Discriminant function analyses in archaeology: are classification rates too good to be true?

The use of discriminant function analyses (DFA) in archaeological and related research is on the increase, however many of the assumptions of this method receive a mixed treatment in the literature. Statisticians frequently use complex statistical models to investigate analytical parameters, but such idealised datasets may be hard to relate to “real-life” examples and the literature difficult to assess. Using two faunal datasets that are more typical of archaeological and related research, one comprised of size-corrected linear measurements of bovid humeri and another of 3D geometric morphometric (GMM) shape data of African monkey skulls, and two simulated datasets, we illustrate some of the most important but often ignored issues of DFA. We specifically show why it is paramount to address “over-fitting” by cross-validation when applying this method and how the probability of correctly classifying cases by chance can be properly and explicitly taken into account.     

CORRESPONDENCE AND DISCRIMINANT ANALYSES OF SAND AND SAND TEMPER COMPOSITIONS,TONTO BASIN,ARIZONA*

Geologists use petrographic modal analysis to relate fluvial sand composition to source rock composition, thus establishing provenance. Archaeologists seeking to establish provenance of sand temper in pottery can use similar petrographic methods, but their finer scale of investigation requires more precise statistical tools than those employed by geologists. A quantitative method for performing that task is presented. It utilizes correspondence analysis and discriminant analysis of logratio transformed point‐count data to define petrofacies, or sand temper resource procurement zones. The procedure is illustrated with sand and sand‐tempered sherd samples collected from the Tonto Basin, central Arizona; temporal trends in utilitarian ceramic production c. AD 100–1350 are reviewed.     

Boards and Cords: Discriminating Types of Artificial Cranial Deformation in Prehispanic South Central Andean Populations

For over a century, a number of ambiguous typologies have been employed to distinctly categorise types of artificial cranial deformation. This paper provides a quantitative method, based on multiple dimensions and discriminant function analysis, by which to assign skulls not only into discrete categories: deformed or not, but also by type: annular or tabular. A series of prehispanic, adult, human crania (n = 469) from archaeological sites in Argentina, Bolivia, Chile and Peru represented by both normal and artificially deformed specimens, provide craniometric data for four measurements across the vault: maximum cranial length, breadth and height and the frontal chord. These data are used to develop three indices which in turn are used to compute two discriminant functions. Results are plotted on a territorial map whereby the type of deformity can be determined. When these methods were applied to a comparative cranial sample of nondeformed skulls from South America, 100% of the samples was found to be nondeformed. When these methods were applied to the samples which were subjectively classified a priori by the first author as nondeformed, 81.3% of the samples were found to be nondeformed. This study demonstrates the value of a more objective and quantitative method by which to classify artificial cranial deformation, and thus provides a new approach. Copyright © 2011 John Wiley & Sons, Ltd.     

Characterization of New Zealand obsidian using PXRF

New Zealand has some of the most active areas of rhyolitic volcanism in the world and this has produced numerous obsidian sources in the northern half of the North Island. In total archaeologists have recognized 27 named locations from which obsidian can be obtained scattered across 4 geological source regions. Shortly after colonization in the late 13th century AD Polynesian settlers began transporting this material some thousands of kilometers throughout the country and across the sea in small quantities to distant neighbors in the Kermadecs and Chatham islands. Although considerable research has been conducted on obsidian sourcing in New Zealand the complexity of geochemical source discrimination and the lack of a practical method of non-destructive geochemical analysis has hindered progress. We present the results of our use of PXRF to provide geochemical data on New Zealand obsidian sources and to compare the use of discriminant analysis and classification tree analysis to discriminate among sources and attribute archaeological samples to sources. Our research suggests that classification tree analysis is superior to discriminant analysis in sourcing studies. A large case study using an important settlement phase site (S11/20) from the Auckland region demonstrates the utility of the methods and the results support a model of high degrees of mobility and interaction during the early settlement of New Zealand.     

Age estimation of children from prehistoric Southeast Asia: are the dental formation methods used appropriate?

Inter-population differences in skeletal and dental growth and maturation are acknowledged frequently in the biological anthropological literature. These growth differences have implications for the reliability of standards for the estimation of age at death of archaeological subadults. The number of archaeological projects that are recovering human burials from non-European contexts, including Southeast Asia, and the increasing interest in subadult bioarchaeological studies provides the impetus for investigating this issue of ageing subadult individuals from these populations. This paper aims to address some of the problems of the representativeness of ageing standards for non-European children in bioarchaeology. This is achieved through a literature review of the issue of growth variability and age estimation, and a basic comparison of the commonly applied age estimation method based on North American children with a dental formation study of modern Thai children. Although these studies do not employ similar methods the Thai study is the only comparable data available and therefore serves as a starting point to address these issues. The results raise an important question for bioarchaeologists of the appropriateness of available ageing methods. In addition this paper emphasises the need for the use of appropriate methodologies in the collection and presentation of dental formation data.     

Recent carbon isotope research and its implications for African archaeology

A number of new developments in the carbon isotope field are reviewed, some of these having immediate and others potential application to African archaeology. Mass spectrometric analysis of¹³C/¹²C ratios in human and animal bone collagen makes it possible to reconstruct prehistoric foodwebs and to draw conclusions about dietary adaptations. Alternatively, where dietary behaviour is known, analysis of the bone of certain animal species allows for reconstruction of past environments. Ratio mass spectrometers are widely available in research institutions, and provided that the proper techniques for sample preparation are followed, this method of analysis should be of immediate use to most Africanists. It is already making an impact on African archaeology. The development of accelerator-based or high energy mass spectrometry (HEMS) radiocarbon dating provides the potential for extending the method back to 100,000 years, particularly in the case of bone samples. Practical applications, however, are still a few years off. In the immediate future HEMS dating is likely to be applied to small samples of ages less than 50,000 years. In competition with HEMS is the use of mini-counters for conventional radiocarbon dating of small samples. This procedure is available in a few laboratories with more under development. Dating of small samples has potential applications in many areas, specifically in the direct age measurement of critical specimens as opposed to the dating of associated materials.     

The Sensitivity of Country Ranks to Index Construction and Aggregation Choice: The Case of Immigration Policy

How sensitive are country ranks to the aggregation function used in index construction? This paper tests whether different aggregation functions come to different results in regard to the ranking of countries. Indices within the field of immigration and integration policy are analyzed, yet, the results pertain to index building across the social sciences. The paper discusses three aggregation methods: the arithmetic mean, the geometric mean, and a noncompensatory/non‐linear aggregation function based on the Condorcet method. In the empirical part, these three aggregation functions are applied to the family indicators for the year 2010 of the Immigration Policies in Comparison (IMPIC) dataset, a new dataset which measures immigration policies’ restrictiveness, as well as to the eight policy strands of the Migrant Integration Policy Index for the year 2014. Results show that the methods react differently to extreme values and thus result in different rank orders in the middle range. In the politicized field of immigration and integration policies, country ranks play a crucial role and this is shown to have profound real‐world implications. The paper thus urges researchers to be reflective of the assumptions of different aggregation functions, as these lead to different results.     

Subadult Age‐at‐Death Estimation From the Human Calcaneus

The estimation of age from subadult skeletal remains relies on the measurement of bones, which when unavailable or damaged hampers the ability to generate a reliable age estimate. The goal of this project was to demonstrate two methods for estimating age at death from the developing human calcaneus. These methods are generated from a sample of 32 European American and African American males and females with ages ranging from 1 to 19 years from the Hamann–Todd Collection. The first method was based on linear regression from two standard measurements of the calcaneus (maximum length and middle breadth); the second was based on transition analysis of fusion states of the calcaneal epiphysis. Results suggest that both methods perform well in estimating subadult age at death. Additional testing with larger contemporary samples would likely increase the accuracy of both methods. Copyright © 2011 John Wiley & Sons, Ltd.     

An X-ray Diffraction (XRD) and X-ray Fluorescence (XRF) investigation in human and animal fossil bones from Holocene to Middle Triassic

We examined by Rietveld refinement of X-ray Diffraction patterns a series of 61 human and animal fossil bones in an age range from present time to Middle Triassic (around 245 Ma). This approach, supplemented by elemental analysis according to X-ray Fluorescence, has permitted to obtain a quantitative evaluation of the mineralogical phases in the specimens, thus allowing to reconstruct the mineralization process involved. Concerning the apatite phase, after adopting a monoclinic geometry for the unit cell, the method permits to determine with fair degree of precision the unit cell volume, which is found to decrease in relatively short geological times as a function of the fluorine substitution process for the hydroxyl group –OH. After excluding the role of a high-temperature fire treatment to the bones, it is found that a certain linear correlation may exist over the geological time scale involved between the age of the specimen and the average crystallite size. This observation permits to use the XRD pattern as an evaluation of the age of the fossil, although the stratigraphic observations, where available, remain as the main reliable source for dating such biomaterials. The uncertainty related to this age estimation may be hardly better than 15–20% in absolute, because of various assumptions involved in the XRD methodology used and in the variability of the burial environment that may be subjected to discontinuous changes over the very long time of deposition.     

Anisotropic Variance Functions in Geographically Weighted Regression Models

Most standard methods of statistical analysis used in the social and environmental sciences are built upon the basic assumptions of independence, homogeneity, and isotropy. A notable exception to this rule is the collection of methods used in geographical analysis, which have been designed to take into account serial dependence often observed in spatial data. In addition, recent developments, in particular the method of geographically weighted regression, have provided the tools to model non‐stationary processes, and thus evidence that challenges the assumption of homogeneity. The assumption of isotropy, however, although suspect, has received considerably less attention, and there is thus a need for tools to study anisotropy in a more systematic fashion. In this paper we expand the method of geographically weighted regression in a simple yet effective way to explore the topic of anisotropy in spatial processes. We discuss two different estimation situations and exemplify the proposed technical development by means of a case study. The results suggest that anisotropy issues might be a fairly common occurrence in spatial processes and/or in the statistical modeling of spatial processes.     

A STATISTICAL APPROACH TO THE CALIBRATION OF FLOATING TREE-RING CHRONOLOGIES USING RADIOCARBON DATES

The bristlecone pine tree-ring calibration of radiocarbon dates, while necessitating changes of up to 700 years in Holocene chronology before 1000 b.c. , offers possibilities of very accurate dating when ¹⁴C determinations from floating tree-ring chronologies are utilized. A statistical approach assuming linear regression is developed and used to position the floating tree-ring chronologies at Swiss neolithic sites, using radiocarbon dates published by Ferguson, Huber and Suess and by Suess. The statistical method gives objective estimated dates with estimates of error related, in a consistent and explicit manner, to the inherent inaccuracies of the radiocarbon dates. Most of the method may readily be tested by standard statistical procedures. For the particular cases considered the assumptions of linearity and parallelism are investigated, and the precision of the estimated dates is comparable with that claimed by Suess and his co-workers. A precise calibration is thus possible without utilizing the short-term fluctuations in the Suess calibration curve. The analysis, while avoiding some assumptions of Suess and his collaborators, offers an explicit procedure for establishing controlled teleconnections with the Ferguson dendrochronology, and supports their emphasis on the importance of radiocarbon dates from floating tree-ring sequences for the construction of precise prehistoric chronologies.     

Women and the social construction of gender in African development

Because a footnote of Marxism teaches that capitalism must first destroy primitive cultures that lack a dynamic social change mechanism and then rejuvenate them as modern industrialized states, the economic and cultural bases of social relationships in developing countries have been deemed irrelevant. In a similar way, Western feminist paradigms fail to acknowledge epistemological differences from those of African women. This article explores these contradictions and analyzes social change mechanisms within the Igbo culture in Africa that were stunted by colonialism. The first topic considered is the relationship of African literature (using Toni Morrison's "Beloved" as a point of reference) with sustainable African development and African women. The remainder of the article is devoted to an examination of the role of women in light of precolonial and colonial literary traditions. It is noted that continued use of Western feudal and capitalist terms for self-identification alienates Africans from Africa's problems. Traditional African thought assigned women the power to feed the family and to serve as protectors of children and society, and ancestral wisdom directed how societies responded to threats, took charge of their world, and resolved conflict. Problems faced by contemporary African researchers are shown to center on the dilemma faced by those who wish to design a program that analyzes the content of African development and provides contemporary solutions without completely deriving the program completely from contemporary thought. It is, thus, concluded that redefinition of the African development agenda must involve recognition of the essential role of African women as a change agent and a rearticulation of the male role within traditional thought.     

An evaluation of the site specificity of soil elemental signatures for identifying and interpreting former functional areas

Soil multi-element analysis is now a routine technique employed to help answer questions about space use and function in and around archaeological sites. The pattern of enhancement of certain elements, including P, Pb, Ca, Zn, and Cu, has been shown by numerous studies to correlate closely with the archaeological and historical record. Interpretation of these soil signatures, however, has generally been more problematic. One approach to the problem has been the use of ethnographic or “known” sites to guide interpretation, but how confidently can results from one site be extrapolated to another? This study of abandoned farms tests the site specificity of soil multi-element signatures of past space use through the use of discriminant models. Data analysis suggests that one to one comparisons of similar sites are much less accurate (38% accuracy) than comparisons based on a wider range of sites (59.3% accuracy), even when the latter have contrasting geology. The results highlight the importance of individual anthropogenic practices during occupation and abandonment in the development of diagnostic soil geochemical signatures.     

Rethinking Primitive Accumulation: Theoretical Tensions and Rural Southeast Asian Complexities

Abstract: This paper poses theoretical and empirical questions to the resurgent litera‐ture on primitive accumulation in critical political economy. The first section outlines the different understandings of capitalism, and of its relationship to primitive accumulation, in the literature, and argues that they complicate efforts to identify instances of primitive accumulation. The second section examines the history of frontier agricultural expansion in Southeast Asia to critique the literature's assumptions about who carries out, and who resists, primitive accumulation. The third section draws on work on Southeast Asian political economy to show that the literature pays insufficient attention to the institutions that govern capitalist social relations. The paper argues that these questions of agency, governance, and the nature of capitalism need to be answered in order to make effective use of the concept of primitive accumulation and to distinguish it from cognate concepts like enclosure and commodification.     

Geochemical characterization of ochre from central coastal British Columbia,Canada

The use of ochre and its presence in archaeological contexts is well documented archaeologically, ethnographically and historically. Elemental analysis of ochre is becoming increasingly common as a method for identifying ancient quarrying and mining practices, and for identifying patterns of resource use, trade and exchange. As this type of work has become more common it has become apparent that two critical issues need to be considered: (1) the need for systematic identification of trends and patterns in ochre geochemistry using appropriate statistical analyses, and, (2) consideration of geographic and geologic scale in relation to ochre chemistry. Because ochre is a heterogeneous material relative to other raw material types, it is necessary to apply multivariate and discriminant statistics to differentiate geochemical groups within a sample set. However, caution must be taken when interpreting statistical results at face value. Local geologic and geomorphologic conditions play a significant role in ochre chemistry and need to be taken into account when interpreting analytical results. The purpose of this project was to determine if geochemically distinct groups of ochre could be distinguished through neutron activation analysis (NAA) of archaeological and geological ochres from the central coast of British Columbia, Canada. The results show that it is possible to satisfy the provenance postulate and to differentiate chemical groups through elemental characterization and using multivariate statistical methods.     

Integrating Multi‐Sensor Remote Sensing Data for Land Use/Cover Mapping in a Tropical Mountainous Area in Northern Thailand

Accurate mapping of land use/cover conditions provides essential information for managing natural resources and is critical for further examination of land use/cover change and its subsequent impacts on the environment. Remote sensing offers a means of acquiring land use/cover data in a timely manner, with optical remote sensing images commonly being used in land use/cover related studies. The persistent cloud cover during the rainy season in Southeast Asia, however, presents a challenge for using optical images in land use/cover mapping. Integrating multi‐sensor images of different spectral domains is thus desirable because more information can be extracted to improve the mapping accuracy. The purpose of this study is to assess the potential of using multi‐sensor data sets for land use/cover mapping in a tropical mountainous area in northern Thailand. Optical data from Landsat Thematic Mapper, radar images from Advanced Land Observing Satellite/Phased Array type L‐band Synthetic Aperture Radar (PALSAR), and topographical data were used, providing complementary information on land use/cover. Classification and accuracy assessment were conducted for 12 different combinations of the data sets. The results suggested that short crop mapping using multi‐temporal Phased Array type L‐band Synthetic Aperture Radar images offered insights into the distributions of crop and paddy fields. Because of the mountainous environment of the study area, combining topographic data of elevation and slope into the classification greatly reduced the confusion between different land use/cover types. Improvement of classification accuracy was evident especially in separating evergreen and deciduous forests from other vegetation types and discriminating urban village and the fallow field classes.     

Habitat preference of extant African bovids based on astragalus morphology: operationalizing ecomorphology for palaeoenvironmental reconstruction

The habitat preferences of fauna found at palaeontological and archaeological sites can be used to investigate ancient environments and hominin habitat preferences. Here we present a discriminant function model linking astragalus morphology to four broadly defined habitat categories (open, light cover, heavy cover, and closed) using modern bovids of known ecology. Twenty-four measurements were taken on a sample of 286 astragali from 36 extant African antelope species. These measurements were used to generate ratios reflecting shape. An 11 variable discriminant function model was developed that had high classification success rates for complete astragali. Resubstitution analysis, jackknife analysis, and the classification of several “test samples” of specimens suggest that the predictive accuracy of this model is around 87%. The total classification success rates of 87% (jackknifed) or 93% (resubstitution) are considerably higher than those derived in another study of bovid astragalus ecomorphology (67%; [DeGusta, D., Vrba, E.S., 2003. A method for inferring palaeohabitats from the functional morphology of bovid astragali. J. Archaeol. Sci. 30, 1009–1022]) that used a more limited measurement scheme and a smaller sample of bovids than the present study. Different approaches to operationalizing ecomorphic analyses are considered in order to best extract accurate palaeoenvironmental information from palaeontological and archaeological datasets.     

Investigating the production provenance of iron artifacts with multivariate methods

The quest for suitable data, data treatments and statistical methods for identifying the provenance of iron artifacts has led to a variety of analytical strategies. Researchers working on the problem have been slow to develop or adopt the use of multivariate statistical techniques, despite their successful implementation in other archaeomaterials sourcing frameworks. This paper explores the analytical potential of a comprehensive multivariate statistical strategy for identifying the primary production origins of bloomery iron artifacts using bulk chemical analyses of bloomery smelting slag and slag inclusions in iron artifacts. This strategy includes a multivariate model for identifying distinct slag inclusion types introduced during smelting and refining. Principal component analysis and linear discriminant analysis are then applied to smelting slag training sets to create multivariate provenance fields, the chemical distributions of which are defined by kernel density estimation. Single and multi-group evaluation methods are examined. Appropriate data transformations are discussed to facilitate the projection of the chemistry of “unknown” slag inclusions into the multidimensional space generated by the smelting slag groups of known provenance. The efficacy of this strategy is demonstrated through its application to a previously examined data set derived from three iron production experiments and a published archaeological example. Results indicate that an appropriately designed multivariate strategy can be an effective tool for evaluating provenance hypotheses for bloomery iron artifacts.     

Multiscalar Settlement Ecology Study of Piedmont Village Tradition Communities,A.D. 1000–1600

This research analyzes the spatial patterning of settlement sites in relation to landscape features to determine the factors that influenced settlement location choices for Late Precontact (A.D. 1000–1600) Piedmont Village Tradition (PVT) communities in the Yadkin, Dan, Haw, and Eno river valleys of the Piedmont Southeast. We employ geographic information systems to estimate characteristics of past landscapes, nearest neighbor analysis to describe basic settlement patterns, and discriminant function analysis to determine spatial correlations between settlements and landscape features. We examine the data on three scales and also assess potential changes over time. Results indicate that settlement location choices were broadly similar on the regional scale, but specific influences varied between and within valleys and over time. When examined with current archaeological, ethnohistoric, and linguistic information, the results suggest that PVT communities engaged in regional interaction networks in highly variable ways and that the relationship between subsistence and settlement varied according to settlement size. Using these results, we explore the roles PVT communities played in the formation and maintenance of natural and cultural landscapes in the Late Precontact Southeast.