TFQA: Tools for Quantitative Archaeology
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ARRANGE: Estimate Site Occupation SpansThis program estimates the dates of historic (or prehistoric) sites based on the proportions of dated ceramic types in the assemblage. The method was developed in collaboration with Vincas Steponaitis and is described in Steponaitis and Kintigh (1993). The discussion that follows is adapted from that source. The program is available as freeware in arrange.zip. THE METHOD The method implemented by ARRANGE is related to techniques for estimating occupation spans suggested by Bartovics (1980, 1981) and Carlson (1983). Their methods both rely on a graph of what Carlson calls a "composite ceramic distribution." For each type, the number of sherds in the assemblage is mathematically distributed over the known range of that type's manufacture or use. The distribution can be assumed to be uniform, Gaussian (i.e., "normal"), or of any other shape. The distributions of the individual types are then added together to produce the composite distribution for a given assemblage. This can be viewed as a kind of probability distribution, the area under the curve suggesting the likelihood that the site was occupied over any given interval of time. Beginning and ending dates are then estimated by visual inspection; the site's span of occupation is assumed to correspond to the "fattest" part of the curve. This approach has the advantage of being based on an explicit mathematical model, but, in the absence of any rules for bracketing occupation spans, it shares the drawback of South's (1972, 1977) "visual bracketing method" of being highly subjective in its application. Following Bartovics and Carlson, ARRANGE takes into account the relative frequencies of artifact types, supplies a graphical representation of the data, and provides an explicit algorithm for estimating starting and ending dates within the constraints of the mathematical model outlined earlier. It assumes that the evidentiary value of a type for dating a site's occupation depends on at least two factors: (1) the type's abundance in an assemblage (the more abundant a type, the more important it is for dating a site), and (2) the length of the type's period of use (a type that was distributed for 300 years is generally of less value for questions of dating than one that was produced for only 30 years). Since all types are affected by both of these factors, often in opposite directions, we need a way to balance their effects. For example, the importance for dating of an abundant, but long-lived type is increased by its frequency, but decreased because of the length of its period of manufacture. In addition, we need a way to combine the information contributed by several types to derive estimated starting and ending dates for an occupation. Let us observe that each sherd contributes chronological information of a probabilistic sort. Lacking any better information, the probability that a sherd was deposited in a given year depends on the frequency distribution of its type through time. Prior to the type's starting date, the probability of sherd being deposited is zero, but during and after the period of manufacture, we assume that the frequency distribution looks like a unimodal "battleship curve." This curve can be assumed to be either symmetrical (i.e, a gradual increase in popularity followed by an equally gradual decline) or asymmetrical and skewed to the right (i.e., a rapid increase in popularity followed by an extended and more gradual decline). If we view this curve as a probability density function, then it will have a total area of 1.0, and by determining the area between any two points on the time axis, we in effect calculate the probability that a given sherd was deposited during the interval defined by those points. Next, let us transform that curve into one with an area that is equal to the number of sherds of this type at a particular site. Now, the area between any two points along the time axis is a probabilistic estimate of the number of sherds of this type that were deposited at the site during that interval. If we add together the temporal distribution plots for all types present at the site, we end up with what Carlson (1983) calls a composite ceramic distribution curve. The area under this curve is simply the total assemblage size, and, loosely speaking, the area within any temporal interval estimates the number of sherds that may have been deposited during that period. Given this model, it seems reasonable to interpret the higher parts of this curve as times of denser occupation. One might, more tentatively, identify the major positive and negative inflection points with the beginning or end of occupation. Note that in spite of certain dubious assumptions, this procedure has the desired effects. First, types with greater frequencies do have greater influence on the results, because they contribute more total area to the composite distribution. Second, the importance of types with long production periods is reduced, because their area is more spread out along the time axis. While these graphs clearly have interpretive value, we have not yet specified how we might use them to derive estimated starting and ending dates for a site's occupation. In the absence of additional information, we suggest placing the estimated starting date (EstSD) and estimated ending date (EstED) in such a way that 75% of the area of the curve is between these two points, and the remaining area is split equally on the two sides. This procedure is analogous in statistical terms to constructing a 75% confidence interval around the distribution's mean. Thus, the EstSD is placed at the 12.5th percentile, and the EstED at the 87.5th percentile. Hence, the occupation period of the site is identified with the "deposition" of 75% of the probabilistic sherds. One further qualification is necessary: the EstSD and EstED must fall within the plausible ranges defined by the earliest and latest starting and ending dates based on type presence (see Steponaitis and Kintigh 1993; the EstSD must fall between ESD and LSD and EstED must fall between EED and LED). If either of the "boundary percentiles" falls outside of its plausible range, then the estimated starting or ending point becomes the date within the plausible range that is closest to the percentile originally chosen. SEQUENCE OF PROGRAM PROMPTS Listing File {.TXT} File for output. Make sure you have adequate disk space as this output can be lengthy. You will probably want to review it before printing it. Type Information File {.TYP} ? Input file for ceramic type information (see example below). Each line consists of the type name (up to 20 characters), the starting date, the median date, the ending date, the "significance" code (1=use/0=don't use in computations), the "print" code (1=print/0=don't print in graphs), the "shape" code (1=uniform 2=gamma 3=triangular 4=Gaussian distribution) through time. Note the uniform or flat distribution assumes uniform production from beginning to end of the production span. A triangular distribution assumes that the production increases linearly from 0 at the introduction date to the median (i.e. peak) date and declines linearly to 0 at the termination date. A gamma distribution is a battleship-shaped distribution with an infinite right tail. Read Type Names Types Read: ?? Here the program is telling you what it is doing. Count Input File {.ADF} ? Input file for ceramic count information (see example, below). The file must be arranged in ANTANA format: the first two numbers specify the number of sites and types, respectively; the rest of the file is in free format, with individual values separated by at least one space. The program will expect to find counts of all the types for the first site, then counts of all the types for the second site, and so forth. The order of the type-counts within each site must be the same as that of the type-names in *.TYP. Similarly, the order of the sites must be the same as that in *.ARL. Anything placed between pound-signs (#), or between a pound sign and a carriage return, is considered a comment and is ignored by the input routine. Read Counts Reading Counts for 78 Types at 9 Sites Continuing log of program operation. Site or Provenience Label File (NUL for none) {.ARL} ? Input file for site or provenience labels (see example, below). Each line corresponds to a site or provenience; the order of these lines must correspond to the order of the sites/proveniences in *.ADF.
Input Complete Earliest Date {1520} ? Latest Date {1920} ? Enter the earliest and latest dates to be considered. Default values are derived from the type data. Left Percentile Cutoff {12.5} ? Right Percentile Cutoff {87.5} ? The percentiles to use to estimate occupation spans. Minimum Time Increment=1 Time Increment {10} ? The program allows rounding into intervals of several years. Override Input File Distribution Function {N} ? N Use if you wish a universal override of the type distribution shapes supplied in the type input file. Gamma Parameter Alpha {3} ? The parameter the defines the shape for any type for which a Gamma distribution is requested. The numbers 2 or 3 seem reasonable in most cases. The parameter varies the peakedness of the distribution. Integer values between 1 and 4 are permitted.
Tail Years (or -%) to Ignore for Gamma and Normal {1} ? Tells the program how to deal with infinite tails on the gamma or normal distributions. An infinite right tail on the gamma and normal distributions essentially models the deposition of a type after its nominal production span. The left tail on the normal distribution is just an unrealistic characteristic of that model. The default is to assume one average year's output of the type is in the tail. For a type that is produced for 200 years, a value of 1 for tail years puts 1/200 or .5% in the tail. Alternately with a negative number the total percentage of the type assumed to be deposited outside the production range. Thus, -2 indicates that 2% of the type is deposited in the tail. For a normal distribution, the specified amount is in each tail. Minimum Sample to Print Graph {10} ? Listing Level {3} ? These parameters control the amount of output. A level of 2 or more produces the histogram, the list of types and the list of sites. A listing level of 3 produces the graphical type time lines by site illustrated below. Arrange Program End The program completed its job successfully. SAMPLE INPUT FILES SOUTH.TYP 1 Brown St Bottle 1820 1860 1900 1 1 2 2 Whiteware 1820 1860 1900 1 1 2 3 Ironstone/Granite 1813 1857 1900 1 0 2 ... 78 Luster Dec Ware 1790 1815 1840 1 0 2 SOUTH.ADF 9 #sites# 78 #types# # Data from South # 1st Fort Moore, SC 38AK4-15 1716-1747 (1725-1775) 1732 (1726) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 38 0 0 0 35 0 0 0 0 1 64 0 0 0 0 4 0 18 0 0 0 0 42 0 0 0 0 39 0 0 0 0 0 0 0 0 0 0 0 0 # Ft. Moore, SC 38AK5-A 1716-1766 (1725-1775) 1741 (1742) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 2 0 18 0 0 0 13 4 0 0 0 0 17 0 0 0 3 4 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ... # Brunswick Dump (S10), NC 1776-1830 (1740-1820) 1803 (1794) 0 45 0 0 0 0 0 0 0 0 136 44 32 0 0 0 1 0 47 0 0 17 0 0 0 13 0 0 0 0 0 0 10 0 0 0 0 0 37 0 0 0 21 12 0 0 2 0 16 0 0 0 15 0 0 15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SOUTH.ARL 1st Fort Moore, SC 38AK4-15 1716-1747 (1725-1775) 1732 (1726) Ft. Moore, SC 38AK5-A 1716-1766 (1725-1775) 1741 (1742) Ft. Prince George, SC 38PN1 1753-1768 (1740-1775) 1761 (1763) Brunswick Ruin S7, NC 1734-1776 (1740-1775) 1755 (1755) Brunswick Ruin S15, NC 1726-1776 (1740-1775) 1751 (1746) Brunswick Ruin N1, NC 1731-1776 (1740-1775) 1754 (1750) Brunswick Ruin S2, NC 1731-1776 (1740-1775) 1754 (1749) Brunswick Ruin S18, NC 1763-1776 (1740-1775) 1770 (1776) Brunswick Dump (S10), NC 1776-1830 (1740-1820) 1803 (1794) SAMPLE PROGRAM OUTPUT SITE OCCUPATION ARRANGEMENT PROGRAM - K KINTIGH & V STEPONAITIS 8/18/1993
Earliest Date 1520
Latest Date 1920
Percentile Estimate
Percentile Range: 12.50- 87.50 Included: 75.00
Time Increment 10
Gamma Parameter Alpha 3
Minimum for Print 10
Listing Level 3
Total Sherds In All Sites: 7890
Basic Type Information - 8/18/1993
Type Name Introduced Middle Terminated Sample Pct Total Coll w/ Type Signif Print Shape
---- ---- ---------- ------ ---------- ------ --------- ------------ ------ ----- -----
1 Brown St Bottle 1820 1860 1900 0 0.000 0 yes yes Gamma
2 Whiteware 1820 1860 1900 45 0.570 1 yes yes Gamma
3 Ironstone/Granite 1813 1856 1900 0 0.000 0 yes no Gamma
...
78 Luster Dec Ware 1790 1815 1840 0 0.000 0 yes no Gamma
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