How to Display a Range?
The table provides two dates for each object. The earliest possible dating (DAT_min) and the latest possible dating (DAT_max). In order to be able to process this to a density graph, which is the most elegant means of visualization for continuous distributions (see also Crema, Bevan, and Lake (2010), 1123 or Baxter and Cool (2016), 125–126). (At least if the goal is merely to evaluate changes over time and the probability of object groups dating to a certain point in time, and not to look at actual objects counts, which will be obscured.) The scale we use is only pseudo-continuous, as the data actually comprises of intervals (1 year, or 25 years, etc.), but we nonetheless treat it as a continuous one.
Objects that can be dated with greater confidence should have a
larger impact on the overall visualization. The core function of this
package (datsteps()) produces a column named either
‘weight’ or ‘probability’ which contains a value that reflects the
quality of dating (‘weight’) or the probability of an object being dated
to a certain year (‘probability’). For the calculation of ‘weight’, see
(Weissova and Steinmann 2021). The formula
for probability calculation is simply ‘1 / ((max - min) + 1)’.
In any case, the greater the time span, the lower the weight value or
probability. This is a generally accepted method of aoristic analysis
(Ratcliffe 2000, 671–72 with Fig. 1) and
explained in greater detail in (Weissova and
Steinmann 2021). In the case of a stepsize of 1, the weight value
can be seen as an actual dating probability to the specific year. As an
example, a coin dated between 36 and 37 CE will thus have a probability
of 0.5 for the year 36, and 0.5 for the year 37. The calculation of
probability does, however not work with greater stepsizes. It is
possible to switch between both variants of calculation by using
datsteps(x, calc = "weight") or
datsteps(x, calc = "probability"). When the probability is
calculated, there is an option to add a cumulative probability column
(datsteps(x, calc = "probability", cumulative = TRUE)).
Secondly, every object is duplicated a number of times equal to the dating range divided by the stepsize-variable. Each duplicate has its own ‘DAT_step’ – one single value between the two extremes. The above mentioned weight variable is divided by the number of steps, so that each new fictional object or ‘date step’ counts only as a fraction of the actual object. With this, we hope to achieve a greater influence of closely dated objects and a higher emphasis on overlap.
This method will not be useful for dating specific contexts, since any concept of terminus post/ante quem is lost here, which is important on a smaller scale. It may however be applicable for contexts that are disturbed, as a noticeable overlap of objects could give an indication for the original tpq-date. The method is suitable also for the visualization of changes in trends over time, e.g. the popularity of pottery types, or overall peaks in occupation from survey data (Orton, Morris, and Pipe 2017, 5).
Other approaches, e.g. using the median date of each object, may in some cases produce similar outcomes, but create other problems. A lot of information is lost on the way when employing averaged or median data, as large amount of loosely dated objects will produce peaks at unreasonable values. (Consider a large amount of objects dated between 600 and 400 BCE all attributed to the year 500 BCE.)
Beazley$DAT_mean <- (Beazley$DAT_max + Beazley$DAT_min) / 2
library(ggplot2)
ggplot(Beazley, aes(x = DAT_mean, fill = Technique)) +
geom_histogram(binwidth = 25, position = "dodge") + Plot_Theme + Plot_Fill
Employing dating steps will even out unreasonable peaks. Note especially the gap between -425 and -300 in the plot above, that is – in the plot below – filled with a constant amount of objects in each year. This is due to the data containing large amounts of objects dating from -400 to -300 BCE. Of course, due to duplicating each object numerous times (see table below), the counts represented on the y-axis now inform us of the maximum amount of objects that might be dated to a given bin rather than the actual amount.
The method datplot uses for partitioning steps an be explained as follows: If any given object had been dated as ‘475 to 425 BC’ and steps of 25 years were used for each object, this would result in the creation of three sub-objects with the respective dating of: 475 BC, 450 BC, 425 BC. For an interval of 5 years, the same object would be partitioned into 11 sub-objects, each dating to 475 BC, 470 BC, 465 BC, 460 BC, 455 BC, 450 BC, 445 BC, 440 BC, 435 BC, 430 BC and 425 BC respectively. In order to keep the data comparable, the interval (expressed as the stepsize-variable in the R-package) must be chosen globally for all objects. As the time span an object is dated to can in many cases not be divided without remainder by the value given as a stepsize (i.e. may only be divided with the modulus of the division being greater than 0), datplot resolves these conflicts by temporarily modifying the size of steps for the objects in question without deviating significantly from the size set beforehand, so that the output is representative and comparable. Objects which are dated to a time span undercutting the stepsize-variable can either be assigned to one year (for objects dated precisely to one year), to two years (for objects dated to a number of years less than or equal to 40% of the stepsize) or to three years (for objects dated to a number of years exceeding 60% of the stepsize).
system.time(result <- datsteps(Beazley, stepsize = 25))[3]
#> Using 'weight'-calculation (see https://doi.org/10.1017/aap.2021.8).
#> elapsed
#> 0.04
system.time(result <- datsteps(Beazley, stepsize = 1))[3]
#> Using 'weight'-calculation (see https://doi.org/10.1017/aap.2021.8).
#> elapsed
#> 0.13Using larger step sizes is only recommended if the stepsize of 1 year leads to significant delays in processing while yielding no additional information. If one where to look at a total time span of 10000 years, step sizes of 1 no longer seem very reasonable or rather necessary, as such detailed changes should not be visible or graspable at all, and using steps of 100 years will lead to the same outcome. As classical archaeologists a duration of more than 1000 years mostly exceeds our area of study. We seem to get good results with stepsizes between 1 and 25.
library(datplot)
result <- datsteps(Beazley, stepsize = 25)
#> Using 'weight'-calculation (see https://doi.org/10.1017/aap.2021.8).
ggplot(result, aes(x = DAT_step, fill = variable)) +
geom_histogram(binwidth = 25, position = "dodge") + Plot_Theme + Plot_Fill
datsteps() can also calculate a stepsize on its own. It
equals the closest possible dating of any object. As the stepsize used
is saved in an attribute, this can be recycled to dynamically chose the
binwidth for histograms:
result <- datsteps(Beazley, stepsize = "auto")
#> Using 'weight'-calculation (see https://doi.org/10.1017/aap.2021.8).
#> Using stepsize = 50 (auto).
ggplot(result, aes(x = DAT_step, fill = variable)) + Plot_Theme + Plot_Fill +
geom_histogram(binwidth = attributes(result)$stepsize, position = "dodge")
| ID | variable | DAT_min | DAT_max | weight | DAT_step |
|---|---|---|---|---|---|
| 10957 | BLACK-FIGURE | -550 | -500 | 0.02 | -550 |
| 10957 | BLACK-FIGURE | -550 | -500 | 0.02 | -500 |
| 352414 | RED-FIGURE | -525 | -475 | 0.02 | -525 |
| 352414 | RED-FIGURE | -525 | -475 | 0.02 | -475 |
| 220668 | RED-FIGURE | -450 | -400 | 0.02 | -450 |
| 220668 | RED-FIGURE | -450 | -400 | 0.02 | -400 |
As the sample we use here only encompasses objects dated with a resolution of 50 years, we it would be best to also proceed with this stepsize. A smaller stepsize would not paint a more detailed picture, it just uses up computing time without any benefit.
Due to the impossibility of displaying object counts as well, it is ideal to use kernel density estimates for visualization. The density plot below shows the result. The peak at around -500 indicates that is area has the highest overlay, so a large part of the objects in our sample have been dated around this time. The same distribution can also be seen in the bar plots above. This, however, is not yet very informative.
result <- datsteps(Beazley, stepsize = 25)
#> Using 'weight'-calculation (see https://doi.org/10.1017/aap.2021.8).
dens <- result
dens <- scaleweight(result, var = "all")
dens <- density(x = dens$DAT_step, weights = dens$weight)
plot(dens)
