Perform fast and memory efficient time-weighted averaging of values measured over intervals into new arbitrary intervals.

This package is useful in the context of data measured or represented as constant values over intervals on a one-dimensional discrete axis (e.g. time-integrated averages of a curve over defined periods).

The intervalaverage package was written specifically to deal with air pollution data recorded or predicted as averages over sampling periods. Data in this format often needs to be shifted to non-aligned periods or averaged up to longer durations (e.g. averaging data measured over sequential non-overlapping periods to calendar years).

This package makes careful use of optimized data.table syntax to reduce copying so it is well suited to deal with large datasets. The function inputs and return values are always data.tables (with values, interval starts and interval ends stored as columns) which provide a straightforward representation of the data facilitating direct inspection and manipulation via data.table’s standard interface. Functions also accept optional grouping variables as arguments; these group-by operations get passed to data.table which avoids the overhead of looping directly in R.

You can install the package from CRAN (pending):

`install.packages("intervalaverage")`

Or you can install the current development version of the from GitHub:

```
# install.packages("devtools")
library(devtools)
install_github("kaufman-lab/intervalaverage","main",build_vignettes=TRUE)
```

or you can manually clone this repository from github and install from source.

Consider some PM2.5 data measured over periods occurring over a repeating 7-day schedule:

```
(x <- data.table(start=seq(1L,by=7L,length=6),
end=seq(7L,by=7L,length=6),
pm25=c(10,12,8,14,22,18)))
#> start end pm25
#> 1: 1 7 10
#> 2: 8 14 12
#> 3: 15 21 8
#> 4: 22 28 14
#> 5: 29 35 22
#> 6: 36 42 18
```

Note that the start and end columns define closed intervals (i.e. inclusive).

Imagine that we would like these PM2.5 measurements to be represented over a different set of intervals, such as the following 7-day schedule which does not align cleanly with the intervals in x:

```
(y <- data.table(start=seq(3L,by=7L,length=6),
end=seq(9L,by=7L,length=6)))
#> start end
#> 1: 3 9
#> 2: 10 16
#> 3: 17 23
#> 4: 24 30
#> 5: 31 37
#> 6: 38 44
```

Representing the PM25 measurements over the exact intervals in y is not strictly possible, since each y interval contains two x intervals which only partially overlap.

While there are several ways to compromise and approximate a representation of x over the periods in y, one reasonable approach is to average all the values of PM2.5 in x occuring over the interval of y. But since the two overlap durations of the two x periods into a single y period are unequal, the PM2.5 values should be averaged in a way that takes the duration of overlap into account. That is to say, we need a time-weighted average of values of x into intervals in y.

This is the exact purpose of the intervalaverage function:

```
(z <- intervalaverage(x,y,interval_vars=c("start","end"),
value_vars=c("pm25")))
#> start end pm25 yduration xduration nobs_pm25 xminstart xmaxend
#> 1: 3 9 10.571429 7 7 7 3 9
#> 2: 10 16 10.857143 7 7 7 10 16
#> 3: 17 23 9.714286 7 7 7 17 23
#> 4: 24 30 16.285714 7 7 7 24 30
#> 5: 31 37 20.857143 7 7 7 31 37
#> 6: 38 44 NA 7 5 5 38 42
```

(Note that the interval average package always assumes specified intervals are closed aka inclusive)

The pm25 value of 10.571429 is equal to `(5/7)*10 + (2/7)*12`

, where `5/7`

and `2/7`

are the respective time-weights of the the PM2.5 values based on their respective durations of overlap with the period `[3,9]`

.

Note that in z the average value of PM2.5 is missing (NA) for the final period in y. This is because there is insufficient PM25 to calculate an average. By using a looser completeness requirements we can get an average for this period in y (in general, this will just be the mean of non-missing values in x):

```
(z <- intervalaverage(x,y,interval_vars=c("start","end"),
value_vars=c("pm25"),required_percentage = 70))
#> start end pm25 yduration xduration nobs_pm25 xminstart xmaxend
#> 1: 3 9 10.571429 7 7 7 3 9
#> 2: 10 16 10.857143 7 7 7 10 16
#> 3: 17 23 9.714286 7 7 7 17 23
#> 4: 24 30 16.285714 7 7 7 24 30
#> 5: 31 37 20.857143 7 7 7 31 37
#> 6: 38 44 18.000000 7 5 5 38 42
```

There is much more described in the vignette. For example, it is possible to calculate averages within a grouping variable. For example if PM2.5 were measured at multiple locations, you could take the average separately at each location in one call to the `intervalaverage`

function. Averaging intervals need not be the same for each locations. See the vignette for examples.

Read the intro vignette for an in-depth demonstration of the package functions.

```
library(intervalaverage)
vignette("intervalaverage-intro")
```

For an overview of the internals of the `intervalaverage`

function, see the technical vignette:

`vignette("intervalaverage-technicaloverview")`