Multilevel networks and world ethnography

Doug White and UC+ team

SFI noon seminar 12:15Wed, Sept 1, 2010

UC+=UCI_imbs+UCSD_econ+sfi, project team

Scott D. White, UCI , One Spot

Halbert White UCSD Karim Chalak BU, Econ

B. Tolga Oztan, IMBS Laura Fortunato, SFIand aunt

Assist fromJudea Pearl Ren Feng. Xi’anUCLA Xiaotung Univ.

Tony Eff, MS, Econ

http://www.nytimes.com/library/national/science/050200sci-genetics-evolution.html

Language families

Folded image: Core, Semi-periphery1, SP2, Periphery1-2

Core

Semi-Peri1

Semi-Peri2

Periphery1

Periphery2

A structurally endogamous kinship network core of a Turkish nomad clan

(White and Johansen 2005: 379; 76-79).

Standard Cross-Cultural Sample (wikipedia page maps by Tony Eff

Afro-Eurasia drawn to a slightly smaller scale

Causal graph, Pearl’s regression method “Say for three variables you are trying to estimate the direct effect c of X on Z given an indirect effect of Y. The causal diagram model gives you a license to do it by the regression method, where, for example ,  

E(y|x, z) – E(y|x´, z) a

c = ————————————— (1) 

x – x´

Controlling for the change from x to x´, E(y|x, z) and E(y|x´, z) are the changes in variable Z due to unit changes in X controlling for Y.” (email from Pearl see Pearl 2000:151; Chalak and White 2010). Because the x,z in (y|x,z) is a joint distribution, eqn (1) means that x→x´ changes y which through the x-y-x path, considered as a joint distribution, changes z. From this it follows, given the single door criterion (Pearl 2000:150). that c + a•b = rxy.z, the coef for total effect of X on Z.

X Y c b Z

Solving Galton’s problem, Two stage OLS Two stage regression with peer effects (different notation)

X1 Y

X2

Stage 1Calculate theInstruments

Stage 2 use Instruments in OLS

Nodes are variables in regression analyses of variables from the Standard Cross-Cultural Sample of 186 societies (SCCS).

Lines represent independent variables. They point down to 13 dependent variables in successive colored layers.

Black lines are positive effects, red lines negative effects from regression results.

Colors of nodes for variables show depth in a causal hierarchy with net effects estimated as causal graphs (Pearl 2000).

At level 4 the Evil eye dependent variable has a triangular relationship with money and milked domestic animals.

The regressions control for peer effects of spatial transmission (distance) and cultural transmission (language phylogeny),

incorporated as Instrumental Variables in a second-stage regression, with the IVs estimated in a first-stage regression.

Node sizes reflect the significance of spatial transmission peer effects. Language effects are sometimes negative.

13 linked regressions out of 2000+ SCCS variables http://eclectic.ss.uci.edu/~drwhite/courses/SCCCodes.htm

v1189 Belief in evil eye

v238 Moral gods==4 238. HIGH GODS 18 . = Missing data 68 1 = Absent or not reported 47 2 = Present but not active in human affairs 13 3 = Present and active in human affairs but not supportive

of human morality 40 4 = Present, active, and specifically supportive of human morality

v1189 Belief in evil eye (dichotomy)Large nodes red

Small nodes orange

v155 True money==5155. SCALE 7- MONEY (here, an independent variable) 77 1 = None 14 2 = Domestically usable articles 43 3 = Alien currency 27 4 = Elementary forms 25 5 = True money

v1189 Belief in evil eye

v272 Caste stratification

272. CASTE STRATIFICATION (ENDOGAMY) (two cases have secondary castes) 5 . = Missing data (154) 0 = (Omitted from map) Absent or insignificant 17 1 = Despised occupational group(s) 3 2 = Ethnic stratification 7 3 = Complex

v1189 Belief in evil eye

v245 Milked animals

v1189 Belief in evil eyeModel 1

Description Re: Evil eye Eff-Dowcoef

pvalue VIF Var. Probitcoef

pvalue

(Intercept) -0.247 0.775 NA 1.1715 0.12

Wy fydd Spatial transmission 0.763 .0000022 3.452 NA *** 0.6944 0.00004

Wy fyll Cultural transmission -0.228 0.362 2.329 NA -0.2267 0.38

Milk Milking of animals 0.664 0.080 2.328 245 * 0.3235 0.48

CaststratLDg Degree of caste stratification 1.372 0.017 1.225 272 * * 0.5078 0.04

Money >1>3>4 Degree of monetization 0.597 0.017 1.152 155~v17 ** 0.1011 0.05

Moral gods Degree of morality of gods 0.294 0.020 1.664 238 ** 0.1161 0.04

Diagnostics Fstat df pvalue Fstat

RESET test. H0: model has right functional form 3.400 1801.470 0.065 0.717 0.397

Wald test. H0: appropriate variables dropped 0.476 308.949 0.491 0.431 0.512

Breusch-Pagan test. H0: residuals homoskedastic 1.193 3282.405 0.275 8.753 0.003

Shapiro-Wilk test. H0: residuals normal 16.146 9268.270 0.000 3.618 0.057

LM test. H0: Cultural lag (language) not needed 0.713 1877017. 0.398 1.086 0.297

LM test. H0: Spatial lag (distance) not needed 1.768 20982.58 0.184 2.214 0.137

Notes: R2 = 0.513; N=186; number of imputations=10; standard errors and R2 adjusted for two-stage least squares. “***” p-value ≤ 0.01, “**” p-value ≤0.05, “*” p-value ≤ 0.10. Language non-significant (p > .33).

v155 MoneyModel 2

Description Re: Money Eff-Dowcoef

pvalue VIF Var. Probitcoef

Pvalue

(Intercept) -0.775 0.002 NA 0.2316

Wy fydd Spatial transmission 0.954 .0000279 3.644 NA *** 0.9057 3.758

Wy fyll Cultural (language) transmission -0.928 0.003 4.190 NA *** -0.9220 4.309

Foodtrade Imported food 0.430 0.134 1.219 819 0.1005 1.228

Fratgrpstr Fraternal interest group strength+ 0.120 0.092 1.840 570 * 0.1663 1.757

Milk Milking of animals -0.393 0.012 1.560 245 * -0.2394 1.478

Caststrat LGd Degree of caste stratification+,++ 0.430 0.134 1.219 272

Moral gods Degree of morality of gods+.++ 0.102 0.142 1.502 238 0.1021 0.142

Popdens Population density 0.206 .0000053 1.552 156 *** 0.3147 1.627

Superjh PCsize Supra cmnty jurisdictional hier. 0.304 .0000002 1.633 237 ***

Diagnostics Fstat df pvalue Fstat

RESET test. H0: model has right functional form 1.943 5301.617 0.163 2.187 0.139

Wald test. H0: appropriate variables dropped 15.266 17.503 0.001 13.332 0.000

Breusch-Pagan test. H0: residuals homoskedastic 13.833 950.560 0.000 4.995 0.027

Shapiro-Wilk test. H0: residuals normal 0.267 282.276 0.606 0.363 0.548

LM test. H0: Cltural lag (language) not needed 1.287 657642. 0.257 1.773 0.183

LM test. H0: Spatial lag (distance) not needed 1.352 991.504 0.245 1.902 0.168

Notes: R2 = 0.490; N=186; number of imputations=10; standard errors and R2 adjusted for two-stage least squares. “***” p-value ≤ 0.01, “**” p-value ≤0.05, “*” p-value ≤ 0.10. Language non-significant (p > .33).Probit note: R2 = 0.481; IV(distance)=0.9911; (language)=0.9957 see last two columns for coef and pvalue.

v238 Moral godsModel 3 Description Re: Moral gods Eff-Dow

coefpvalue VIF Var. Probit

Coefpvalue

(Intercept) 0.725 0.477 NA 1.076 0.166 Fydd Spatial transmission 0.917 .00000003 2.526 NA *** 0.881 .0000007 Fyll Cultural-language-transmission -0.700 0.140 2.579 NA -.471 0.311 PCAP PC Agricultural potential -0.038 0.075 1.148 921 * -.097 0.059 PCsize PC Juris. Hierarchy 0.554 0.035 23.844 63^2 ** 0.212 0.002 PCsize2 PC Juris. Hierarchy squared -0.076 0.107 23.404 245 0.344 0.022 Milk Milking of animals 0.403 0.065 2.287 245^2 * 0.135 0.031 Foodstress Chronic food stress 0.207 0.152 1.103 1685 -.190 0.003 Eextwar Frequency of external war -0.032 0.006 1.124 1650 ** -.187 0.024 bridewealth Bridewealth payments 0.194 0.221 1.307 208=1 0.155 0.146 caststratLgd Log of Caste stratification 0.704 0.030 1.276 272 ** 0.183 0.035 Diagnostics Fstat Df Pvalue Fstat RESET test. H0: model has right functional form 0.236 182.981 0.628 0.287 0.593

Wald test. H0: appropriate variables dropped 1.602 24.460 0.217 1.958 0.165

Breusch-Pagan test. H0: residuals homoskedastic 3.115 121.839 0.080 2.133 0.144

Shapiro-Wilk test. H0: residuals normal 7.527 1106.014 0.006 1.201 0.273

LM test. H0: Cultural lag (language) not needed 1.486 29167.282 0.223 1.228 0.268

LM test. H0: Spatial lag (distance) not needed 0.921 46574.050 0.337 0.809 0.368

Notes: R2 = 0.504; N=186; number of imputations=10; standard errors and R2 adjusted for two-stage least squares. “***” p-value ≤ 0.01, “**” p-value ≤0.05, “*” p-value ≤ 0.10. Language non-significant (p > .33).Probit note: R2 = 0.481; IV(distance)=0.9942; (language)=0.9861 see last two columns for coef and pvalue.

Table 4: Transmission effects (Galton’s problem): Spatial and cultural

The negative peer effects for language indicate that, for each of these dependent variables, there is a tendency, strong for Money and weak for the other two variables, NOT to be the result of cultural tradition but of innovation that differentiates the societies with Money, Moral gods and Evil eye from the norms in their respective language families. This tendency is nearly significant (pvalue < 0.15) for societies with Moral gods.

Peer Effect Variable coef pvalue Spatial Money .960 .0000009 Transmission Moral gods .824 .0000014 (Distance) Evil eye .767 .000002 Cultural Money -.988 .002 Transmission Moral gods -.672 p > 0.14 (Language) Evil eye -.228 p > 0.36

Milking animals A -0.393 B Money (v155)

(v245) 0.484 0.597 0.102 p<0.14 Moral gods D 0.664 (v238) 0.294 0.792 0.430 1.372 C Evil eye (v1188) Caststrat LGd E

Figure 3: Causal graph with multiple triangular regression coefficients, excluding peer effects (numbers are the regression coefficients)

Table 6: Causal graph total effects and bivariate table regression slopes

Independent Variable

Dependent Variable

Net effects=Direct and Indirect Causal Graph Effects

=Total effects

Fig. Slope

Money Evil eye 0.597 0.597 .741Moral gods Evil eye 0.294+(0.102*.597) 0.355 .950Milking Evil eye 0.664+(-.393*.597)+(.484*.104*.597) 0.744 .810

Moral gods Money 0.102 0.102 .482Milking Money -.393+(0.484*.102) -0.344 .244

Other kinds of cross-cultural data structures and analyses:

Statistical Entailment Analyses: Society sets for variables tend to form chains of sets ABCD

Galois duality lattice (Concept lattices):Society sets for variables tend to form chains of sets ABCD

and intersections, and opposite ordering of Sets of variables that tend to form chains of sets

VS1VS2VS3VS4

Intrasocietal network structure overlays on genealogyFor each society these will define new variables such as1) sidedness, reciprocal marriage to opposites.2) structurally endogamous groups3) marriage-type census as against random simulation4) distribution of structural features over generations

Multilevel analysis e.g. regional or world system effects on

local societies.

Fig. 3: An exact world entailment digraph for the sexual division of laborLate Task A Early Task B

Female FemaleMale Male

Fig. 3: An exact world ethnographic lattice of kin avoidances has a four-

dimensional partial ordering of distributions: 1) parents of Hu, Wi (opp/same sex, within circles), 2)

siblings and siblings-in-law of Hu and Wife (opp/same sex, in

parallelograms), 3) opposite sex siblings & parents siblings & parallel cousins (White 1995). Lower types of

avoidances entail upper ones features in perfect inclusion relations, found by statistical

entailment analysis (White 1999b). Of the 250 societies, names attached

to each node show each subset of avoidance relations.

Table 1 Pajek Repast Simulation Cohesion Peer Effects ArcGIS.com New Codes New Ethnogr. Cases

80KinSources1 X X X X X 3

400 foragers2 X X (Binford & Boehm)

85 World-system 3X X 2 (country data)

1294 Atlas4 X X 0

186 SCCS5 X X 0

28 1945-19656 X X X 28 (SCCS)

30 Post 19657 X X X 308 (eSCCS)

1 http://kinsource.net/kinsrc/bin/view/KinSources archives kinship network data contributed by anthropologists. Only three KS ethnographies remain for conversion from paper-based genealogies to e-networks for analysis with Pajek, but others will be added.2,5 Binford’s (2001) Constructing Frames of Reference forager database has been spreadsheeted by Boehm and Hill. Non-foragers from the SCCS will be analyzed separately. Extensive testing of “peer effects” methods have established their validity.3 Smith and White (1992) have postwar WS commodity flow time series in 5yr intervals; capital and migration flow will be added. 4 Murdock’s Ethnographic Atlas (EA) in Spss format has been supplemented by newly authored installments 30-31.5 Murdock and White’s (1969) Standard Cross-Cultural Sample dataset on 186 societies in Spss and R formats has coded data contributions from 80+ different authors on 2008+ variables. Citations to SCCS are now 95+/year and growing.

Table 1 Pajek Repast Simulation Cohesion Peer Effects ArcGIS.com New Codes New Ethnogr. Cases

80 KinSources1 X X X X X 3

400 foragers2 X X (Binford & Boehm)

85 Wrld-system3 X X 2 (country data)

1294 Atlas4 X X 0

186 SCCS5 X X 0

28 1945-19656 X X X 28 (SCCS)

30 Post 19657 X X X 308 (eSCCS)

5 Murdock and White’s (1969) Standard Cross-Cultural Sample dataset on 186 societies in Spss and R formats has coded data contributions from 80+ different authors on 2008+ variables. Citations to SCCS are now 95+/year and growing. 6 109 missing codes for 28 SCCS variables 1006-1115 will be coded for 28 SCCS societies on the world-system impacts variables partially coded in White and Burton’s (1985-1988) NSF 8507685 funded research on “World-Systems and Ethnological Theory.”7 To bring the SCCS societies up to date for post-1965 societies, 30 well described post-1965 ethnographic cases will be added to an (expanded) eSCCS and coded for EA variables and the CDC Cultural Diversity Codebook of 180 SCCS variables.8 Given that the SCC Sample was published in 1969, the eSCCS additions to the sample will bring it up to date temporally. This will allow study of world-system impacts on 37 well-described ethnographic cases in the contemporary post-war period.

A structurally endogamous kinship network core of a Turkish nomad clan (White and Johansen 2005: 379; 76-79).

Fig. 1.A. Gmap of Cultural Survival (2010) 100+ recent trouble spot study cases: Gmaps extend to networks at the global level, clicking into cases at the local level. Live: http://bit.ly/c1funC

Fig. 1.B. This google map tracks cases of swine flu in 2009, types of cases are color coded, fatal cases have no dot, clicking a region gives a more detailed map of cases within the region.

Similarly, Wolf (1982) drills down at several hundred ethnographically data points to analyze how commodity exchange affected indigenous societies in the 1500-1980 period of overseas conquest and modern world-systems. Interactive maps provide for drilling down from a network at one level (network spread of disease not shown here) by clicking a node to see a more detailed map or a network within that node. The upper level nodes can be societies with organizations networks reached by a click of a given node.