# Galton's problem and autocorrelation

This is a list of references that includes phylogenetically-based comparative methods. Wikipedia:Galton's problem - http://eclectic.ss.uci.edu/~drwhite/courses/ArticleSearchSCCSpdfs.htm -- http://eclectic.ss.uci.edu/~drwhite/courses/Articles4SCCS.pdf

"In his exchange with Tylor in 1888, Galton questioned whether observations of marriage laws across areal entities constituted independent observations such they could just reflect a general pattern from which they had all descended" -- p.238 Bivand, Roger, Edzer J. Pebesma, Virgilio Gómez Rubio. 2008. Applied spatial data: analysis with R.
• Tylor, Edward B. 1889 ‘On a method of investigating the development of institutions; applied to laws of marriage and descent’ JAI vol 18 (1889) 245 - 272. Wikipedia:Galton's_problem
Wikipedia:Tobler's first law of geography

## Biogeography

Keynote Address: A tribute to Prof. D.G. Krige for his contributions over a period of more than half a century-Compiled by Prof. R.C.A. Minnitt and Dr W. Assibey-Bonsu-Presented by Dr F.A. Camisani-Calzolari. Application of Computers and Operations Research in the Minerals Industries, South African Institute of Mining and Metallurgy, 2003. 405-407.

```The basic form of the kriging estimator is
n(u)
Z*(u)−m(u)= ∑λα[Z(uα )−m(uα )]
α=1
The goal is to determine weights, λ , that minimize the variance of the estimator
α
σ 2 (u ) = V a r {Z * (u ) − Z (u ) } E
the basic form of the kriging estimator is
n(u)
Z*(u)−m(u)= ∑λα[Z(uα )−m(uα )]
α=1
```

So what does all this math do? It finds a set of weights for estimating the variable value at the location u from values at a set of neighboring data points. The weight on each data point generally decreases with increasing distance to that point, in accordance with the decreasing data-to-estimation covariances specified in the right-hand vector, k. However, the set of weights is also designed to account for redundancy among the data points, represented in the data point-to-data point covariances in the matrix K. Multiplying k by K-1 (on the left) will downweight points falling in clusters relative to isolated points at the same distance.

## Getis

• Aldstadt, Jared and Arthur Getis (2006) “Using AMOEBA to create a spatial weights matrix and identify spatial clusters.” Geographical Analysis 38(4) 327-343.
• Getis, Arthur and Jared Aldstadt (2004) “Constructing the spatial weights matrix using a local statistic.” Geographical Analysis 35(2) 90-104. Reprinted in Anselin, Luc and Sergio J. Rey (2010) Perspectives on Spatial Data Analysis. Springer, 147-163.
• Folmer H, Oud J, 2008, "How to get rid of W: a latent variables approach to modelling spatially lagged variables" Environment and Planning A 40(10) 2526 – 2538. Abstract. In this paper we propose a structural equation model (SEM) with latent variables to model spatial dependence. Rather than using the spatial weights matrix W, we propose to use latent variables to represent spatial dependence and spillover effects, of which the observed spatially lagged variables are indicators. This approach allows us to incorporate and test more information on spatial dependence and offers more flexibility than the representation in terms of Wy or Wx. Furthermore, we adapt the ML estimator included in the software package Mx to estimate SEMs with spatial dependence. We present illustrations based on Anselin’s Columbus, Ohio, crime dataset.

## Autocorrelation - additional references

• Moran, Patrick A. P. 1950. "Notes on Continuous Stochastic Phenomena". Biometrika 37 (1): 17–23. doi:10.2307/2332142.
• Exploring the Roots of Culture Using Spatial Autocorrelation

Paul Dobson, Garry A. Gelade 1City University, London, UK Paul Dobson, Cass Business School, City University, 106 Bunhill Row, London, EC1Y 8TZ, UK Email: P.M.Dobson@city.ac.uk

Abstract: This article examines the distribution of some well-established dimensions of national culture within geographic and ecosocial space. Using spatial autocorrelation to quantify the relationships between geographical location, distance from the equator, physical climate, religion, and national development and 38 cultural dimensions, we find a substantial degree of spatial organization; some cultural dimensions are as spatially organized as temperature or rainfall. Overall, we find that culture as measured by aggregated personal values covaries to about the same extent with geographical proximity, national development and religion, and significantly less with the physical climate and distance from the equator. It is also found that there are significant differences in the spatial patterning of GLOBE societal-level values and the personal value measures of previous researchers. GLOBE values are also strongly organized by geographical proximity and religion but unlike personal value measures only weakly organized by level of national development. GLOBE practices are not strongly spatially organized at all suggesting that practice in a nation does not evolve simplistically from national values or vice versa. Religion, a major organizing variable for how people believe things should be in society, has little relationship with how people believe things are. We conclude that the approach taken by the project GLOBE is a valuable contribution to our understanding of national culture and that spatial autocorrelation is an exploratory method of analysis that is underused in cross-cultural research.
• Griffith, Daniel A. 1996. Some guidelines for specifying the geographic weights matrix contained in spatial statistical models. In S. Arlinghaus (Ed.), Practical handbook of spatial statistics (Chap. 4, pp. 65-82). Boca Raton, FL:CRC Press.
Referenced in Dow, M.M., & Eff, E.A. 2008. Global, regional, and local network autocorrelation in the Standard Cross-Cultural Sample. Cross-Cultural Research 42: 148-171. pp 158-159 show variables in the SCCS with high spatial autocorrelation.

## Current authors

Entries below from http://scholar.google.com

## Early work

Tylor, Edward E. 1889. On a Method of Investigating the Development of Institutions Applied to the Laws of Marriage and Descent. Journal of the Royal Anthropological Institute 18(3):245–72.

### 1960s

Crano, William D. 1968 "An extension of Naroll's linked pair solution to Galton's problem" in American Anthropologist, 70, 2, Apr, 336-337.

Naroll, Raoul. 1961. Two Solutions to Galton’s Problem. Philosophy of Science 28:15-39.

Naroll, Raoul and Roy G. D'Andrade. 1963. Two Further Solutions to Galton’s Problem. American Anthropologist 65: 1053-1067.

Naroll, Raoul. 1964. A Fifth Solution to Galton’s Problem. American Anthropologist 66:863-867.

### 1970s

Divale, William. 1974. Migration, External Warfare, and Matrilocal Residence Cross-Cultural Researc 9(2):75-133

Divale, William. 1977 From Correlations to Causes: A New and Simple Method for Causal Analysis in Cross-Cultural Research. Annals of the New York Academy Of Sciences 285:66-74. Vol. titled: "Issues in Cross-Cultural Research," Leonore Loeb Adler, ed.

Loftin-Simonton

Naroll, Raoul.

Naroll, Raoul. 1976. Galton's Problem and HRAFLIB Cross-Cultural Research 11(2):123-148.

Naroll, R. & Michik, G.L. 1975 "Hraflib - computer-program library for hologeistic research" in Behavior Science Research, v10, n4, p283-296.

Ord, Keith. 1975. Estimation Methods for Models of Spatial Interaction. Journal of the American Statistical Association 70:120-126.

Schaefer, James M. & Evascu T.L. 1976 "Data quality and modes of marriage - some holocultural evidence of systematic-errors" in Behavior Science Research, v11, n1, p25-37.

Schaefer, James M. 1975. Studies in cultural diffusion: Galton's problem, Volume 1. Human Relations Area Files, inc.

Schaefer, James M. 1974. "Galton's problem in a new holocultural study of drunkenness" in Behavior Science Research, v9, n1, p15-16.

Simonton, Dean K. 1975. Galton's Problem, Autocorrelation, and Diffusion Coefficients Cross-Cultural Research 10(4):239-248

Vermeulen, C.J. 1975 "Dominant epistemological presuppositions in use of cross-cultural survey method" in Current Anthropology, v16, n1, p29-52.

Vermeulen, C.J.J. & Ruijter, A.D. 1975 "Cross-cultural survey method - reply" in Current Anthropology, v16, n2, p297.

Witkowski, Stanley. 1974. Galton's opportunity - hologeistic study of historical processes. Cross-Cultural Research 9(1):11-15. (Behavior Science Research)

James M. Schaefer. Studies in Cultural Diffusion: Galton's Problem A Preview. Cross-Cultural Research 1974 9: 1-3. [PDF] [References]
Richard Paul Chaney. Anthropologies and Histories and Philosophies of Scientific Inquiry. Cross-Cultural Research 1974 9: 3-4.
Loftin, Colin. 1972. Galton's problem as spatial autocorrelation: Comments on Ember's empirical test. Ethnology 11:425–35.
Ember, Melvin. 1971. An Empirical Test of Galton’s problem. Ethnology 10: 98-106.
Loftin, Colin, and Sally K. Ward. 1981. Spatial autocorrelation models for Galton's problem. Behavior Science Research 16:105–28.
Loftin, Colin, and Robert H. Hill. A Comparison of Alignment Procedures for Tests of Galton's Problem. Cross-Cultural Research 1974 9: 4-6.
Ying, Sam. Colin Loftin and Sally K. Ward: Application of Spatial Autocorrelation in Sociology http://www.csiss.org/classics/content/61
[[Harold Gene Zucker]. 1976. The Standardized Diffusion Test. Cross-Cultural Research 11(2): 71-102. Abstract: An accurate and flexible method for measuring cultural diffusion is presented. When the diffusion of pairs of traits is measured, the method constitutes a solution to Galton's problem. Application of the method to data on the association of patrilocal residence with patrilineal descent indicates that the association is based on diffusion rath]er than function.
Erickson, Edwin E. 1974. “Galton's Worst: A Note on Ember's Reflection”. Pp 62-83. In, James Schaefer. Studies in Cultural Diffusion: Galton's Problem, New Haven, HRAFlex Books, W6-002.
Edwin E. Erickson. Galton's Worst: A Further Note on Ember's Reflection. Cross-Cultural Research 1974 9: 7-11.
James M. Schaefer. Galton's Problem in a New Holocultural Study of Drunkenness. Cross-Cultural Research 1974 9: 15-16.
Lenora Greenbaum. Statistical Probabilities, Functional Relationships, and Galton's Problem. Cross-Cultural Research 1974 9: 16-17.
Harvey G. Carroll. Testing Some Assumptions of the Cross-Cultural Survey Method Regarding Sampling and Galton's Problem. Cross-Cultural Research 1974 9: 17-19.
Rolf Wirsing. Measuring Diffusion: The Geary Method and the Dacey Method. Cross-Cultural Research 1974 9: 20-21

## The big lie

Get a clue: Sorry, but random sampling is NOT a solution to empirical nonindependence or autocorrelation The relevant quote here is "Those who are not worried about Galton's problem think that random sampling is the best way to avoid sampling bias, which is what Galton and others have worried about. The latter is simply a lie. The source here is Cross-cultural research methods by Carol Ember and Melvin Ember (2001:89), Walnut Creek, CA: AltaMira Press. See Ember and Ember (1998:678) below.

Anthropologists today have split into different groups over this issue. In cultural anthropology the predominant view is that it is ok to use descriptive statistics for household censuses and inventories of the features of individual communities but not to make inferences about larger historical or functional relations from correlations about samples of different societies. This majority view is critical of what is called the “HRAF” method of comparison, in which inferences are made about functional relations among features of different societies from correlations based on samples that are drawn by methods of probability sampling from a larger universe. It is well known that by such means (Kish 1965) it is possible to get an unbiased estimate of the mean of the larger universe of cases from which the sample is drawn, and that the error bounds of these descriptive means can be accurately estimated. The descriptive mean and standard deviation is derived from the assumption that cases are sampled independently, i.e., without a sampling bias.

This is quite different from Galton’s problem, however, in which even with a complete population, and no sampling whatsoever, the cases are not historically independent. This is the problem of autocorrelation, which may take the form of historically replicated copies of the same originals, borrowing or diffusion, similarities or differences produced through interaction or splitting off from the same historical antecedents. The “HRAF” brand of contemporary positivism (valuing or prescribing preferred methodology above logically scientific practice) prefers not to recognize the problem as posed by Galton. As distinguished a methodological source as Bernard’s Handbook (1998:678-679) allows misleading statements by its authors. First (Ember and Ember 1998:678): “We suggest that those who worry about Galton's Problem misunderstand two requirements of statistical inference—that sample cases be independent and that the measures on them be independent…. Independence of cases means only that the choice of one case is not influenced by the choice of any other case (which random sampling guarantees).” To imply that random sampling guarantees “that the measures on them be independent” across cases an egregious falsehood, as we see clearly in Ember and Ember (2001:89). Second (p. 678-79): “whether or not you worried about Galton's Problem made a big difference in how you would do a study. Naroll’s tests for the possibility of diffusion were quite time consuming to carry out. This was probably why most cross-culturalists altered their sampling strategy so as to eliminate multiple cases from the sample culture area,” i.e., favoring smaller sample sizes rather than larger well-coded samples that provide better statistical estimations if done correctly. These authors are conflating the two meanings of nonindependence: (1) in picking cases and defining variables, and (2) in the interactions between societies and between the variables that characterize them, which the Embers fail to recognized as the twin aspects of Galton's problem. The latter aspects of nonindependence are what the DOW-EFF functions are all about: controlling for autocorrelation, and testing whether the marginal variance of correlations or error terms of regression are independent of the variables tested. In other terms: whether correlations are spurious, or regression models fail to recognize effects of additional variables that would alter the relations among the variables chosen for analysis.

Bernard, H. Russell (ed.) 1998. Handbook of Methods in Cultural Anthropology. Walnut Creek, CA: Rowman & Littlefield.

Ember, Carol, and Melvin Ember. 1998. Cross-Cultural Research. Chapter 17, pp. 695-687, in, H. Russell Bernard(ed.) 1998. Handbook of Methods in Cultural Anthropology. Walnut Creek, CA: Rowman & Littlefield.

Ember, Carol, and Melvin Ember. 2001. Cross-cultural research methods. Walnut Creek, CA: AltaMira Press.

## Work from the 1980-2005

Borgerhoff Mulder, M. 2001. Using phylogenetically based comparative methods in anthropology: More questions than answers. Evolutionary Anthropology, 10, 99-111.

Borgerhoff Mulder, M., George-Cramer, M., Eshleman, J., & Ortolani, A. 2001. A study of East African kinship and marriage using phylogenetically controlled comparison. American Anthropologist, 103, 1059-1082.

Boyd, R., Borgerhoff Mulder, M., Durham, W. H., & Richerson, P. J. 1997. Are cultural phylogenies possible? In P. Weingart et al. (Eds.), Human by nature: Between biology and the social sciences (pp. 355-386. Mahwah, NJ: Lawrence Erlbaum.

Burton, Michael L., Douglas R. White. 1984. Sexual Division of Labor in Agriculture. American Anthropologist, New Series, 86(3):568-583.

Cavalli-Sforza, L. L., & Feldman, M. W. 1981. Cultural transmission and evolution. Stanford, CA: Stanford University Press.

Cheverud, James M., Malcolm M. Dow and Walter Leutenegger. 1985. The quantitative assessment of phylogenetic constraints in comparative Sexual dimorphism in body weight among primates. Evolution 39: 1335-1351.

Chick, Garry, 2000. Editorial: Opportunities for Cross-Cultural Comparative Research on Leisure Leisure Sciences: An Interdisciplinary Journal 22(2):79-91. 1521-0588

Collard, M., Shennan, S. J., & Tehrani, J. J. (in press). Branching versus blending in macroscale cultural evolution: A comparative study. In C. P. Lipo et al. (Eds.), Mapping our ancestors: Phylogenetic approaches in anthropology and prehistory. New York: Transaction.

Cowlishaw, G., & Mace, R. 1996. Cross-cultural patterns of marriage and inheritance: A phylogenetic approach. Ethology and Sociobiology, 17, 87-97.

Dow, Malcolm M. 1989. Categorical analysis of cross-cultural survey data: Effects of clustering on chi-square tests. Journal of Quantitative Anthropology, 1, 335-352.

Dow, Malcolm M. 1991. Statistical Inference in Comparative Research: New Directions. Cross-Cultural Research 25(1-4): 235-257.

Deflation factor for contingency tables
Multilevel linear model
Significance by Data Permutation
Correcting for Effects of Sample Selection Bias

Dow, Malcolm M., Michael L. Burton, Douglas R. White, Karl P. Reitz. 1984. Galton's Problem as Network Autocorrelation. American Ethnologist 11(4):754-770. http://www.jstor.org/pss/644404

Dow, Malcolm M., Michael L. Burton, & Douglas R. White. 1982. Network Autocorrelation: A Simulation Study of a Foundational Problem in the Social Sciences. Social Networks 4(2):169-200. http://eclectic.ss.uci.edu/~drwhite/pw/NetworkAutocorrelation_A_SimulationStudy.pdf

Dow, Malcolm M., & Cheverud, J. M. 1985. Comparison of distance matrices in studies of population structure and genetic microdifferentiation: Quadratic assignment. American Journal of Physical Anthropology, 68, 367-373.

Dow, Malcolm M., Cheverud, J. M., & Friedlaender, J. S. 1987. Partial correlation of distance matrices in studies of population structure. American Journal of Physical Anthropology, 72, 343-352.

Dow, Malcolm M., D. R. White, M.L.Burton. 1982. Multivariate Modeling with Interdependent Network Data. Cross-Cultural Research 17:216-245.

Durham, W. H. 1990. Advances in evolutionary culture theory. Annual Review of Anthropology, 19, 187-210.

Durham, W. H. 1992.Applications of evolutionary culture theory.Annual Review of Anthropology, 21, 331-355.

Felsenstein, J. (1985. Phylogenies and the comparative method. American Naturalist, 125, 1-15.

Felsenstein, J. 1988. Phylogenies and quantitative characters. Annual Review of Ecology and Systematics, 19, 445-471.

Garland, T. J., Harvey, P. H., & Ives, A. R. 1992. Procedures for the analysis of comparative data using phylogenetically independent contrasts. Systematic Biology, 4, 18-32.

Gray, R. D., & Atkinson,Q. D. 2003. Language-tree divergence times support the Anatolian theory of Indo-European origin. Nature, 426, 435- 439.

Gray, R. D., & Jordan, F. M. 2000. Language trees support the expresstrain sequence of Austronesian expansion. Nature, 405, 1052-1055.

Guglielmino, C. R., Viganotti, C., Hewlett, B., & Cavalli-Sforza, L. L. 1995. Cultural variation in Africa: Role of mechanisms of transmission and adaptation. Proceedings of the National Academy of Sciences USA, 92, 7585-7589.

Harvey, P. H., & Pagel, M. D. 1991. The comparative method in evolutionary biology. Oxford, UK: Oxford University Press.

Harvey, P. H., & Rambaut, A. 1998. Phylogenetic extinction rates and comparative methodology. Proceedings of the Royal Society of London: Series B, 265, 1691-1696.

Holden, C. J. 2002. Bantu language trees reflect the spread of farming across sub-Saharan Africa: A maximum-parsimony analysis. Proceedings of the Royal Society of London: Series B, 269, 793-799.

Korotayev, Andrey. 2000. Polygyny and Democracy: A Cross-Cultural Comparison.

Korotayev, Andrey. 2004. World Religions and Social Evolution of the Old World Oikumene Civilizations: A Cross-cultural Perspective, Lewiston, NY: Edwin Mellen Press.

Korotayev, Andrey. 1999. Sexual Equality and Romantic Love: A Reanalysis of Rosenblatt's Study on the Function of Romantic Love // Cross-Cultural Research 33 (1999): 265–277 (co-authored).

Korotayev, Andrey. 2000, Democracy, Christianization and Unilineal Descent Groups: A Cross-Cultural Comparison // Hieararchy and Power in the History of Civilizations / Eds.: D. M. Bondarenko, I. V. Sledzevski, A. V. Korotaev et al. Moscow: CCR RAN – RSUH, 2000: 65.

Korotayev, Andrey. 2000. Polygyny vs. Monogamy: Democracy vs. Non-Democracy? // Hieararchy and Power in the History of Civilizations / Eds.: D. M. Bondarenko, I. V. Sledzevski, A. V. Korotaev et al. Moscow: CCR RAN – RSUH, 2000: 65–66 (co-authored).

Korotayev, Andrey. 2000. Family size and community organization: a cross-cultural comparison // Cross-Cultural Research. The Journal of Comparative Social Science 34/2:152–189 (co-authored).

Korotayev, Andrey. 2000. Polygyny and Democracy: a Cross-Cultural Comparison // Cross-Cultural Research. The Journal of Comparative Social Science. 34/2: 190–208 (co-authored).

Korotayev, Andrey. 2000. Regions Based on Social Structure: A Reconsideration // Current Anthropology 41/5: 668–690 (co-authored).

Korotayev, Andrey. 2000. Parallel Cousin (FBD) Marriage, Islamization, and Arabization // Ethnology 39/4: 395–407.

Korotayev, Andrey. 2001. An Apologia of George Peter Murdock. Division of Labor by Gender and Postmarital Residence in Cross-Cultural Perspective: A Reconsideration. World Cultures 12/1: 179–203.

2003. “Galton’s Asset” and “Flower’s Problem”: Cultural Networks and Cultural Units in Cross-Cultural Research (or, the Male Genital Mutilations and Polygyny in Cross-Cultural Perspective) // American Anthropologist. 105 (2003): 353–358 (co-authored).

Andrey Korotayev, Alexander Kazankov, Leonid Dreier, Natalia Dmitrieva, 2003. Evolutionary Implications of Cross-Cultural Correlations Cross-Cultural Research 37(3):247-264.

Korotayev, Andrey, and Victor De Munck. 2003. [ "Galton's Asset" and "Flower's Problem Cultural Networks and Cultural Units in Cross-Cultural Research (Or, Male Genital Mutilations and Polygyny in Cross-Cultural Perspective)] American Anthropologist 105(2):353-358.

Lipo, C.P., et al (Eds.), 2005. Mapping human history: Phylogenetic approaches in anthropology and prehistory. New York: Transaction.

Mace,R.,& Holden,C.J.2005. A phylogenetic approach to cultural evolution. Trends in Ecology and Evolution, 20, 116-121.

Mace, R., & Pagel, M. 1994. The comparative method in anthropology. Current Anthropology, 35, 549-564.

Mace, R., & Pagel, M. 1997. Tips, branches, and nodes: Seeking adaptation through comparative studies. In Laura Betzig (Ed.), Human nature (pp. 297-310). New York: Oxford University Press.

Martins, E. P., & Garland, T. 1991. Phylogenetic analyses of the correlated evolution of continuous characters: A simulation study. Evolution, 45, 534-557.

Martins, E. P., & Hansen, T. F. 1997. Phylogenies and the comparative method: A general approach to incorporating phylogenetic information into the analysis of interspecific data. American Naturalist, 149, 646- 667.

Mesoudi,A.,Whiten,A.,& Laland,K.N.2004. Perspective: Is human cultural evolution Darwinian? Evidence reviewed from the perspective of The Origin of Species. Evolution, 58, 1-11.

Moore, J. H. 1994. Putting anthropology back together again: The ethnogenetic critique of cladistic theory. American Anthropologist, 96, 925-948.

Moylan, J. W., Borgerhoff Mulder, M., Graham, C. M., Nunn, C. L., & Håkansson, T. 2005. Cultural traits and linguistic trees: Phylogenetic signal in East Africa.In C.P. Lipo et al.(Eds.), Mapping human history: Phylogenetic approaches in anthropology and prehistory. New York: Transaction.

Murdock, George P. and Douglas R. White, 2006 Standard Cross-Cultural Sample: on-line edition. Social Dynamics and Complexity. Working Papers Series. Reprinted in modified form with permission of the journal editorial office as published in Ethnology 8:329-369.

Nee, S., May, R. M., & Harvey, P. H. 1994. The reconstructed evolutionary process. Philosophical Transactions of the Royal Society of London: Series B, 344, 305-311.

CL Nunn (Primatology)

Nunn, C. L. 1995. A simulation test of Smith's "degrees of freedom" correction for comparative studies. American Journal of Physical Anthropology, 98, 355-367.

Nunn, C. L., Mulder, M. B., and Langley, S. 2006) Comparative Methods for Studying Cultural Trait Evolution: A Simulation Study. Cross-Cultural Research, 40(2):177-209.

Pagel, M., & Mace., R. 2004. The cultural wealth of nations. Nature, 428, 275-278.

Purvis, A., Gittleman, J. L., & Luh, H. 1994. Truth or consequences: Effects of phylogenetic accuracy on two comparative methods. Journal of Theoretical Biology, 167, 293-300.

Shennan, S. 2000. Population, culture history, and dynamics of culture change. Current Anthropology, 41, 811-835.

Smouse, P. E., Long, J. C., & Sokal, R. R. 1986. Multiple regression and correlation extensions of the Mantel test of matrix correspondence. Systematic Zoology, 35, 627-632.

Sutherland, W. J. 2003. Parallel extinction risk and global distribution of languages and species. Nature, 423, 276-279.

Terrell, J. E., Hunt, T. L., & Gosden, C. 1997. The dimensions of social life in the Pacific: Human diversity and the myth of the primitive isolate. Current Anthropology, 38, 155-195.

White, Douglas R. 1993. Spatial Levels in Cultural Organization: An Empirical Study. Handbuch der Ethnologie, pp. 459-88. Edited by Thomas Schweizer, Margarete Schweizer, and Waltraud Kokot. Berlin: Reimer Verlag.

White, Douglas R. 2008. Standard Cross-Cultural Sample International Encyclopedia of the Social Sciences, 2nd Edition.

White, Douglas R., Michael L. Burton, Malcolm M. Dow. 1981. Sexual Division of Labor in African Agriculture: A Network Autocorrelation Analysis. American Anthropologist, New Series, 83(4):824-849.

## Most recent work 2006-forward

Network Autocorrelation: Effects and Disturbances Models
Estimating the Multiple Network Effects Model: 2SLS
This study replicates White, Douglas R. and Michael L. Burton. 1988. Causes of Polygyny: Ecology, Economy, Kinship, and Warfare. American Anthropologist, New Series, Vol. 90, No. 4. (Dec., 1988), pp. 871-887. http://eclectic.ss.uci.edu/~drwhite/pw/AA88num4.pdf
"One reason for the general tendency to ignore interdependence in crosscultural survey data appears to stem from the persistent confusion over the role

of random sampling for dealing with nonindependence in comparative data sets and the assumptions of statistical models. For example, the usual regression model assumes that the errors are independently and identically distributed. Contrary to incorrect claims made about random sampling being sufficient to deal with nonindependence (Ember & Ember, 2000), all random sampling does is to give the researcher an expectation that the assumption of independence of cases required by the statistical model they use will have at least a chance of being right. Random sampling by itself is not at all sufficient to guarantee that there will be no dependencies among the units in any sample, especially when the sampling is done using large cross-cultural data sets as the sampling frame. Dow and Eff (2007) report extensive dependencies with respect to five types of processes in the SCCS data, so all random sampling from the SCCS can do is to guarantee that a reasonable representation of these interdependencies will also appear in the random sample, and the independence assumption underlying most classical statistical methods, as in regression, will continue to be violated. The possibility of nonindependence must either be tested and rejected before making statistical inferences, or control variables that capture the expected form of nonindependence, that is, trait transmission variables, must be included in the model. It is the latter omitted variable approach that we emphasize in the present study. In the current study, trait transmission (ie, nonindependence of cases with respect to a particular dependent variable) is clearly shown here to be fatal to statistical inference if the variable is theoretically relevant but is omitted. The sampling strategy used to obtain the data is secondary to meeting the assumptions of the statistical model being used to analyze the data. In comparative research, failure to test for, or failure to otherwise control for, nonindependence is a serious, potentially devastating, threat to inference." (p145)

See: http://ccr.sagepub.com/cgi/reprint/41/4/428
• Eff, E. Anthon. 2008. "Weight Matrices for Cultural Proximity: Deriving Weights from a Language Phylogeny." Structure and Dynamics: eJournal of Anthropological and Related Sciences 3(2), Article 9. http://repositories.cdlib.org/imbs/socdyn/sdeas/vol3/iss2/art9
• Eff, E. Anthon, and Malcolm M. Dow. 2008. Do Markets Promote Prosocial Behavior? Evidence from the Standard Cross-Cultural Sample. http://econpapers.repec.org/paper/mtswpaper/200803.htm.
• Eff, E. Anthon, and Malcolm M. Dow. 2009. Market integration and pro-social behavior. To appear in Robert C. Marshall, Editor. Cooperation in Economic and Social Life. Society for Economic Anthropology Monographs Vol 26. AltaMira Press: Walnut Creek, CA.

## Political Science and International development

Beck, Nathaniel; Gleditsch, Kristian Skrede; Beardsley, Kyle 2006), ``Space Is More than Geography: Using Spatial Econometrics in the Study of Political Economy, International Studies Quarterly, 50(1), (Mar., 2006), p. 27-44.

Berry, Brian J. L.; Griffith, Daniel A.; Tiefelsdorf, Michael R. 2008. From Spatial Analysis to Geospatial Science, Geographical Analysis, 40(3), (Jul., 2008), p. 229-238.

Detlef, Jahn. 2006. Globalization as ‘Galton's Problem’: The Missing Link in the Analysis of Diffusion Patterns in Welfare State Development International Organization 60(2):401-431. pdf

## Spatial autocorrelation

Dow, M.M., & Eff, E.A. 2008. Global, regional, and local network autocorrelation in the Standard Cross-Cultural Sample. Cross-Cultural Research 42: 148-171. pp 158-159 show variables in the SCCS with high spatial autocorrelation.

White, Douglas R. 1993. [http://eclectic.ss.uci.edu/~drwhite/pub/DRW1993Spatial.pdf Spatial Levels in Cultural Organization: An Empirical Study. Handbuch der Ethnologie, pp. 459-88. Edited by Thomas Schweizer, Margarete Schweizer, and Waltraud Kokot. Berlin: Reimer Verlag. pp 487-488 show variables in the SCCS with high spatial autocorrelation.

Getis, Arthur 2008. A History of the Concept of Spatial Autocorrelation: A Geographer's Perspective, Geographical Analysis, 40(3), (Jul., 2008), p. 297-309.

Haining, Robert. 1990. Spatial data analysis in the social and environmental sciences. Cambridge University Press.

Mizruchi, Mark S., and Eric J. Newman. 2008. The effect of density of the level of bias in the network autocorrelation model, Social Networks, 30, p. 190-200.

## Use of space

Marcus J. Hamilton, Bruce T. Milne, Robert S. Walker, and James H. Brown Nonlinear scaling of space use in human hunter–gatherers

## Use of time

See the work of Trevor Denton on temporal trends in cross-cultural data, which suggests that time should also be considered as a potential autocorrelation effect.

## Autocorrelation and the Nervous System=

Reichardt, W. 1961. Autocorrelation, a principle for the evaluation of sensory information by the central nervous system. FULL TITLE UNKNOWN.

B. Hassenstein and W. Reichardt," …, 1956