the path passing through any one of the grid cells. The entropy is then calculated using Shannon’s equation: \(-\sum(p\times log(p))\). This value is then normalised by dividing by the log of the total number of grid cells present in the arena (so that the final value ranges between 0 and 1). A roaming entropy of 1 means that the path covers the entire arena and it is impossible to predict a point on the path. A roaming entropy of 0 occurs when the entire path is within one grid cell. Lower entropy values indicate a more predictable path. The idea behind the roaming entropy measure is demonstrated at http://www.brandmaier.de/roamingentropy/.

The speed at which the subject is moving in each zone. This is a list, with values computed for each of the defined zones.

The total duration that the subject was immobile in each zone. This is a list, with values computed for each of the defined zones.

The time at which the subject first crossed each zone. This is a list, with values computed for each of the defined zones.

The summary metrics are derived from the core metrics above, but are each only a single value (typically the mean).

This vector of (normalised) values is used for strategy calling using
the machine learning model implemented in `call_strategy`

.
These are not useful for further analysis on their own.

This is a selection of summary metrics that make sense for downstream
analysis. These values use the same units as the raw input data. That
is, the distances are in whatever units the track acquisition software
used (this may be centimetres, inches or even just pixels from the video
analysis—you will need to check with your acquisition software if you
are unsure of what these are). Times are in the units specified in the
arena description file. These will be ( *must* be!) the units of
the timestamps in the raw acquisition data. Most of these values are
*medians* of the metrics calculated for each point on the path^{1}.

The total length of the path. This is just the sum of the distance between each point and the next point in the path.

The total time the subject spent in the arena. This is not necessarily the same as the maximum trial duration; e.g. in cases where the subject finds the platform early.

The median `velocity`

. The speed of movement at each time
interval. In path units per second.

The median angle of each point on the path from the leading edge of the aversive zone (see angle.from.aversive.zone above).

The median angle of each point on the path from the leading edge of the old aversive zone (see angle.from.aversive.zone above).

The roaming entropy (see roaming.entropy above).

The time at which the subject first crossed the aversive zone (see latency.to.zone above). This will be
`NA`

if the aversive zone was never entered

The time at which the subject first crossed the old aversive zone
(see latency.to.zone above). This will be
`NA`

if the old aversive zone was never entered or if there
was no old aversive zone defined.

The number of times the path crossed the aversive zone (see goal.crossings above).

Below is an overview of the hierarchy of the
`rtrack_metrics`

object together with the names and classes
of each component. Where the class is not part of the R base package, it
is given in square brackets after the class name.

```
metrics : rtrack_metrics [Rtrack]
id : character
arena : rtrack_arena [Rtrack]
id : character
type : character
description : data.frame
type : character
time.units : character
arena.bounds : character
goal : character
(old.goal : character) **this component is optional and may be missing**
correction : list
t : numeric
x : numeric
y : numeric
r : numeric
pool : list
shape : character
x : numeric
y : numeric
radius : numeric
goal : list
shape : character
x : numeric
y : numeric
radius : numeric
old.goal : list
shape : character
x : numeric
y : numeric
radius : numeric
zones : list
arena : PackedSpatVector [terra]
centre : PackedSpatVector [terra]
wall : PackedSpatVector [terra]
aversive.zone : PackedSpatVector [terra]
(old.aversive.zone : PackedSpatVector [terra]) **this component is optional and may be missing**
n.quadrant : PackedSpatVector [terra]
e.quadrant : PackedSpatVector [terra]
s.quadrant : PackedSpatVector [terra]
w.quadrant : PackedSpatVector [terra]
area : list
arena : numeric
centre : numeric
wall : numeric
aversive.zone : numeric
(old.aversive.zone : numeric) **this component is optional and may be missing**
n.quadrant : numeric
e.quadrant : numeric
s.quadrant : numeric
w.quadrant : numeric
path : rtrack_path
id : character
raw.t : numeric
raw.x : numeric
raw.y : numeric
t : numeric
x : numeric
y : numeric
path.length : numeric
velocity : numeric
immobile : numeric
immobile.x : numeric
immobile.y : numeric
immobility : numeric
total.time : numeric
angle.from.aversive.zone : numeric
angle.from.old.aversive.zone : numeric
goal.crossings : numeric
coverage : numeric
roaming.entropy : numeric
velocity.in.zone : numeric
immobility.in.zone : numeric
latency.to.zone : numeric
time.in.zone : numeric
zone.crossings : numeric
features : numeric
path.length : numeric
lower.velocity : numeric
median.velocity : numeric
upper.velocity : numeric
lower.immobility : numeric
median.immobility : numeric
upper.immobility : numeric
coverage : numeric
turning : numeric
absolute.turning : numeric
lower.angle.from.aversive.zone : numeric
median.angle.from.aversive.zone : numeric
upper.angle.from.aversive.zone : numeric
lower.angle.from.old.aversive.zone : numeric
median.angle.from.old.aversive.zone : numeric
upper.angle.from.old.aversive.zone : numeric
roaming.entropy : numeric
velocity.in.centre.zone : numeric
velocity.in.wall.zone : numeric
velocity.in.aversive.zone : numeric
velocity.in.old.aversive.zone : numeric
immobility.in.centre.zone : numeric
immobility.in.wall.zone : numeric
immobility.in.aversive.zone : numeric
immobility.in.old.aversive.zone : numeric
latency.to.centre.zone : numeric
latency.to.wall.zone : numeric
latency.to.aversive.zone : numeric
latency.to.old.aversive.zone : numeric
time.in.centre.zone : numeric
time.in.wall.zone : numeric
time.in.aversive.zone : numeric
time.in.old.aversive.zone : numeric
centre.zone.crossings : numeric
wall.zone.crossings : numeric
aversive.zone.crossings : numeric
old.aversive.zone.crossings : numeric
summary : numeric
path.length : numeric
total.time : numeric
velocity : numeric
immobility : numeric
angle.from.aversive.zone : numeric
angle.from.old.aversive.zone : numeric
roaming.entropy : numeric
latency.to.aversive.zone : numeric
latency.to.old.aversive.zone : numeric
time.in.centre.zone : numeric
time.in.wall.zone : numeric
time.in.aversive.zone : numeric
time.in.old.aversive.zone : numeric
aversive.zone.crossings : numeric
old.aversive.zone.crossings : numeric
```

Most of the metrics are not normally distributed so so-called parametric statistics may not be appropriate. For this reason, Rtrack defaults to using non-parametric descriptive statistics such as median and the upper/lower quartiles.↩︎