Introduction
Temporal data typically arrives as a set of many observational units measured over time. Some variables may be categorical, containing a hierarchy in the collection process, that may be measurements taken in different geographic regions, or types of products sold by one company. Exploring these multiple features can be daunting. Ensemble graphics (Unwin and Valero-Mora 2018) bundle multiple views of a data set together into one composite figure. These provide an effective approach for exploring and digesting many different aspects of temporal data. Adding interactivity to the ensemble can greatly enhance the exploration process.
This paper describes new software, the tsibbletalk package, for exploring temporal data using linked views and time wrapping. We first provide some background to the approach based on setting up data structures and workflow, and give an overview of interactive systems in R. The section following introduces the tsibbletalk package. We explain the mechanism for constructing interactivity, to link between multiple hierarchical data objects and hence plots, and describe the set up for interactively slicing and dicing time to wrap a series on itself to investigate periodicities.
Background: tidy temporal data and workflow
The tsibble package (Wang et al. 2020) introduced a unified temporal data structure, referred to as a tsibble, to represent time series and longitudinal data in a tidy format (Wickham 2014). A tsibble extends the data.frame and tibble classes with the temporal contextual metadata: index and key. The index declares a data column that holds time-related indices. The key identifies a collection of related series or panels observed over the index-defined period, which can comprise multiple columns. An example of a tsibble can be found in the monthly Australian retail trade turnover data (aus_retail), available in the tsibbledata package (O’Hara-Wild et al. 2020c), shown below. The Month column holds year-months as the index. State and Industry are the identifiers for these 152 series, which form the key. Note that the column Series ID could be an alternative option for setting up the key, but State and Industry are more readable and informative. The index and key are “sticky” columns to a tsibble, forming critical pieces for fluent downstream temporal data analysis.
#> # A tsibble: 64,532 x 5 [1M]
#> # Key: State, Industry [152]
#> State Industry `Series ID` Month Turnover
#> <chr> <chr> <chr> <mth> <dbl>
#> 1 Australian Capital Territory Cafes, r… A3349849A 1982 Apr 4.4
#> 2 Australian Capital Territory Cafes, r… A3349849A 1982 May 3.4
#> 3 Australian Capital Territory Cafes, r… A3349849A 1982 Jun 3.6
#> 4 Australian Capital Territory Cafes, r… A3349849A 1982 Jul 4
#> 5 Australian Capital Territory Cafes, r… A3349849A 1982 Aug 3.6
#> # … with 64,527 more rowsIn the spirit of tidy data from the tidyverse (Wickham et al. 2019), the tidyverts suite features tsibble as the foundational data structure, and helps to build a fluid and fluent pipeline for time series analysis. Besides tsibble, the feasts (O’Hara-Wild et al. 2020b) and fable (O’Hara-Wild et al. 2020a) packages fill the role of statistical analysis and forecasting in the tidyverts ecosystem. During all the steps of a time series analysis, the series of interest, denoted by the key variable, typically persist, through the trend modeling and also forecasting. We would typically want to examine the series across all of the keys.
Figure 1 illustrates examining temporal data with many keys. The data has 152 series corresponding to different industries in retail data. The multiple series are displayed using an overlaid time series plot, along with a scatterplot of two variables (trend versus seasonal strength) from feature space, where each series is represented by a dot. The feature space is computed using the features() function from feasts, which summarises the original data for each series using various statistical features. This function along with other tidyverts functions is tsibble-aware, and outputs a table in a reduced form where each row corresponds to a series, which can be graphically displayed as in Figure 1 (right).
Figure 1: Plots for the data, with the series of strongest seasonal strength highlighted. (a) An overlaid time series plot. (b) A scatter plot drawn from their time series features, where each dot represents a time series from (a).
Figure 1 has also been highlighted to focus on the one series with the strongest seasonality. To create this highlighting, one needs to first filter the interesting series from the features table, and join back to the original tsibble in order to examine its trend in relation to others. This procedure can soon grow cumbersome if many series are to be explored. It illustrates a need to query interesting series on the fly. Although these two plots are static, we can consider them as linked views because the common key variables link between the two data tables producing the two plots. This motivates the work in this package, described in this paper, to enable interactivity of tsibble and tsibble-derived objects for rapid exploratory data analysis.
Overview of interactivity
There is a long history of interactive data visualization research and corresponding systems. Within R, the systems can be roughly divided into systems utilizing web technology and those that do not.
R shiny (Chang et al. 2020) and htmlwidgets (Vaidyanathan et al. 2019) provide infrastructure connecting R with HTML elements and JavaScript that support the interactivity. The htmlwidgets package makes it possible to embed JavaScript libraries into R so that users are able to write only R code to generate web-based plots. Many JavaScript charting libraries have been ported to R as HTML widgets, including plotly (Sievert 2020), rbokeh (Hafen and Continuum Analytics, Inc. 2020), and leaflet (Cheng et al. 2019) for maps. Interactions between different widgets can be achieved with shiny or crosstalk (Cheng 2020). The crosstalk extends htmlwidgets with shared R6 instances to support linked brushing and filtering across widgets, without relying on shiny.
Systems without the web technology include grDevices, loon (Waddell and Oldford 2020), based on Tcl/Tk, and cranvas (Xie et al. 2014) based on Qt. They offer a wide array of pre-defined interactions, such as selecting and zooming, to manipulate plots via mouse action, keyboard strokes, and menus. The cranvastime package (Cheng et al. 2016) is an add-on to cranvas, which provides specialized interactions for temporal data, such as wrapping and mirroring.
The techniques implemented in the work described in this paper utilize web technology, including crosstalk, plotly, and R shiny.
Using a shared temporal data object for interactivity
The tsibbletalk package introduces a shared tsibble instance built on a tsibble. This allows for seamless communication between different plots of temporal data. The as_shared_tsibble() function turns a tsibble into a shared instance, SharedTsibbleData, which is a subclass of SharedData from crosstalk. This is an R6 object driving data transmission across multiple views, due to its mutable and lightweight properties. The tsibbletalk package aims to streamline interactive exploration of temporal data, with the focus of temporal elements and structured linking.
Linking between plots
As opposed to one-to-one linking, tsibbletalk defaults to categorical variable linking, where selecting one or more observations in one category will broadcast to all other observations in this category. That is, linking is by key variables: within the time series plot, click on any data point, and the whole line will be highlighted in response. The as_shared_tsibble() uses tsibble’s key variables to achieve these types of linking.
The approach can also accommodate temporal data of nesting and crossing structures. These time series are referred to as hierarchical and grouped time series in the literature (Hyndman and Athanasopoulos 2017). The aus_retail above is an example of grouped time series. Each series in the data corresponds to all possible combinations of the State and Industry variables, which means they are intrinsically crossed with each other. When one key variable is nested within another, such as regional areas within a state, this is considered to be a hierarchical structure.
The spec argument in as_shared_tsibble() provides a means to construct hybrid linking, that incorporates hierarchical and categorical linking. A symbolic formula can be passed to the spec argument, to define the crossing and/or nesting relationships among the key variables. Adopting Wilkinson and Rogers (1973)’s notation for factorial models, the spec follows the / and * operator conventions to declare nesting and crossing variables, respectively. The spec for the aus_retail data is therefore specified as State * Industry or Industry * State, which is the default for the presence of multiple key variables. If there is a hierarchy in the data, using / is required to indicate the parent-child relation, for a strictly one directional parent/child.
To illustrate nesting and crossing we use the tourism_monthly dataset (Tourism Research Australia 2020) packaged in tsibbletalk. It contains monthly domestic overnight trips across Australia. The key is comprised of three identifying variables: State, Region, and Purpose (of the trip), in particular State nesting of Region, crossed together with Purpose. This specification can be translated as follows:
library(tsibble)
library(tsibbletalk)
library(dplyr)
tourism_shared <- tourism_monthly %>%
# Comment out the next line to run the full example
filter(State %in% c("Tasmania", "Western Australia")) %>%
mutate(Region = stringr::str_replace(Region, "Australia's ", "WA's ")) %>%
as_shared_tsibble(spec = (State / Region) * Purpose)
There is a three-level hierarchy: the root node is implicitly Australia, geographically disaggregated to states, and lower-level tourism regions. A new handy function plotly_key_tree() has been implemented to help explore the hierarchy. It interprets hierarchies in the shared tsibble’s spec as a tree view, built with plotly. The following code line produces the linked tree diagram (left panel of Figure 2). The visual for the tree hierarchy detangles a group of related series and provides a bird’s eye view of the data organization.
p_l <- plotly_key_tree(tourism_shared, height = 800, width = 800)
The tree plot provides the graphics skeleton, upon which the rest of the data plots can be attached. In this example, small multiples of line plots are placed at the top right of Figure 2 to explore the temporal trend across regions by the trip purpose. The shared tsibble data can be directly piped into ggplot2 code to create this.
library(ggplot2)
p_tr <- tourism_shared %>%
ggplot(aes(x = Month, y = Trips)) +
geom_line(aes(group = Region), alpha = .5, size = .4) +
facet_wrap(~ Purpose, scales = "free_y") +
scale_x_yearmonth(date_breaks = "5 years", date_labels = "%Y")
These line plots are heavily overplotted. To tease apart structure in the multiple time series, the features() function computes interesting characteristics, including the measures of trend and seasonality. These are displayed in the scatterplot at the bottom right, where one dot represents one series.
There is one final step, to compose the three plots into an ensemble of coordinated views for exploration, shown in Figure 2. (This is the interactive realization of Figure 1).