"Not all of the characteristics which are conversationally
described in terms of `more' or `less' can actually be measured.
But any characteristic which lends itself to such a description has
the possibility of being measured"
L.L. Thurstone. Measurement of social attitudes. J Abnormal & Soc Psych 1931; 26: 257.
"An important advantage of having mathematical models is that
they can transcend various applications"
D. Andrich. A general form of Rasch's extended logistic model. Applied Measurement in Education. 1988: 363.
Most of archaeology is concerned with material that has been accidentally left behind by previous generations. Burial artifacts constitute one of the few purposeful depositions available to the archaeologist, because burial artifacts were included in burials for specific reasons. Many of the social processes that govern human life become encoded in graves, i.e., religious beliefs, social status, age, sex, eschatological beliefs, etc. It is the job of the archaeologist to develop ways to decode this information.
A field of specialization within archaeology, mortuary studies, involves the analysis of burial remains to learn about the society that generated them. The application of the Rasch model to archaeological data offers a way of investigating one aspect of particular interest in this field: the hierarchical relationship of the status of persons and items in burial sites.
Rasch analysis is particularly useful for the detection of social status based on the configuration of burial artifacts. Within any society, an individual, during the course of a lifetime, achieves or is ascribed a certain degree of social status. Quite frequently, in the absence of an overriding egalitarian ideology, this status receives public display through the selective use of material items. These items serve as markers of social status and, thus, acquire a symbolic status that is recognized throughout the society in which they are used. Such markers were frequently included in the graves of ancient Mesopotamia as a way of displaying and representing the status of the individuals being buried.
A Rasch Model of Status
The theoretical position that underlies the application of the Rasch model to mortuary analysis can be stated as follows:
1) There are two objects, persons and marker items, that interact through the burial process in a way that is dominated by one measurable quantity: status.
2) Person status (S) can be represented on the same variable as item status (I).
3) PSI represents the probability of an item of a given status being present in the grave of a person of a particular status.
4) If a person's status is higher than an item's status, then PSI > .5. If a person's status is lower than an item's status, then PSI < .5. If a person's status equals an item's status, then PSI = .5.
The Rasch model for this is:
Loge ( PSI / (1-PSI) ) = S - I
The analysis of model fit statistics provides a valuable means of interpreting the results of the calibration. Persons or items that misfit can be identified and then subjected to more detailed examination. Misfitting persons or items may occur because the compositions of these particular burials were governed by factors other than status such as sex or age. In this case, these burials should probably be excluded from the analysis even though they provide other information about the society under investigation.
This model has been applied to several burial samples from a site in ancient Mesopotamia. Preliminary results can be summarized as follows:
1) Variables representing the relative status of persons and items can be calibrated.
2) The vast majority of persons and items fit the expectations of the model. For example, in one sample only six out of 270 persons and only 4 out of 21 items misfit.
3) In analyzing the item status calibrations, the outfit statistic appears to be particularly useful in recognizing consistent status indication. High status items tend to have high negative outfit statistics, i.e., their use is more than usually predictable. This is because they are generally found exclusively in burials that received high status calibrations. This is analogous to only allowing very high ability students the opportunity to answer the most difficult questions.
4) Certain low status items were absent from high status burials. This is contrary to the expectations of the model and so these items had high positive outfit statistics, analogous to "careless mistakes". In burial sites, however, this lack of low status items in high status burials is deliberate. Such cases can be shown to be logical and so can be easily understood. Adjustments for this lack of fit are easy to make and correspond to the "sleeper" pattern correction that may be more familiar to measurement specialists in the field of education. Alternatively, field reports of artifacts could be scored on a rating scale of "0 = unobserved because item has too high a status", "1 = observed", "2 = not observed because item has too low a status." Initial choices of "0" or "2" by the analyst can be checked, and improved as desired, by printing the data matrix as a Scalogram.
5) The person separation index is higher in periods of status competition than in periods of social stability. This indicates that more status items are interred and that they may be more carefully selected when the status of the individual being buried status is of greater importance to the surviving relatives.
The exploration of the application of objective measurement to archaeological data is just beginning, but these initial results are encouraging. The Rasch model can clearly enable archaeology to take advantage of meaningful methods of measurement.
John A. Stahl
American Society of Clinical Pathologists
Archaeology and objective measurement. Stahl JA. Rasch Measurement Transactions, 1989, 3:3 p.70
Please help with Standard Dataset 4: Andrich Rating Scale Model
|Rasch Measurement Transactions (free, online)||Rasch Measurement research papers (free, online)||Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch||Applying the Rasch Model 3rd. Ed., Bond & Fox||Best Test Design, Wright & Stone|
|Rating Scale Analysis, Wright & Masters||Introduction to Rasch Measurement, E. Smith & R. Smith||Introduction to Many-Facet Rasch Measurement, Thomas Eckes||Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, George Engelhard, Jr.||Statistical Analyses for Language Testers, Rita Green|
|Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar||Journal of Applied Measurement||Rasch models for measurement, David Andrich||Constructing Measures, Mark Wilson||Rasch Analysis in the Human Sciences, Boone, Stave, Yale|
|in Spanish:||Análisis de Rasch para todos, Agustín Tristán||Mediciones, Posicionamientos y Diagnósticos Competitivos, Juan Ramón Oreja Rodríguez|
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