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Mn/Model Research Design
Appendix B: Modeling theory and assumptions


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The locational behavior of Indian peoples in the pre-Euroamerican contact period in North America is most often interpreted by after-the-fact "common sense" notions of why particular archaeological resources are located where they are. These various notions, when systematically compared, often prove to be inconsistent, in part contradictory, and without theoretical foundation. The result is a body of "theory" whose capacity for actually predicting phenomena as complex as human locational behavior is very low. In archaeology, the solution to this problem - a problem recently made more pressing by the legally mandated requirements of cultural resource management - has been the development of unified predictive frameworks that include testing and self-correction components.

While there are many approaches to the development of predictive locational models, all must choose between various kinds of units of analysis, dependent and independent variables, types of models and decision rules, and modeling testing procedures. Each of these issues is briefly reviewed below and an equally brief argument is made to justify the choice in this project of one option rather than another. The essential role of Geographic Information Systems (GIS) in modeling locational behavior is also discussed, along with certain issues and concerns about the predictive capacity of the models being proposed.


The purpose of this section of the Research Design is to demonstrate how and why locational models, like the ones proposed here, can produce fairly accurate predictions, and why their construction, besides being good science, is also good cultural resource management. Although this section is somewhat technical, an understanding of the tasks assigned each of the three phases of the project depends on understanding the assumptions and principles reviewed in this section.


Units of Analysis

In archaeological modeling studies, the unit of investigation is a parcel of land. The purpose of the studies is to determine the degree of association of the presence or absence of archaeological resources (the dependent variables) in these parcels with their non-archaeological characteristics (the independent variables) (e.g., Carr 1985:125). This process resembles a simple experiment that produces a single well-defined result, that is, the presence or absence of archaeological resources, which is determined through field survey. Archaeologists deduce from a modeling study that the presence or absence of particular characteristics of parcels predicts the presence or absence of archaeological resources. Land parcels are most often defined in these studies by superimposing a regular grid over the study region or by using some pre-existing grid, such as Public Land Survey (PLS) sections.


The size of units of analysis in archaeological modeling studies can vary widely, depending on the intent of the modeling project (Parker 1986:410-414; Kvamme 1990:268-269). As a general rule, however, parcels should be of equal area if possible to facilitate probabilistic interpretation and calculation. Where a fine-grained level of predictive resolution is called for, parcel size should be small; where the intent is to identify broad regions of higher or lower resource density, parcel size can be quite large. In general, high resolution models have parcel sizes equal to or less than 10 acres, while models of very low resolution have parcel sizes equal to or greater than about 250 acres. A PLSS quarter-quarter section parcel size (40 acres) was chosen as the basic unit for field sampling for this project for two reasons. First, it was the parcel size used in the Minnesota Statewide Archaeological Survey (Minnesota Historical Society 1981), and its use here will allow the incorporation of those data. Moreover, a quarter-quarter section is a reasonable field-survey search unit for, in general, the smaller and more scattered search units are, the greater the expense of the survey.


A thirty by thirty meter square cell will be chosen for the resolution of the GIS database and model. This is the resolution of the USGS 7.5 minute Digital Elevation Models (DEMs), a key data layer. It is also an appropriate resolution for gridding data taken from other 1:24,000 scale maps. This will result in a very high resolution model, particularly considering the statewide extent of Mn/Model. A larger cell size would make more efficient use of computer resources, but would not be capable of detecting many important landscape features. A smaller cell size might perform better, but would increase the demand for computer resources, thus increasing the cost of the project dramatically. Moreover, there is very little data available at a high enough resolution to support a cell size smaller than thirty meters.


Dependent Variables: Archaeological Events

The definition of archaeological events in modeling projects depends on the purpose of the project. In most academic projects, the goal is to model the locational behavior of different functional, chronological, and cultural types of occupations (components). By contrast, the goal of most cultural resource management projects is to conserve resources and limit cost by identifying areas with and without resources regardless of the nature of the resources themselves. Given this goal, and the difficulty involved in clearly identifying meaningful functional and cultural types of occupations that are securely anchored in time in most archaeological sites, it is not surprising that the most frequently used dependent variable in these contexts is the simple dichotomous case of 'archaeological resources are present (S)' and 'archaeological resources are not present (S')' (E.G., Scholtz 1981; Parker 1985; Bradley et al. 1986; Warren et al. 1987; Kvamme 1984, 1986, 1990; Stone 1984; Tipps 1983; Larralde and Chandler 1981). Because this approach lumps occupations of various kinds together, it incorporates a great deal of locational variability that reduces the potential predictive power of the model (e.g., Judge 1973; Roper 1979). However, the approach has the advantage of minimizing complexity by focusing on defined events that form a mutually exclusive, exhaustive, and non-ambiguous partitioning of the region being investigated and of producing large sample sizes, because of the use of the single 'resource present/absent class. In addition, the approach allows the use of Minnesota Statewide Archaeological Survey data that were collected according to a variety of criteria.


The approach depends as well on the fact that there are common locational tendencies that cross-cut functional and cultural categories, such as proximity to water and preference for level ground, and that many locations in a region are unsuitable for most kinds of activities for similar environmental reasons, such as the presence of swamps or very steep slopes (e.g., Kvamme 1985; Kvamme and Jochim 1989). Moreover, many powerful predictive models have been built using this simple solution to defining all the possible events that can occur in a land parcel (e.g., Parker 1985; Kvamme 1988, 1990; Kvamme and Jochim 1989; Limp et al. 1987:299). Note that the requirement of an exhaustive partitioning of all land parcels means that the event of no archaeological resources present (S') must also be defined to allow model performance to be assessed and a priori probabilities to sum to unity (see the Model Testing sub-section below).


The success of this modeling approach depends on the use of unambiguous definitions for 'archaeological resource present (S)' and 'archaeological resource not present (S')'. In this project, a site, or archaeological resource, will be defined using criteria established by the State Archaeologist of Minnesota. In addition, the project will focus primarily on the location of what are generally called "open-air" sites, for the available digital environmental data are not particularly suited to identifying the location of caves, rockshelters, overhangs, rock faces suited for rock art, and other special sites, although the general suitability of a region for their presence can be determined.


Other choices of dependent variables in locational modeling in archaeology have included multiple site types (e.g., Limp et al. 1987; Scholtz 1981; Parker 1986; Kvamme 1988), counts of artifact density (Green 1973; Zubrow and Harbaugh 1978; Nance et al. 1983), and various measures of site significance (e.g., James and Knudson 1983; Woodward Clyde Consultants 1978). The advantages and disadvantages of these choices are reviewed in Kohler and Parker (1986), Judge and Sebastian (1988), and Kvamme (1990).


Independent Variables: Non- Archaeological Characteristic of Locations

A variety of independent variables have been used in archaeological models of locational behavior, including sociocultural (Zimmerman 1977; Scholtz 1981) and radiometric (e.g., Custer et al. 1986) characteristics and positional parameters (Parker 1985; Limp et al. 1987). However, most modeling projects in North America have focused on the economic component of site location, for environmental factors are generally considered intimately related to locational decisions by hunter-gatherers without advanced transportation. It is the remains of these types of societies that are the main focus of cultural resource management surveys in most parts of North America (e.g., Bettinger 1980; Jochim 1976; Wood 1978). The argument is (1) in these types of societies the most important economic transactions are with the regional environment, and (2) people in these societies tend to minimize the time and effort they expend in these transactions (Kvamme 1990:271). The effect was to encourage location close to important environmental resources. Since these assumptions "break down" in relatively complex societies engaged in a market economy, the model developed here is intended to apply to settlements in Minnesota before Euroamerican social and political factors began to "control" settlement locations. The end of that period is set here at 1821, the date of the establishment of Fort Snelling, when written records - and historical methods of investigation - become a more effective avenue for determining site location.


The focus on environmental or biophysical characteristics of the landscape, such as slope, soil type, elevation, plant community type, and distance to water, is also a practical one. These variables are relatively easy to identify today through measurements or observations made on maps, aerial photographs, and remotely sensed data sets that can be readily converted to digital spatial information in a GIS (see The Role of Geographic Information Systems sub-section below). Environmentally-based predictive locational models work by correlating the location of a sample of sites with the environmental characteristics of the land parcels they are in and predicting that other, unknown sites will be present in parcels with similar sets of characteristics. The goal then is to define those characteristics of the landscape that have some bearing on the distribution of archaeological resources in a study area.


Prior research and hunter-gatherer settlement theory demonstrate that open-air site placements were most often a function of a matrix of environmental factors that have been found to be quite consistent from study to study (e.g., Jochim 1976; Thomas and Bettinger 1976; Williams et al. 1973; Shermer and Tiffany 1985; Larralde and Chandler 1981; Roper 1979; Scholtz 1981). As a general rule, the variables chosen are restricted to those that reflect relatively stable landscape characteristics through time, such as elevation, slope, and aspect, to insure that there is some correspondence between modern map-measured data and the prehistoric-early historic environment. Some potentially important variables, such as plant community composition and water table elevation, are notoriously sensitive to climatic changes and, as a result, are difficult to use without recourse to proxy measures (Kohler and Parker 1986:415). Nonetheless, distance to nearest water can be made operational by using major drainage locations and lakes, and distances to them, which are landscape features. The assumption is that, even though lake size, for instance, has changed though time (e.g., through the construction of a dam), distance to a lake's edge today serves as a useful proxy measure of distance to water in the past.


The particular environmental variables most suited to a particular model depend in part on the physical nature of the region under investigation and cannot be determined completely a priori (that is, without analysis). Therefore, this project will initially measure a relatively large number of landform, hydrological, soil, and geologic characteristics, including slope, aspect, elevation, local relief, landform type, horizontal distance to the nearest permanent water and stream confluence, and distance to streams. Variables with low predictive power will be filtered out throughout the model development process. It is probable, however, that some characteristics will prove to be important in only some areas of the state, necessitating the construction of multiple models. Justification for the adoption of these characteristics and procedures for operationalizing their measurement can be found in Scholtz (1981), Parker (1985, 1986), Kvamme (1986), Kvamme and Kohler (1988), Limp et al. (1987), Warren et al (1987), Hasenstab (1983), and Roper (1979), among other authors. General reviews of the issues involved are provided by Kohler and Parker (1986), Judge and Sebastian (1988), and Kvamme (1990). Because measurements on all of these characteristics must be obtained by GIS, they must be made operational in computer terms (e.g., Kvamme 1990). A detailed description of the GIS algorithms that will be employed to compute the environmental data is not provided here.


Although this "empirical correlation" procedure must by necessity be used in the formation of predictive locational models today, the importance of social and political factors in the spatial location of settlements cannot be ignored. Their identification should become an important focus of the modeling process as more is learned about the archaeology of the state.


Types of Models and Decision Rules

The modeling approach chosen here is based on the assumption that human behavior is nonrandom and, therefore, that settlements and other activity places are nonrandomly distributed, too. This means that significant regional patterning should exist in the distribution of archaeological resources, an implication of the assumption supported by numerous studies of settlement data (e.g., Judge 1973; Kvamme 1985; Roper 1979; Thomas and Bettinger 1976). More directly relevant to this project are the subsidiary assumptions that (1) archaeological resource locations in Minnesota are nonrandomly distributed with respect to identifiable environmental variables, and that (2) the site samples that will be obtained are representative of resource locations in this region. While the second assumption can be satisfied through the use of some form of random sampling design (see Survey Procedures in the Basic Data Accumulation and Model Development section), the first requires a more complex statistical examination of environmental data (the independent variables) that is capable of isolating patterns and differences between types of locations that generally possess or do not possess open-air sites.


Both univariate and multivariate statistical models will be used to identify on which environmental variables the distributional differences of the dependent variable (archaeological resources present/absent) are most pronounced. A variety of univariate statistical tests will be performed on the data, and logistic regression and other multivariate techniques will be used to explore differences between parcels with and without resources. Many researchers have adopted multiple logistic regression models, because they make no assumptions about the form of the distribution of the data (i.e., they are a nonparametric technique), are robust classifiers regardless of distributional form (which presumably will be important in a region as diverse as Minnesota), can handle nominal, ordinal, and interval level independent variables, and seem to produce better results than other multivariate modeling strategies. However, multiple discriminant analysis, maximum distance classifiers, quadratic classification procedures, and maximum likelihood distance classification techniques all have their adherents (e.g., Maynard and Strahler 1981; Warren 1990; Press and Wilson 1978; Wrigley 1977; Scholtz 1981; Kvamme 1983, 1984, 1985, 1986; Parker 1985, 1986; Bradley et al. 1986; Custer et al. 1986; Warren et al. 1987; Marozas and Zack 1987; see Kohler and Parker 1986, and Kvamme 1988 and 1990, for general reviews).


The results of the statistical analysis will be used, at least initially, to formulate decision rules that indicate whether archaeological resources are likely present or not within a parcel of land. The product of a logistic regression is an equation which assigns weights to a group of significant environmental variables. When this equation is applied to all cells in a grid it creates a map of values from 0 to 1 indicating the potential of finding archaeological resources in each cell. This kind of map is known as a probability surface. A decision rule might be that all cells with values higher than x are considered to be high probability locations and all cells with values lower than y are considered to be low probability. The decision rule will first be calibrated on sample data, for instance so that 85% of sample sites fall in high or medium probability areas, then tested on a separate set of data. If the decision rules capture a real pattern in the archaeological record, about 85% of the additional sites should fall within high and medium probability areas as well. For a review of the wide variety of algorithms used in archaeology to develop model decision rule strategies, see Kohler and Parker (1986) and Kvamme (1988, 1990).


In archaeology, a locational model is essentially a decision rule applied to the results of an equation that assigns land parcels to event classes (here the presence or absence of archaeological resources) on the basis of environmental or other non-archaeological characteristics of the parcels. The GIS uses the model to assign cells of unknown archaeological class membership to one (resources are present) or another (resources are not present) membership option. The statistical techniques employed here facilitate cultural resource management planning by abstracting the environmental patterns exhibited by cells known to contain or not contain archaeological sites and mapping them across the entire region (see The Role of Geographic Information Systems sub-section below).


Model Testing

As outlined above, a predictive model in archaeology is simply a decision rule that assigns cells in a study area to one of a number of mutually exclusive and exhaustive archaeological events (here, again, merely resources present or absent) on the basis of environmental or other non-archaeological characteristics of the locations. Assessment of model performance and accuracy are obviously necessary, for, at the very least, a predictive model must be able to perform better than chance alone. Model testing involves, then, (1) the determination of the a priori or chance probability of the occurrence of certain archaeological events, and (2) an independent test of the model's effectiveness against this probability. Presumably, the identification of the key non-archaeological characteristics of the cells that are associated with the presence or absence of an archaeological resource is a guarantee that the predictive model will be more effective than the by-chance model -- but it must be demonstrated that this is so. In addition, a good test will specify the degree of effectiveness of the predictive archaeological model over the by-chance model.


An a priori probability is the "pure chance" probability that a land parcel does or does not contain archaeological resources. As a by-chance locational model, it provides a baseline that helps define what other models must accomplish. In regional studies, by-chance models can be calculated by determining the relative frequency of the presence or absence of resources in a random sample of surveyed land parcels (e.g., Hord and Brooner 1976; Kvamme 1983, 1988; Parker 1985:187). For instance, if 50 land parcels contain resources and 450 do not in a surveyed sample of 500 parcels, then the probability that a land parcel contains resources by chance is 0.1 or 0.9 that it does not. Since the probability of correctly assigning a land parcel is no better than chance, these probabilities can be considered by-chance locational models. In this project, a priori probabilities for various regions of the state will be estimated from the results of the random survey in the second field season.


The second phase of model testing involves the comparison of the actual presence or absence of archaeological resources in cells against model assignments in an independent random sample of locations, for the two classifications may not agree. In fact, since models are imperfect predictors, many misassignments will undoubtedly occur. A completely independent assessment of model performance must be made, because the use of the same land parcels surveyed to develop the model results in test sample dependency, which produces overly optimistic assessments of model performance (e.g., Kohler and Parker 1986:431; Kvamme 1988, 1990:263; Mosteller and Tukey 1977). Other strategies developed to surmount problems that result from testing a model on data from which it was derived, such as split sampling (Limp et al. 1987; Mosteller and Tukey 1977), jackknife methods (Mosteller and Tukey 1977; Kvamme 1988), and sequential analysis methods (Limp and Lafferty 1981), have drawbacks, but can also be used. Although a second completely independent random sample survey seems expensive, it greatly improves the accuracy of models and thus their value in the planning process (e.g., Rose and Altschul 1988). Land parcels for this test will be selected from grid cells in the GIS matrix using a random numbers procedure that should insure a uniform sampling of the region's environmental variation.


The predictive power of a model is determined by calculating its percent of correct predictions in the test sample and comparing this percent with the likelihood of a correct prediction by chance alone. These calculations determine the model's specific percent of predictive accuracy over chance alone. Regardless of this percent, a suitable level of performance of a good model should correctly predict about 85 percent of open-air sites. The main method of assessing model performance in archaeology is usually some form of cross-tabulation that compares the actual and model assigned presence or absence of resources. One of a number of statistical tests can then be used to determine the significance of these frequencies (e.g., Congalton et al. 1983; Kvamme 1988, 1990). Since the performance or accuracy of the model is evaluated statistically, field data must be collected within a sampling framework that utilizes the basic principles of elementary probability theory. It is this foundation that also gives a model the ability to assign a probability to the occurrence of archaeological resources in a land parcel.


By providing an independent data set, the second survey also allows an assessment of the actual performance of the decision rule and an opportunity to calibrate its position on the regression scale. Binomial confidence limits can then be established to delineate the bounds of the expected performance of the model in planning, and Bayes Theorem can be used to estimate the probability of the presence or absence of archaeological resources in future samples (Kvamme 1988). Because of the sampling and testing design, the refined model's projected performance probabilities should apply to the study region - the state - as a whole.


The Role of Geographic Information Systems

The effective and efficient application of the predictive archaeological models developed in the 1980s was severely hampered by the labor effort required to manually measure map variables in large-scale government-funded projects. In fact, the application of high-resolution models was virtually impossible without restricting sample size and the range of variables investigated. Nearly all of these limitations have been successfully overcome in recent years, however, through the application of Geographic Information Systems (GIS) technology (e.g., Hasenstab 1983; Kvamme 1986, 1989, 1990; Limp et al. 1987; Marozas and Zack 1987; Warren et al. 1987). Unlike traditional database management systems, GIS has a spatial or mappable component that allows the capture, efficient manipulation, analysis, and storage of geographical information. In addition, GIS is easily capable of producing maps of this information in various formats on a video monitor or on paper.


GIS technology can be used in all phases of the employment of predictive archaeological models, that is, in their development, testing, and application. For instance, GIS can measure five or ten environmental variables across the entire surface of an impact zone and then apply the model decision rule to this surface. By using a cell-based system that represents continuous variation in the landscape, GIS can store separate thematic map layers that contain values for environmental variables, like proximity to water, aspect, slope, and elevation, for each cell (e.g., Wansleeben 1988). Two important properties of GIS are its ability to encode information from diverse sources and to generate new data. Geographically distributed information can be encoded from such diverse sources as aerial photographs, remotely sensed digital imagery, and conventional maps, like geologic, soils, and topographic maps. Since much of this information is already being mapped into GIS systems by the Minnesota DNR and other state agencies, including the location of known archaeological sites, this aspect of predictive modeling is not as time consuming as it may seem. GIS is also able to generate data from other data sources. Elevation data, for example, can be electronically digitized over a study area using 1:24,000 scale U. S. Geological Survey maps and then employed to obtain measures for other layers, such as slope, aspect, land relief, and local terrain variability (Kvamme and Kohler 1988). In applications of the predictive model, the independent environmental predictor variables are electronically measured across the area of interest, and the model (the decision rule) is applied electronically to determine the assignment of a parcel of land within the area to one or another of the dependent archaeological event classes (here 'resources are present or 'resources are not present ).


Large-scale, government-funded projects in the 1980s have been responsible for the development of sophisticated procedures for developing and assessing the application of predictive archaeological models. Recent innovations in GIS technology have made the application of these models a realistic and sensible component of cultural resource management. See Appendix D for further discussion of the definition and functions of GIS.


Issues and Concerns

Sample-based modeling approaches in archaeology face ubiquitous problems that limit the predictive accuracy of models and should be considered when using modeling results. Three problems with the characteristics of the site samples employed in modeling are briefly reviewed here to provide some insight into the nature of these issues and concerns.


A key problem is the accessibility of archaeological resources. In any region, many archaeological sites will have been destroyed by erosion or human activities. Other sites will be deeply buried, well-hidden in sealed rockshelters or under dense vegetation, covered by towns or lakes, on property to which access is denied, or so small as to easily fall between transects in a field survey. Predictive models, because they are necessarily based on sample survey data, are only sensitive to the types of archaeological resources included in the initial samples. This means that they are usually only sensitive to certain types of surface distributions, for the distribution of geologically-buried sites is rarely explored in a systematic manner.


A second problem is the difficulty in archaeology of satisfying statistical assumptions, such as the requirement of multivariate normality or homogeneity of variance. For this reason, modelers usually remain somewhat skeptical of statistical indicators of the importance of independent variables in the developmental phase of model building and employ robust mathematical procedures to identify decision rules. It is in the better controlled testing phase where the requirements of statistical assumptions can be more fully met that statistical inference and probability theory play their primary role.


Still a third problem is the presence of patterned variation (i.e., spatial autocorrelation) in the distribution of archaeological phenomena. Its existence violates the assumption of independent observations and generally results in overestimates of the significance of independent variables. This problem can be partially controlled by adopting a sampling procedure that widely separates surveyed parcels of land.


Still other kinds of problems exist that planners must be familiar with. One is the importance in site location of social and political factors ("sociocultural noise"). The difficulty of taking such factors into account is one reason why nearly all predictive archaeological models have accuracy rates less than 85 percent. It is also the main reason why field survey must remain an integral component of cultural resource management.


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