The purpose of interpolation is to replace gaps of missing values using an estimation function. See https://dr-jt.github.io/pupillometry/ for more information.

```
pupil_interpolate(
x,
type = "cubic-spline",
maxgap = Inf,
hz = "",
plot = FALSE,
plot_trial = "all"
)
```

- x
dataframe.

- type
What type of interpolation to use? "linear" or "cubic-spline".

- maxgap
Maximum number of NAs to interpolate over. Any gaps over this value will not be interpolated.

- hz
The recording frequency (used to calculate maxgap).

- plot
Logical. Inspect a plot of how pupil values changed?

- plot_trial
what trial(s) to plot. default = "all"

Changes values in the column containing pupil data.

This function applies either a linear or cubic-spline interpolation.

The linear interpolation is the most straighforward to understand. It basically draws a straight line from one end of the missing data to the other end. Linear interpolation is adequate if the actual curve of the pupil response is not of interest, such as when looking at summary statistics (mean, standard deviation) over fairly large intervals.

The cubic-spline interpolation will more accurately reflect the actual curve of the pupil response over gaps of missing values. This is more important to use if the actual curve of the pupil response is of interest, such as when looking at peak or minimum values or when doing growth curve analysis.

It may not be a good idea to interpolate over too large of gaps with missing values. For instance, you may not want to interpolate over a gap duration that is equivalent to the length of your time-of-interest. You can specify the maximum gap of missing values to interpolate over using the `maxgap` argument (in milliseconds). If `maxgap` is used, then the sampling frequency (`hz`) needs to be specified.

To inspect how the preprocesing step changed pupil size values, use `plot = TRUE`.

Warning: this will create a separate plot for every trial and therefore can be time consuming and overwhelming. The plot argument is meant for initial exploratory steps to determine the appropriate preprocessing parameters.

There are some advantages to up-sampling the data to a sampling frequency of 1000Hz, and is even a recommended step in preprocessing by Kiret & Sjak-Shie (2019).

Up-sampling, should occur before smoothing and interpolation. In general, it is safer to apply smoothing before interpolation (particularly if cubic-spline interpolation is to be used). However, if up-sampling is to be used, interpolation needs to occur first in order to fill in the missing up-sampled values. The question, then, is how can we apply smoothing first while still doing up-sampling?

This is resolved in this package by first up-sampling with `pupil_upsample()` and then smoothing `pupil_smooth()`. `pupil_upsample()` will not interpolate the missing up-sampled values. Instead, a linear interpolation will be done in`pupil_smooth()`, if `pupil_upsample()` was used prior, followed by smoothing and then after smoothing, originally missing values (including the missing up-sampled values and missing values due to blinks and other reasons) will replace the linearly interpolated values (essentially undoing the initial interpolation). After `pupil_smooth()`, interpolation can then be applied to the up-sampled-smoothed data with `pupil_interpolate()`.

This is all to say that, the intuitive workflow can still be used in which, `pupil_upsample()` is used, followed by `pupil_smooth()`, followed by `pupil_interpolate()`.

Alternatively, to interpolate before smoothing, `pupil_upsample()` is used, followed by `pupil_interpolate()`, followed by `pupil_smooth()`. The difference being that, in this case, no interpolation and then replacing the missing values back in the data is done in `pupil_smooth()` because interpolation was performed first anyways.