Dates and missing dating data in "sdam"

Preliminaries

Install and load a version of "sdam" package.

install.packages("sdam") # from CRAN
devtools::install_github("sdam-au/sdam") # development version
devtools::install_github("mplex/cedhar", subdir="pkg/sdam") # legacy version R 3.6.x

# load and check versions
library(sdam)
packageVersion("sdam")

[1] '1.1.4'

Dating data

Temporal data is significant when it comes to analysing the history of archaeological artefacts like written markers from the Ancient Mediterranean. In the EDH dataset, for example, dates for inscriptions are plausible timespans of existence with the endpoints in variables not_before and not_after that, from the perspective of the timespan, are the terminus ante quem (TAQ) and terminus post quem (TPQ) of the time segment. However, not all inscriptions have these two variables filled by domain experts and replacing missing dating data constitutes a challenge.

Besides EDH, other datasets with "sdam" the package and related functions involve dating data in the ancient Mediterranean like displaying dates and time segments in a plot, by organising dates within Roman provinces, and by performed imputation techniques for missing dating data.

Plotting temporal data

Shipwrecks dataset dating data

An example of plotting dates is with the Shipwrecks external dataset, which is a semicolon separated file of different variables.

References for shipwrecks data are in

Vignette Datasets in "sdam" package

When reading the shipwrecks external dataset with read.csv make sure to use the right separator in sep and leave untouched the names of the variables.

# load shipwrecks external dataset
sw <- system.file("extdata","StraussShipwrecks.csv",package="sdam") |> 
  read.csv(sep=";", check.names=FALSE)

# variables in shipwrecks dataset
colnames(sw)

 [1] "Wreck ID"                "Strauss ID"              "Name"                   
 [4] "Parker Number"           "Sea area"                "Country"                
 [7] "Region"                  "Latitude"                "Longitude"              
[10] "Min depth"               "Max depth"               "Depth"                  
[13] "Period"                  "Dating"                  "Earliest date"          
[16] "Latest date"             "Date range"              "Mid point of date range"
[19] "Probability"             "Place of origin"         "Place of destination"   
[22] "Reference"               "Comments"                "Amphorae"               
[25] "Marble"                  "Columns etc"             "Sarcophagi"             
[28] "Blocks"                  "Marble type"             "Other cargo"            
[31] "Hull remains"            "Shipboard paraphernalia" "Ship equipment"         
[34] "Estimated tonnage"       "Amphora type"

Plot the time segments with function plot.dates() and a customized 'id' where variables 15 to 16 in sw have timespans of existence as 'taq' and 'tpq'.

# shipwrecks dates with Wreck ID
plot.dates(sw, id="Wreck ID", type="rg", taq="Earliest date", tpq="Latest date", col=4)

Range of timespans in Shipwrecks dataset

Mid points and range of timespan

The mid points and range of shipwrecks data are explicitly computed by function prex() with the mp option in the 'type' argument. 'vars' stands for the variables that in this case are TAQ and TPQ, and the 'keep' option allows maintaining the rest of the variables in the output that for prex() with mid points is a data frame.

# add mid points and range to shipwrecks data
prex(sw[c(1,7,15:16)], type="mp", vars=c("Earliest date", "Latest date"), keep=TRUE) |> 
  tail()

     Wreck ID   Region Earliest date Latest date Mid point Range
1779     9057 Sardinia            50         200     125.0   150
1780     9058 Sardinia           400         500     450.0   100
1781     9059 Sardinia          1000        1500    1250.0   500
1782     9060  Liguria          -100          -1     -50.5    99
1783     9061   Sicily          1100        1200    1150.0   100
1784     9063 Calabria           300         500     400.0   200

The default 'type' option and chronological phase in prex() are the aoristic sum with a five periods bin or bin5.

# aoristic sum shipwrecks
prex(sw[c(1,7,15:16)], vars=c("Earliest date", "Latest date"))

      Arch      Class       Hell        Rom        Byz 
  202.5187   312.0645  4460.9831 13235.0372   622.2608

For an eight chronological periods bin in the shipwrecks dataset

# aoristic sum shipwrecks 8 bin
prex(sw[c(1,7,15:16)], vars=c("Earliest date", "Latest date"), cp="bin8")

     Arch     Class      Hell      ERom      MRom      LRom      EByz      MByz 
 202.5187  312.0645 4460.9831 2431.3934  881.8685 1197.9617  101.5077  226.2947

For aoristic sum algorithm, cf. Temporal Uncertainty.

Dating data in the Roman world

Many functions and datasets in "sdam" are related to temporal information of the Roman world, particularly from the Roman Empire during the classical ancient period.

Function plot.map() is to depict cartographical maps per Roman province or region, and it has a 'date' argument to display dates within the caption. Dates in this case are one or two years either for the consolidation of the Italian peninsula or the affiliation of the region to the Roman Empire.

# silhouette of Italian peninsula
plot.map(x="Ita", date=TRUE)
## not run

The built-in dataset rpmcd has the shapes and colours used in the cartographical maps with plot.map(), and some dates related to provinces as well.

# 59 provinces dates, colors, and shapes
data("rpmcd")

# province acronyms as in EDH
names(rpmcd)

 [1] "Ach" "Aeg" "Afr" "AlC" "AlM" "AlP" "Aqu" "Ara" "Arm" "Asi" "Ass" "Bae" "Bel" "BiP" "Bri"
[16] "Cap" "Cil" "Cor" "Cre" "Cyp" "Cyr" "Dac" "Dal" "Epi" "Gal" "GeI" "GeS" "HiC" "Ita" "Iud"
[31] "Lug" "Lus" "LyP" "MaC" "Mak" "MaT" "Mes" "MoI" "MoS" "Nar" "Nor" "PaI" "PaS" "Rae" "Sar"
[46] "Sic" "Syr" "Thr" "Aem" "ApC" "BrL" "Etr" "LaC" "Lig" "Pic" "Sam" "Tra" "Umb" "VeH"

Roman provinces establishment dates

The establishment dates of Roman provinces used in the cartographical map captions are in the second component of rpmcd.

# pipe dataset for dates in second component
rpmcd |> 
  lapply(function (x) x[[2]]) |> 
  head()

$Ach
[1] "27 BC"

$Aeg
[1] "30 BC"

$Afr
[1] "146 BC"

$AlC
[1] "63AD or 58AD"

$AlM
[1] "63AD or 14BC"

$AlP
[1] "63AD or 14BC"

A vector of establishment dates in years from the "rpmcd" dataset is recorded in object est that allow making a chronology of the Roman provinces.

# second component in dataset
est <- rpmcd |> 
  lapply(function (x) x[[2]]) |> 
  unlist(use.names=FALSE)
est

 [1] "27 BC"              "30 BC"              "146 BC"             "63AD or 58AD"      
 [5] "63AD or 14BC"       "63AD or 14BC"       "51 BC"              "105 AD"            
 [9] "114 AD"             "133 BC"             "116 AD"             "197 BC"            
[13] "51 BC"              "74BC or 64BC"       "43 AD"              "17 AD"             
[17] "64 BC"              "238 BC"             "66 BC?"             "58 BC -30 BC"      
[21] "74 BC"              "106 AD"             "32BC or 10AD"       "148 BC"            
[25] "25 BC"              "27 BC"              "27 BC"              "197 BC"            
[29] "272 BC"             "6 AD"               "51 BC"              "197 BC"            
[33] "43 AD"              "42AD or 44AD"       "148 BC?"            "42 AD or 44 AD"    
[37] "116 AD"             "6 AD"               "6 AD"               "121 BC"            
[41] "16BC or 15BC"       "9AD or 10AD"        "9AD or 10AD"        "16BC or 15BC"      
[45] "238 BC"             "241 BC"             "64 BC"              "46 AD"             
[49] "272 BC (Ita cons.)" "272 BC (Ita cons.)" "272 BC (Ita cons.)" "272 BC (Ita cons.)"
[53] "272 BC (Ita cons.)" "272 BC (Ita cons.)" "272 BC (Ita cons.)" "272 BC (Ita cons.)"
[57] "272 BC (Ita cons.)" "272 BC (Ita cons.)" "272 BC (Ita cons.)"

Formatting dates

The establishment dates of Roman provinces and regions are in vector est, and these dates can become more standard with the function cln() for further processing. This is a cleaning function where, for instance, level 9 removes all content after the first parenthesis in the input while the other levels are for specific needs.

# clean levels are 0-9
cln(est, level=9)

 [1] "27 BC"          "30 BC"          "146 BC"         "63AD or 58AD"   "63AD or 14BC"  
 [6] "63AD or 14BC"   "51 BC"          "105 AD"         "114 AD"         "133 BC"        
[11] "116 AD"         "197 BC"         "51 BC"          "74BC or 64BC"   "43 AD"         
[16] "17 AD"          "64 BC"          "238 BC"         "66 BC"          "58 BC-30 BC"   
[21] "74 BC"          "106 AD"         "32BC or 10AD"   "148 BC"         "25 BC"         
[26] "27 BC"          "27 BC"          "197 BC"         "272 BC"         "6 AD"          
[31] "51 BC"          "197 BC"         "43 AD"          "42AD or 44AD"   "148 BC"        
[36] "42 AD or 44 AD" "116 AD"         "6 AD"           "6 AD"           "121 BC"        
[41] "16BC or 15BC"   "9AD or 10AD"    "9AD or 10AD"    "16BC or 15BC"   "238 BC"        
[46] "241 BC"         "64 BC"          "46 AD"          "272 BC"         "272 BC"        
[51] "272 BC"         "272 BC"         "272 BC"         "272 BC"         "272 BC"        
[56] "272 BC"         "272 BC"         "272 BC"         "272 BC"

After this transformation of the data in est, is possible to format dates as numerical data with function dts(), which takes the first value when there are two competing dates in the input; unless the opposite is specified in the 'last' argument.

# update object with establishment dates
est <- est |> 
  cln(level=9) |> 
  dts()

Error in `isTRUE(length(x) > 1) == TRUE && is.na(suppressWarnings(as.numeric(x))) == FALSE`:
! 'length = 59' in coercion to 'logical(1)'

est

 [1] "27 BC"              "30 BC"              "146 BC"             "63AD or 58AD"      
 [5] "63AD or 14BC"       "63AD or 14BC"       "51 BC"              "105 AD"            
 [9] "114 AD"             "133 BC"             "116 AD"             "197 BC"            
[13] "51 BC"              "74BC or 64BC"       "43 AD"              "17 AD"             
[17] "64 BC"              "238 BC"             "66 BC?"             "58 BC -30 BC"      
[21] "74 BC"              "106 AD"             "32BC or 10AD"       "148 BC"            
[25] "25 BC"              "27 BC"              "27 BC"              "197 BC"            
[29] "272 BC"             "6 AD"               "51 BC"              "197 BC"            
[33] "43 AD"              "42AD or 44AD"       "148 BC?"            "42 AD or 44 AD"    
[37] "116 AD"             "6 AD"               "6 AD"               "121 BC"            
[41] "16BC or 15BC"       "9AD or 10AD"        "9AD or 10AD"        "16BC or 15BC"      
[45] "238 BC"             "241 BC"             "64 BC"              "46 AD"             
[49] "272 BC (Ita cons.)" "272 BC (Ita cons.)" "272 BC (Ita cons.)" "272 BC (Ita cons.)"
[53] "272 BC (Ita cons.)" "272 BC (Ita cons.)" "272 BC (Ita cons.)" "272 BC (Ita cons.)"
[57] "272 BC (Ita cons.)" "272 BC (Ita cons.)" "272 BC (Ita cons.)"

Chronology of Roman provinces

Object est has a chronology for the establishment dates of Mediterranean regions and territories as Roman provinces that corresponds to the provinces in "rpmcd" dataset. The union of the names of provinces and dates of establishment as a Roman province is a data frame object rpde that better displays without the row names.

# Roman province dates of establishement (strings still strings)
rpde <- cbind(names(rpmcd),dts(est)) |>
  as.data.frame(stringsAsFactors=FALSE)

Error in `isTRUE(length(x) > 1) == TRUE && is.na(suppressWarnings(as.numeric(x))) == FALSE`:
! 'length = 59' in coercion to 'logical(1)'

rownames(rpde) <- NULL

Error:
! object 'rpde' not found

head(rpde)

Error:
! object 'rpde' not found

Because the dates have a numerical format from function dts(), the data frame allows producing a chronology of affiliation dates for the provinces and regions to the Roman Empire by ordering the second variable in rpde.

# order of affiliation of provinces
rpde[order(as.numeric(rpde$V2)),1]

Error:
! object 'rpde' not found

The regions in the Italian peninsula have the earliest affiliation dates, and Mesopotamia has the latest affiliation date to the Roman Empire.

Roman influence periods

Dataset "rpcp" has influence periods of the Roman Empire.

# list with 45 early and late influence dates provinces
data("rpcp")

# look at data internal structure
str(rpcp)

List of 2
 $ Early:'data.frame':  45 obs. of  3 variables:
  ..$ Province: chr [1:45] "Italia (Final Consolidation)" "Sicilia" "Sardinia & Corsica" "Hispania Ulterior (Later Baetica)" ...
  ..$ EarInf  : num [1:45] -509 -241 -238 -206 -206 -206 -202 -202 -188 -188 ...
  ..$ OffPrv  : num [1:45] -272 -241 -238 -197 -197 -197 -146 -81 43 -133 ...
 $ Late :'data.frame':  45 obs. of  3 variables:
  ..$ Province: Factor w/ 45 levels "Achaea","Aegyptus",..: 30 43 42 27 28 26 3 23 32 9 ...
  ..$ LateInf : num [1:45] 476 436 436 409 409 ...
  ..$ Fall    : num [1:45] 476 436 436 409 409 409 409 418 1400 1500 ...

Early period of Roman influence

Visualize time intervals of early Roman influence in provinces and regions.

# early influence dates are in first list of 'rpcp'
plot.dates(x=rpcp[[1]], taq="EarInf", tpq="OffPrv", main="Early period", ylab="province")

Late period and fall from the Roman Empire

Time intervals of late Roman influence in provinces and regions depicted with mid points and range interval if longer than one.

# late influence dates are in second list of 'rpcp'
plot.dates(x=rpcp[[2]], type="mp", taq="LateInf", tpq="Fall", lwd=5, col="red", 
           main="Late period", ylab="province")

Restricted imputation of missing dating data

Dataset rpd has time intervals for "not_before" and "not_after" that corresponds to the dating data in the EDH dataset.

# Roman provinces dates from EDH
data("rpd")

# Rome
summary(rpd$Rom)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
 -301.0    50.0   372.0   330.2   652.2   878.0

# Aegyptus
summary(rpd$Aeg)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
 -71.00   90.25  322.00  286.00  517.75  571.00

These intervals are the basis for a restricted imputation of missing dating data in EDH

Imputation of dates by province

Function edhwpd() constructs, for a chosen province, a list of data frames with the components made of its inscriptions related by attribute co-occurrences. The replacement of missing dates occurs in this setting with function rmids() that stand for restricted multiple imputation on data subsets.

An example of restricted multiple imputations is the province of Armenia which has the fewest inscriptions in the EDH dataset. Dataset rpd is a list where each component corresponds to a province and where the component class provides the HD ids of inscriptions.

# Armenia
rpd$Arm

[1] 116 114 116   2
attr(,"class")
[1] "HD015521" "HD015524" "HD029916"

Imputation of inscriptions by similarity

Imputation from similarities of attribute variables per province and dates is organised with wrapper function edhwpd() having different argument options.

# list with arguments
formals(edhwpd)

$x
[1] "EDH"

$vars


$province


$dates


$clean


$...

By default, the input data for this function is the EDH dataset and the organisation is based on characteristics of the artefacts in vars.

# characteristics of inscriptions
vars = c("findspot_ancient", "type_of_inscription", "type_of_monument", "language")

Function rmids() performs the multiple imputation of missing dating data in EDH by default or in another dataset as input. In the case of Arm, record HD015521 has censored data in dates while the other two records have complete missing dating data.

# Armenia: restricted imputation of dates
edhwpd(vars=vars, province="Arm") |> 
  rmids()

Warning in edhwpd(vars = vars, province = "Arm"): "x" is for dataset "EDH".

max TPQ taken from province.

avg len TS taken from province.

avg taken from province.

min TAQ taken from province.

max TPQ taken from province.

avg len TS taken from province.

[[1]]
[[1]][[1]]
[[1]][[1]]$`taq-NA`
              id type_of_monument             type_of_inscription not_before not_after language
15521.1 HD015521           tabula building/dedicatory inscription       0116       116    Latin
15521.2 HD015521           tabula building/dedicatory inscription       0116       118    Latin
        findspot_ancient
15521.1    Artaxata, bei
15521.2    Artaxata, bei

[[1]][[1]]$`NA-NA`
              id type_of_monument type_of_inscription not_before not_after language
15524.1 HD015524            stele             epitaph        116       116    Latin
15524.2 HD015524            stele             epitaph        116       118    Latin
15524.3 HD015524            stele             epitaph        114       116    Latin
15524.4 HD015524            stele             epitaph        116       116    Latin
        findspot_ancient
15524.1    Artaxata, bei
15524.2    Artaxata, bei
15524.3    Artaxata, bei
15524.4    Artaxata, bei



[[2]]
[[2]]$`NA-NA`
              id type_of_monument type_of_inscription not_before not_after language
32270.1 HD029916             <NA>                <NA>        114       116    Latin
32270.2 HD029916             <NA>                <NA>        114       116    Latin
32270.3 HD029916             <NA>                <NA>        114       116    Latin
32270.4 HD029916             <NA>                <NA>        116       116    Latin
        findspot_ancient
32270.1             <NA>
32270.2             <NA>
32270.3             <NA>
32270.4             <NA>


attr(,"class")
[1] EDH Arm 3   9

The warnings tell us that the imputation values are taken from the respective province in the rpd dataset where avg len TS stands for average length of timespan, min TAQ is the minimum value of not_before, and max TPQ is the maximum value of not_after.

Pooling results

Since there are multiple imputations of missing dating data, one next step is to combine the data by pooling rules of the m results from function rmids() into final point estimates plus standard error.

Pooling options for time intervals are take:

average time-span with avg len TS
min TAQ and max TPQ
max TAQ and min TPQ

With these options, there is a single imputed value per variable with implied consequences.

Dates and missing dating data in `"sdam"`