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---
title: "A Guide to Working with Quantities"
author: "Iñaki Ucar"
date: "`r Sys.Date()`"
output:
rmarkdown::html_vignette:
toc: yes
vignette: >
%\VignetteIndexEntry{A Guide to Working with Quantities}
%\VignetteEngine{knitr::rmarkdown}
%\VignetteEncoding{UTF-8}
---
```{r, cache = FALSE, include=FALSE}
knitr::opts_chunk$set(collapse = T, comment = "#>",
fig.width = 6, fig.height = 4, fig.align = "center")
```
## Introduction
This document intends to be a guide on how to work with quantities data (magnitudes with units and/or uncertainty) in two distinct workflows: R *base* and the so-called [*tidyverse*](https://www.tidyverse.org/). Units and errors (and, by extension, quantities) objects essentially are numeric vectors, arrays and matrices with associated metadata. This metadata is not always compatible with some functions, and thus we here explore the most common operations in data wrangling (subsetting, ordering, transformations, aggregations...) to identify potential issues and propose possible workarounds.
Let us consider the traditional `iris` data set for this exercise. According to its documentation,
> `iris` is a data frame with 150 cases (rows) and 5 variables (columns) named `Sepal.Length`, `Sepal.Width`, `Petal.Length`, `Petal.Width`, and `Species`.
And values are provided in centimeters. If we consider, for instance, a 5% of uncertainty, the first step is to define proper quantities. Then we will work on the resulting data frame for the rest of this article.
```{r}
library(quantities)
iris.q <- iris
for (i in 1:4)
quantities(iris.q[,i]) <- list("cm", iris.q[,i] * 0.05)
head(iris.q)
```
Note that, throughout this document, and unless otherwise stated, we will talk about *quantities objects* as a shortcut for *quantities, units and errors objects*.
## R Base
In this section, we consider all the methods and functions included in the default packages, i.e., those that are automatically installed along with any R distribution:
```{r, eval=FALSE}
rownames(installed.packages(priority="base"))
```
```{r, echo=FALSE}
print(c("base", "compiler", "datasets", "graphics", "grDevices", "grid", "methods", "parallel", "splines", "stats", "stats4", "tcltk", "tools", "utils"))
```
### Row Subsetting
Quantities objects have all the subsetting methods defined (`[`, `[[`, `[<-`, `[[<-`). Therefore they can be used in the same way as with plain numeric vectors, and in conjunction with `which` and other functions to perform subsetting. The `subset` function is very handy too and achieves the same result:
```{r}
iris.q[which(iris.q$Sepal.Length > set_quantities(7.5, cm)), ]
subset(iris.q, Sepal.Length > set_quantities(7.5, cm))
```
Note that another quantities object is defined for the comparison. This is needed because different units are incomparable. Also note that the first line throws a warning telling us that the uncertainty was dropped for this operation. This kind of warning is thrown once, and this is why `subset` succeeds silently.
### Row Ordering
The `sort` function, as its name suggests, *sorts* vectors, and it is compatible with quantities:
```{r}
iris.q$Sepal.Length[1:5]
sort(iris.q$Sepal.Length[1:5])
```
More generally, the `order` function can be used for data frame ordering:
```{r}
head(iris.q[order(iris.q$Sepal.Length), ])
```
### Column Transformation
The `transform` function is able to modify variables in a data frame or to create new ones. The `within` function provides a similar but more flexible approach though. Both are fully compatible with quantities:
```{r}
head(within(iris.q, {
Sepal.Area <- Sepal.Length * Sepal.Width
Petal.Area <- Petal.Length * Petal.Width
rm(Sepal.Length, Sepal.Width, Petal.Length, Petal.Width)
}))
```
### Row Aggregation
Row aggregation is the process of summarising data based on some grouping variable(s). There are several ways of working with data split by factors in R base, and, although they tend to preserve classes, they are generally not very kind to other metadata (i.e., attributes) by default.
In the following example, the average `Sepal.Length` is computed per `Species`, but the metadata gets dropped:
```{r}
tapply(iris.q$Sepal.Length, iris.q$Species, mean)
```
Many of these functions include a `simplify` parameter which, if set to `FALSE`, preserves quantities metadata:
```{r}
(sepal.length.agg <-
tapply(iris.q$Sepal.Length, iris.q$Species, mean, simplify=FALSE))
```
The only drawback is that the result is a list, and such a list must be unlisted with care, otherwise, metadata gets dropped again:
```{r}
# drops quantities
unlist(sepal.length.agg)
# preserves quantities
do.call(c, sepal.length.agg)
```
The `by` function is an object-oriented wrapper for `tapply` applied to data frames which also provides a `simplify` parameter. A more convenient way of working with summary statistics is the `aggregate` generic, from the `stats` namespace. Although there is a `aggregate.data.frame` method, there is a more intuitive interface to it through the `aggregate.formula` method. Again, it is necessary to set `simplify=FALSE` to keep quantities:
```{r}
(iris.q.agg <- aggregate(. ~ Species, data = iris.q, mean, simplify=FALSE))
```
Apparently, the output has no metadata associated, but what really happens is that the resulting columns are lists:
```{r}
class(iris.q.agg$Sepal.Length)
```
Therefore, as in the `tapply`/`by` case, they must be unlisted with care to still preserve the metadata:
```{r}
unlist_quantities <- function(x) {
stopifnot(is.list(x) || is.data.frame(x))
unlist <- function(x) {
if (any(class(x[[1]]) %in% c("quantities", "units", "errors")))
do.call(c, x)
else x
}
if (is.data.frame(x))
as.data.frame(lapply(x, unlist), col.names=colnames(x))
else unlist(x)
}
unlist_quantities(iris.q.agg)
```
And this method works for the `tapply`/`by` case too:
```{r}
unlist_quantities(sepal.length.agg)
```
### Column Joining
Joining data frames by common columns can done with the `merge` generic. Such operations are based on appending columns, which may be subset or replicated to fit the length of the merged observations. Therefore, quantities should be preserved in all cases. In the following example, we generate a data frame with the height per species and then merge it with the main data set:
```{r}
height <- data.frame(
Height = set_quantities(c(55, 60, 45), cm, c(45, 30, 35)),
Species = c("setosa", "virginica", "versicolor")
)
head(merge(iris.q, height))
```
### (Un)Pivoting
The `reshape` function, from the `stats` namespace, provides an interface for both pivoting and unpivoting (i.e., *tidyfying* data). In the case of the `iris` data set, we would say that it is in the *wide format*, because each row has more than one observation.
This function has a quite peculiar nomenclature. First of all, the unpivoting operation is accessed by providing the argument `direction="long"`. We need to define the `varying` columns (columns to unpivot), as character or indices, and they are unpivoted based on their names. By default, the separator `sep="."` is used, which means that `Sepal.Width` will be broken down into `Sepal` and `Width`, and the former will be unpivoted with the latter as grouping variable. We can specify the name of the grouping variable with the `timevar` argument.
Putting everything together, this is how to unpivot the data set by the dimension (which we will call it `dim`) of the petal/sepal:
```{r}
long.1 <- reshape(iris.q, varying=1:4, timevar="dim", idvar="dim.id", direction="long")
head(long.1)
```
It can be noted that the unpivoting also generates an index to indentify multiple records from the same group. We have changed the name of that identifier to `dim.id` (just `id` by default).
We can further unpivot sepal and petal as the `part` of the flower. First, we need to prepend a common identifier to columns 3 and 4, which are to be unpivoted:
```{r}
names(long.1)[3:4] <- paste0("value.", names(long.1)[3:4])
long.2 <- reshape(long.1, varying=3:4, timevar="part", idvar="part.id", direction="long")
head(long.2)
```
And the final result has one tidy observation per row.
The pivoting operation can be accessed by providing the argument `direction="wide"`. The process is almost symmetrical, but we need to specify `v.names`, as character, instead of `varying` columns. First, we can pivot by flower part:
```{r}
wide.1 <- reshape(long.2, v.names="value", timevar="part", idvar="part.id", direction="wide")
head(wide.1)
```
Then, we remove `"value."` from the column names and pivot by dimension (note that indices are removed to match the initial data frame):
```{r}
names(wide.1)[5:6] <- sub("value\\.", "", names(wide.1)[5:6])
wide.2 <- reshape(wide.1, v.names=c("Sepal", "Petal"), timevar="dim", idvar="dim.id", direction="wide")
wide.2$dim.id <- NULL
wide.2$part.id <- NULL
head(wide.2)
```
We have seen that quantities have been correctly preserved through the whole process. Finally, we can check whether both data frames are identical. Given that the order of columns have changed, we can simply check this column name by column name and then put everything together:
```{r}
all(sapply(colnames(iris.q), function(col) all(iris.q[[col]] == wide.2[[col]])))
```
## Tidyverse
```{r, cache = FALSE, include=FALSE}
required <- c("dplyr", "tidyr")
if (!all(sapply(required, requireNamespace, quietly = TRUE)))
knitr::opts_chunk$set(eval = FALSE)
```
The [*core tidyverse*](https://www.tidyverse.org/packages/) includes the following packages: `ggplot2`, `dplyr`, `tidyr`, `readr`, `purrr`, `tibble`, `stringr` and `forcats`. This section covers use cases for [`dplyr`](https://dplyr.tidyverse.org/) (everything except for pivoting and unpivoting) and [`tidyr`](https://tidyr.tidyverse.org/) (for pivoting and unpivoting).
```{r, message=FALSE, warning=FALSE}
library(dplyr); packageVersion("dplyr")
library(tidyr); packageVersion("tidyr")
```
### Row Subsetting
The `filter` generic finds observations where conditions hold. The main difference with base subsetting is that, if a condition evaluates to `NA` for a certain row, it is dropped. As in the base case, another quantities object must be defined for the comparison:
```{r}
iris.q %>%
filter(Sepal.Length > set_quantities(7.5, cm)) %>%
head()
```
There are also three scoped variants available (`filter_all`, `filter_if`, `filter_at`) and a subsetting function by row number called `slice`. All of them preserve quantities.
### Row Ordering
The `arrange` generic sorts variables in a straightforward way, and it is compatible with quantities:
```{r}
iris.q %>%
arrange(Sepal.Length) %>%
head()
```
The `desc` function can be applied to individual variables to arrange in descending order.
### Column Transformation
There are two generics for column transformations: `mutate` modifies or adds new variables preserving the existing ones, while `transmute` drops the existing variables. The syntax is very similar to base functions `transform` and `within`, and equally compatible with quantities:
```{r}
iris.q %>%
transmute(
Species = Species,
Petal.Area = Petal.Length * Petal.Width,
Sepal.Area = Sepal.Length * Sepal.Width
) %>%
head()
```
### Row Aggregation
`dplyr` breaks down aggregation operations in two distinct parts: grouping (with `group_by`) and summarising (using `summarise` and others). The shortcoming of this approach is that it is possible to apply other operations (such as subsetting) to grouped data, which may lead to performance degradation.
Another shortcoming is that `dplyr`'s grouped operations are not yet fully compatible with quantities (see [tidyverse/dplyr#2773](https://github.com/tidyverse/dplyr/issues/2773)):
```{r}
iris.q %>%
group_by(Species) %>%
summarise_all(mean)
```
As we can see above, although units are correctly preserved, uncertainty is not correctly handled.
```{r}
iris.q %>%
mutate_at(vars(-Species), drop_errors) %>%
group_by(Species) %>%
summarise_all(mean)
```
Units alone work without issue, but errors or full-featured quantities are not compatible with `dplyr`'s grouped operations.
### Column Joining
Several verbs are provided for different types of joins, such as `inner_join`, `left_join`, `right_join` or `full_join`. It seems that, internally, they use the same grouping mechanism than summaries, and therefore they will generally fail for errors and full-featured quantities (note the missing uncertainty, as in the previous case):
```{r}
iris.q %>%
left_join(data.frame(
Height = set_quantities(c(55, 60, 45), cm, c(45, 30, 35)),
Species = c("setosa", "virginica", "versicolor")
)) %>%
head()
```
### (Un)Pivoting
Finally, pivoting and unpivoting is handled by a separate package, `tidyr`, using the verbs `spread` (pivot) and `gather` (unpivot).
The unpivoting operation is substantially more straightforward. In the next example, we directly merge the four columns of interest into the `value` column, and the correspoding column names are gathered into the `key` column. Such a column is then separated into flower `part` (sepal, petal) and `dim` (length, height):
```{r}
iris.q %>%
gather("key", "value", 1:4) %>%
separate(key, c("part", "dim")) %>%
head()
```
Unfortunately, it is evident that the operation completely drops all classes and attributes, and then quantities are not preserved.
The pivoting operation does preserve classes and attributes, but the latter ones are not correctly handled. In the following example, we first gather the original data set, then we assign quantities and try to spread it to obtain `iris.q`:
```{r}
wide <- iris %>%
# first gather, with row numbers as row_id
mutate(row_id = 1:n()) %>%
gather("key", "value", 1:4) %>%
separate(key, c("part", "dim")) %>%
# assign quantities
mutate(value = set_quantities(value, cm, value * 0.05)) %>%
# now spread
unite(key, part, dim, sep=".") %>%
spread(key, value) %>%
select(-row_id)
head(wide)
```
Apparently, everything worked, but in fact it didn't:
```{r, error=TRUE}
all(sapply(colnames(iris.q), function(col) all(iris.q[[col]] == wide[[col]])))
length(errors(iris.q$Sepal.Length))
length(errors(wide$Sepal.Length))
```
As shown above, the uncertainty was not properly subset and pivoted.
## Summary
R base works smoothly with quantities in most cases. The only shortcoming is that some care must be applied to aggregations. In particular, simplification must be explicitly disabled (`simplify=FALSE`), and such a simplification (i.e., converting lists to vectors of quantities) must be applied manually while avoiding `unlist`.
The tidyverse handles quantities correctly for subsetting, ordering and transformations. It fails to do so for aggregations (grouped operations in general), column joining and (un)pivoting. Most of these incompatibilities are due to the same internal grouping mechanism, which is in C and prevents the R subsetting operator from being called (which in turn calls the subsetting operator on the errors attribute). Interestingly, those operations still work for units alone, except for column gathering, which drops all classes and attributes.
## A Note on `data.table`
The [`data.table`](https://github.com/Rdatatable/data.table/wiki) package is another popular data tools, which provides *a high-performance version of base R's `data.frame` with syntax and feature enhancements for ease of use, convenience and programming speed*.
Long story short, we have not included a section on `data.table` because *currently* (v1.11.4) it does not work well with vectorised attributes. The underlying problem is similar to `dplyr`'s issue, but unfortunately it affects more operations, including row subsetting and ordering. Only column transformation seems to work, and other operations generate corrupted objects.
We have found that defining quantities columns as lists (where each element consists of a single value, with unit and uncertainty) may be a workaround, but this probably would be a serious performance penalty for a package that is typically chosen for speed reasons.