Malcolm M. Dow

Methods for the Comparative Analysis of Variation Patterns

-Although comparisons of variation patterns with theoretical expectations and across species are playing an increasingly important role in systematics, there has been a lack of appropriate procedures for statistically testing the proposed hypotheses. We present a series of statistical tests for hypotheses of morphological integration and for interspecific comparison, along with examples of their application. These tests are based on various randomization and resampling procedures, such as Mantels test with its recent extensions and bootstrapping. They have the advantage of avoiding the specific and strict distributional assumptions invoked by analytically-based statistics. The statistical procedures described include one for testing the fit of observed correlation matrices to hypotheses of morphological integration and a related test for significant differences in the fit of two alternative hypotheses of morphological integration to the observed correlation structure. Tests for significant similarity in the patterns and magnitudes of variance and correlation among species are also provided. [Morphometrics; comparative analysis; morphological integration; quadratic assignment procedures; Mantels test; bootstrap.] Comparing observed patterns of morphometric variation to theories of morphological integration (Olson and Miller, 1958; Cheverud, 1982) and among species, or subspecific populations (Arnold, 1981; Riska, 1985), has been a largely ad hoc procedure. Previously, a large body of methods has been used to analyze variation patterns, including various forms of cluster analysis, factor analysis, principal components, multi-dimensional scaling, matrix correlations, and visual inspection. The results of such analyses were then discussed relative to some theory of variation patterns or compared between species or populations. These comparisons might either be verbal or quantitative, but tests of statistical significance were rarely employed. More recently, there has been an increase in statistical rigor in the field, particularly involving the use of quadratic assignment procedures (QAP; sometimes referred to as Mantels test) (Mantel, 1967; Deitz, 1983; Dow and Cheverud, 1985; Smouse et al., 1986; Dow et al., 1987a, b; Hubert, 1987) for testing the statistical significance of matrix comparisons (Cheverud and Leamy, 1985; Lofsvold, 1986; Kohn and Atchley, 1988; Cheverud, 1989a; Wagner, 1989) and the use of confirmatory factor analysis (Zelditch, 1987, 1988) for testing hypotheses concerning levels and patterns of variation. These new methods allow statistical inference for hypotheses of morphological integration and for comparisons across species. We will describe the use of several of these newer methods, especially those using randomization, for testing hypotheses of morphological integration and interspecific comparison and provide brief examples of their use. The procedures described below can be used to rigorously test hypotheses concerning the causes of morphological variation and covariation patterns. A closely related set of procedures can be directed towards comparative, cross-taxon, analyses of variation and correlation patterns. The systematic study of distinction among group means is well known and extensively represented in the literature. However, systematic studies of variation patterns (as measured by a multivariate variance/covariance or correlation matrix) have been relatively rare. This has been due, in part, to a lack of relevant theory and appropriate systematic methodology. Important theoretical advances over the

Regions Based on Social Structure

Boas argued that anthropologists should make historical comparisons within well-defined regional contexts. A century later, we have many improvements in the statistical methodologies for comparative research, yet most of our regional constructs remain without a valid empirical basis. We present a new method for developing and testing regions. The method takes into account older anthropological concerns with relationships between culture history and the environment, embodied in the culture-area concept, as well as contemporary concerns with historical linkages of societies into world systems. We develop nine new regions based on social structural data and test them using data on 351 societies. We compare the new regions with Murdocks regional constructs and find that our regional classification is a strong improvement over Murdocks. In so doing we obtain evidence for the cross-cultural importance of gender and descent systems, for the importance of constraint relationships upon sociocultural systems, for the historical importance of two precapitalist world systems, and for strikingly different geographical alignments of cultural systems in the Old World and the Americas.

Network autocorrelation: A simulation study of a foundational problem in regression and survey research

Social Networks North-Holland Publishing Company NETWORK AUTOCORRELATION: OF A FOUNDATIONAL PROBLEM SURVEY RESEARCH * Malcolm M. DOW Northwestern Unioersity A SIMULATION STUDY IN REGRESSION AND Michael L. BURTON and Douglas R. WHITE University of California, Irvine It is axiomatic to the social sciences, and an essential part of the network perspective, that human performances are intricately linked with their social and enviromental contexts. Researchers in each of the disciplines have rediscovered this in the past decade with respect to a whole host of specific problem areas, under such labels as “context effects”, “index utility”. and “systems analysis”. The earliest mention of the problem with respect to quantitative research occured, to our knowledge, in the debate between the nineteenth century cultural diffusionists and the evolutionists. The latter regarded individual socie- ties as independent instances of uniform causation, and hoped to learn about causation from correlational studies. The former regarded their observations as embedded in an interactive network of historical rela- tionships such as diffusion, migration, conquest, and competition, where the historical, evolutionary and ecological context of each society and the network of interconnectedness between societies plays a major role in multiple causation. In this view, events cannot be regarded as * This research was supported by a grant from the National Science Foundation to Michael Burton and Douglas White. The two Principal Investigators made major and equal contributions to this paper. We are grateful to Linton Freeman, Patrick Doreian, and Karl Reitz for their critical comments on this paper. ** Northwestern University, Evanston, IL 60201, U.S.A. *** University of California, Irvine, CA 92717, U.S.A. 0 1982 North-Holland

Galton's problem as multiple network autocorrelation effects : Cultural trait transmission and ecological constraint

Empirical evidence that cultural traits are often nonrandomly distributed because of the individual or combined effects of common history, diffusion, borrowing, and/or other types of cultural transmission processes has been accumulating for decades. Because many cultural traits have recently been shown to be influenced by more than one transmission process, it has become a methodological priority in comparative research to develop statistical methods that can simultaneously incorporate multiple transmission processes. This article proposes a multiple network autocorrelation effects model and associated two-stage least squares (2SLS) estimation procedures. The network autocorrelation effects model offers an alternative interpretation of how cultural trait transmission processes operate than does the network autocorrelation disturbances model. Conceptual differences between the two classes of models suggest that the network effects specification will be more generally applicable in comparative studies. An empirical example demonstrates the substantive value of the multiple network autocorrelation effects model and the widely available 2SLS estimation procedures.

A Biparametric Approach to Network Autocorrelation

In anthropology, “Galtons Problem” is generally taken to refer to the interdependence of cases in a cross-cultural sample due to various processes of cultural diffusion. Previous attempts to deal with this problem have usually assumed that these types of interdependencies can be characterized adequately in terms of spatial proximity and/or common linguistic history. In regression analysis using such interdependent data, autocorrelation among the error terms can be incorporated into the model by means of a network relational or connectivity matrix, W. The biparametric model is a straightforward generalization that specifies two autocorrelation parameters associated with two network relational matrices. Simultaneous autocorrelation effects for language similarity and geographical distance matrices are empirically demonstrated using cross-cultural data on the sexual division of labor. An alternative to the maximum likelihood approach to estimation of both autocorrelation parameters is suggested and employed.

Global, Regional, and Local Network Autocorrelation in the Standard Cross-Cultural Sample

There is now considerable evidence in the cross-cultural literature that cultural networks need not be based strictly on spatial propinquity but may develop along other dimensions such as common language, religion, and levels of cultural complexity. In this article, the authors generate networks based on sociocultural distance metrics for these three network dimensions in addition to the usual geographical distance measure and a measure of overall ecological niche similarity. The authors report overall levels of autocorrelation for all five networks using 1,156 Standard Cross-Cultural Sample (SCCS) variables at the global level and for a subset of 422 variables within four regions. The extent to which cultural trait distributions appear to be influenced by combinations of network processes also are assessed. Results from an analysis based on a local autocorrelation statistic provide confirmation of the regional levels of autocorrelation within the SCCS data set.

Multivariate Modeling with Interdependent Network Data

In the recent comparative literature the problem of simultaneously modeling func tional and diffusional effects is being penetrated from two directions. One approach emphasizes the similar problem which arises in regression-based time series analysis. A second approach focuses on the difficulties of constructing more realistic formal representations of sample unit interdependencies. Both approaches have yielded important and complementary, but distinct, insights. Here, we outline some recent methodological developments which synthesize both approaches into a comprehen sive and unified analytical framework.

Assignment methods for the analysis of network subgroup interactions

Abstract In studies of social structure, it is often of interest to focus on the interactions of identified subgroups (e.g. females, lineage members) both with respect to the patterns of behavior within the subgroups and in relation to the complement set of group members. For example, it may be of interest to assess the degree of “compactness” of one or more subgroups based on specific behavioral interactions, or to assess the degree of “isolation” of a given subgroup from the rest of the group. In the case of asymmetric behavioral interaction data (e.g. aggression, grooming), the concept of “isolation” can be decomposed further into the flow of actions directed towards a given subgroup and the flow directed outwards from that subgroup. A variety of quadratic assignment methods are outlined that operationalize these compactness/isolation concepts. More general cubic assignment methods are described that focus on the flow of behaviour out of or into a given subgroup in comparison to the flow within it, or in comparison to the flow of behavior within the complement set of members. Sampling distributions for each of the indices described are easily generated using Monte Carlo procedures. All of these assignment methods are illustrated using network interaction data on a group of 14 adult macaque monkeys.

Multiple Imputation of Missing Data in Cross-Cultural Samples

Listwise deletion of cases with missing data prior to statistical analysis, the approach overwhelmingly used by cross-cultural survey researchers, requires the assumption that the missing data are missing completely at random. This assumption is not often likely to hold for cross-cultural sample data, and when it fails statistical analysis based only on complete-case subsamples introduces the possibility of biased estimates and standard errors. Over the past 20 or so years statisticians have made major advances in specifying the conditions under which missing data can be ignored when making inferences based on incomplete data. We review these conditions since they have a direct bearing on when the usual approaches to dealing with missing cross-cultural survey data are invalid.

Network Autocorrelation Regression With Binary and Ordinal Dependent Variables : Galton's Problem

Dow and Eff recently reported high levels of network autocorrelation for over eleven hundred and fifty variables coded for the Standard Cross-Cultural Sample (SCCS) with respect to five distinct measures of network proximity: distance, language, cultural complexity, religion, and ecological niche. Most of the variables were discrete, either binary or ordinal, as are the vast majority of variables in all cross-cultural samples. A large percentage showed significant levels of autocorrelation with respect to two or more networks simultaneously. One implication of these findings is that there is a need in comparative research for statistical models that can deal with binary and ordinal dependent variables while simultaneously controlling for one or more autocorrelation process. The current paper suggests one such regression modeling procedure and applies it in a reanalyses of the causes of polygyny. Both spatial autocorrelation by itself, and spatial and language autocorrelation in combination, were found to be significant predictors of polygyny.