Quick legends with chord plots

Quick legends with circlize chord plots

The circlize package from Zuguang Gu is fantastic for drawing chord plots, amongst other things. It will even allow multiple arrows between two nodes.

library(circlize)

#create quick dataframe

links <- expand.grid(c("From_A","From_B"), c("To_C","To_D", "To_E"), c("cars", "vans"))

names(links) <- c("from", "to", "type")

links$traffic <- sample.int(15, size = nrow(links))

#colours

links$colour <- ifelse(links$type == "cars", "red", "blue")

chordDiagram(links[,c("from", "to", "traffic")],

             col = links$colour,

             directional = 1, direction.type = "arrows", link.arr.type = "big.arrow")

The documentation is excellent. The catch in this case is that, if you want to add a legend, Gu refers you to yet another package ComplexHeatmap, which isn’t (currently?) available on CRAN, but via bioconductor. If, like me, you prefer not to have one package per line of code ;-) , all is not lost. There’s a quick way to get a legend, with base graphics, and another function already in circlize.

You need graphics::legend, plus circlize:add_transparency so that the colours in your legend match those used for the chords.

#for consistency

transparency <- 0.5

chordDiagram(links[,c("from", "to", "traffic")],

             col = links$colour,

             directional = 1, direction.type = "arrows", link.arr.type = "big.arrow",

             transparency = transparency)

legend(x = "bottomleft", inset = 0.05, bty = "n",

           legend = c("Cars", "Vans"),

           fill = add_transparency(c("red", "blue"), transparency),

           border = "white")

Nearly 30% of heavy commercial vehicles transiting Bath pass through Bathampton (on the A36).

We looked in earlier blogs at the overall patterns of traffic transiting Bath, using council and BathHacked data. 

In this blog we drill into the detail by type of vehicle, essentially car, and light- or heavy-commercial vehicle. We show that more transiting heavy commercial vehicles go through Bathampton on the A36 than use the Batheaston dual-carriageway.

For variety, and to show it's not very sensitive to the time threshold, in this blog we use a 45 minute threshold, and a 2-day sample (31 October and 1 November 2017). The chord diagram, which is aligned roughly geographically, looks like this.

Splitting each chord by type of vehicle, and colouring them not by starting point, but by type of vehicle gives this. Although it shows that cars are by far the biggest number of vehicles, it's hard from this to see if there are differences in the patterns.

A diagram for each could be confusing because the scales are now different: total in and out at Bathampton (Dry Arch) is near 2,000 for cars, 700 for light, and 450 for heavy commercial vehicles. 

Cars and light commercial vehicles have quite similar patterns: for light commercials there's perhaps a little higher proportion on the Swainswick-East link. But heavy commercials are very different:

• a much higher proportion are really crossing town: Bathampton - West;
• there's a much smaller proportion of traffic South-South, or South-West.

As a result, Bathampton has more than twice the share of heavy commercial transits than its share of total transits. 12.5% of all transits (3003/23841 in our sample go in or out at Bathampton (Dry Arch), compared to 28.5% (318/1116) of heavy commercials.

In fact, more transiting heavy commercial vehicles go through Bathampton on the A36 than use the Batheaston dual-carriageway.

Bathampton-Swainswick - Already more than half across the toll bridge?

As in the last two posts, I'm working through the excellent traffic data provided by BathHacked. In this post, I find the data saying that already more than half of vehicles entering Bath at Bathampton and leaving on the by-pass at Swainswick use the toll bridge. Not sure if I believe it yet, but let me know what you think.

 The chord plot showed that

1. short transits of Bath (in and out within 30 minutes) were largely split into separate East-North and South-West groupings.
2. there were about 1,800 such transits in a day past the 'Dry Arch' corner of Bathampton (where the Warminster Road becomes 40mph as you leave/enter the village)
3. The large majority of these Dry Arch transits came from or went to the bypass at Swainswick (eg to the M4).

Taking a two-day sample of ANPR data (31 Oct 17 and 1 Nov 17), the Bath data identify 130,000 individual vehicles. Here's an updated chord diagram, showing that the patterns in the list above are true for a larger 2-day sample.

The BANES Breathe project presented their modelling and plans in the Bathampton Village Hall recently. Many were dubious about the traffic projections for traffic across the toll bridge (and hence through Bathampton High Street). So naturally I want to see what the data say.

I define a 'visit' as a sequence of ANPR readings that starts or ends at the 'radial 1' ANPRs, (See the map) which include Dry Arch, and Swainswick on the by-pass.

Zooming in on visits which start or end at Dry Arch, nearly 11,000 vehicles were observed on such visits in the two days. We know from the data which direction the vehicles were heading, so we can take the traffic from the chord plot and insert more detail.

I (a) drop the 30 minute threshold (b) check where the vehicle went between Swainswick and Bathampton. There are lots of answers to (b), but we focus on whether the vehicle was seen on Warminster Road (near Trossachs Drive, so a little further into Bath) or on London Road (just beyond Cavendish Bridge)

I tried a number of ways to visualise this. A straight ggplot may be true to geography, but is hard to read! A Sankey plot is better.

But there are quite a few very small links, so it's easier to understand if we drop the links that are for fewer vehicles than 0.5% of the total. Then we get this. 

Visits start on the left and end on the right.

To give an example, of the 6,438 visits starting at Dry Arch (the orange rectangle "Bathampton_W"):

• the majority head into town passing Trossachs Drive ("Warm'rRd_W"),
• a smaller pale blue subset is next seen leaving heading North at Swainswick,
• even smaller subsets leave again at Dry Arch ("Bathampton_E"): commuters, shoppers or day-trippers,
• or are picked up at London Road (maybe the ANPR missed them at Trossachs).

The sharp-eyed reader will have noticed more visits coming into WarminsterRd_W than leaving: the omissions are those that go on to the car parks (in which case they may account for more visits leaving WarminsterRd_E than arrive), or leave by other routes, so aren't of interest for the current analysis of Bathampton-Swainswick.

We could get more detail, but we are interested in the pale blues: the hypothesis being that these go over the toll bridge. Of the 6,438 visits starting at Dry Arch, 1,126 (17.5%) might have gone over the toll bridge. This is an upper estimate, which could more precisely be put that we know that 82.5% did not.

There are 996 possible toll bridge crossings in the other direction, making for around 1,000 per day, in total in the two directions. 

This 17.5%, however, is not the percentage we are looking for. Instead we need a more interesting one. Note the share of dark and light blue at Swainswick_N. Of our 2,077 total visits coming in at Dry Arch and leaving at Swainswick, 1,126 have possibly crossed the bridge. So 54% are already crossing the toll bridge.

This is a surprisingly high percentage to me, given 

1. that most lorries cannot use the bridge
2. a toll is a toll
3. the queues at the toll bridge are unpredictable
4. we only had about 1,300 30-minute transits (see chord diagram), so what happens to the other 2077-1300 ~ 750?

So this definitely needs further checking. The fact that the situation is similar in these data in the opposite direction gives some confirmation, but further validation, for example looking at travel times and vehicle types is for another day.

Notes

Implicitly, this analysis excludes

• around 5% where the ANPR did not identify the vehicle (I don't know the technology, but perhaps the number plate was obscured by another vehicle, or was in an unknown format), 
• where only a single ANPR reading was made in the 2 days.

and hat-tip to the networkD3 package authors, and all the other contributors to R

Bathampton - transiting traffic

Building on the previous blog post, I've extracted some 13,000 vehicle transits of Bath on 31 October 2017 from data provided by BathHacked. (These are all the entries and exit again within 30 minutes, through the 'radial 1' on the map shown before.)

A chord plot, using the great circlize package in R is a good way to show these flows. The counts around the edge are transit entries or exits - so the total is 26,000. Direction is indicated by the slight point/arrowhead.

You can see a big influence of the Batheaston bypass in the flow between North (Lansdown and Swainswick (dual carriageway)) and East (Box Road & Bathford). That's expected.

But I'm really surprised that the very large majority of vehicles entering or leaving Bathampton (near Dry Arch) and transiting Bath are also heading to, or coming from the North. Around 700 heading North, and 1,000 heading South. Very little traffic transiting and heading West, for example.

Can this be correct? More checking needed, I think.

(Note that one vehicle might generate more than one transit in the day

Bath - location of ANPRs

I didn't manage to make it to the Bath Hacked day on analysing road traffic data, but I'd still like to investigate a little. Big shout to the Bathhacked folks for their work!

First off, a quick visualisation of the locations of the automated number plate readers (ANPRs). I did this in Tableau, since that's quickest for me. If you don't know Bath, sorry that it's a bit cryptic, but if you do, I suspect it gives enough information. Might be better with a bit of road information behind, but that would take longer!

The ANPRs mostly come in in-out pairs, and in 4 "radial groups": basically one a long way out, then 3 concentric circles. They're also identified by direction of travel, NESW, but given what I have in mind, this is less interesting so I didn't show it.