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Multilevel networks and world ethnography

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### Multilevel networks and world ethnography

### Solving Galton’s problem with 2SLS: 2-Stage OLS

### Causal graph, Pearl’s regression method

### Causal analysis: Transformation predictions from Indian Jajmani to market system

Doug White and UC team

UCI human complexity seminar 1:30

Fri, Sept 24, 2010

UCI grads and undergrads can sign up for 1.33 credits:

SOC SCI 240A SEM A (72100)

UCI_imbs+UCSD_econ+UCLA_cs, project team

Scott D. White, UCI , One Spot

B. Tolga Oztan, MBS Ren Feng. Xi’an Xiaotung Univ.

Doug

White, MBS

Assist from

Judea Pearl Karim Chalak BU, Econ Halbert White UCSD

UCLA

Tony Eff, MST,U Econ

- Early best-described ethnographies give our best chance of understanding the evolution of societies and cultures.
- We now have large samples, N=186, 390, 1400, ….
- And many variables, V=2000+(SCCS), 500+ (foragers), 150 (EthnoAtlas), ….
- Problem is that correlations of variables have no meaning.
- Historical interactions have huge effects – splitting, branching , merging, borrowing, migrating, colonizing, conquering.
- We still have, among these ethnographic cases, living societies like the Hadza with the genetic stock of humanity’s common ancestors of 150,000 years ago, or the San with the next-split of 120,000 years ago, etc.
- It’s not a matter of splitting the historical network interaction and regional similarities from functional and causal relations. (Harold Driver’s struggle with Kroeber)
- Its that the statistics for doing so have been so weak as to not be capable of making these inferences, and the concept of inference has been too weak.

Inference, Statistics, Causality

- Statistical inference has to do with replicability, or change, given changing conditions. In survey data, it’s hard to get replication because of changing
- Composition of the sample: location, composition
- Peer effects and interactions within the sample
- Time period

- So results will vary with different (e.g., cross-cultural) samples .
- Looking for invariance is like Norm Schofield ‘s question “What are the causal variables for how people vote” other than the names and parties of the candidates? I.e., no proper nouns in the variables for causality.
- When there are peer effects operating in the sample, significance tests are exaggerated (type 1 error). Cross-cultural studies are full of type 1 error.
- Random sampling (Ember&Bernard solution) does not solve this problem although means and correlations may be estimated correctly.
- But correlations will vary widely with changes in the sample or with time.
- replication is thwarted finding differences in replication when none exist (type 2 error)
- A stronger concept of inference would deal with causation not correlation.
- This began with structural equation models (Sewall Wright 1921, 1935 SEM) and continues with Judea Pearl et al’s extensions of graphical methods

Where we are now: *Rccs*

- new program package *Rccs* takes into account network effect matrices (distance, language, etc.)
- Computes regression coefficients
- R code for 2SLS implemented for classroom use
- (see pdfs attached to intersci wiki talk)
- Compute causal graph models (in development)
- E.g., computes total effects (adding indirect paths)
- Chalak and H. White extension: reciprocal effects x-->y plus y-->x-->y as including the indirect path

Stage 1 OLS

Calculate the

“Instruments”

2nd Stage OLS, Include the “Instruments”

peer effects X1

II WI

independent variables X2 Y dependent variable

X3

X Y

c b

Z

“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, (for reference on the pdf)

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, 368; 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.

Comparing causality in ethnographic data

- R package *Rsccs* takes into account any number of peer effects as Instruments in the previous equations that allow further causal analysis
- Regressions change with time periods
- Correlate total effects to X →Y (time lagged correlations)
- Regressions that yield results for causality can be identified in Pearl’s (2000) single door, back door, and front door causal graph criteria. Some graphical structures may require that some potential confounder variables be blocked, and that direct, indirect and total effects be computed from regression coefficients without those confounders.

Spatial distances as effectsInstrument for measuring peer effects

Standard Cross-Cultural Sample (SCCS wikipedia maps by Tony Eff)

Afro-Eurasia drawn to a slightly smaller scale

Multilevel effect

spatial

World system peer effects -- of exchange – as effectsInstruments

Folded image: Core, Semi-periphery1, SP2, P1-2

Core

Semi-Peri1

Semi-Peri2

Periphery1

Periphery2

Multilevel effects

world system

A structurally endogamous kinship network core of a Turkish nomad clan

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

Multilevel effects

internal networks

Up and down effects

13 linked regressions out of 2000+ SCCS variables nomad clan

http://eclectic.ss.uci.edu/~drwhite/courses/SCCCodes.htm

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.

Paired visual comparison of spatial distributions nomad clan

v1189 Belief in evil eye

v238 Moral gods==4 nomad clan

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

NOTE the circum-Mediterranean overlap with Evil eye (previous slide)

Paired visual comparison of spatial distributions nomad clan

v1189 Belief in evil eye (dichotomy)

Large nodes red

Small nodes orange

v155 True money==5 nomad clan

155. 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

NOTE the circum-Mediterranean overlap with Evil eye (previous slide)

Paired visual comparison of spatial distributions nomad clan

v1189 Belief in evil eye

v272 Caste stratification nomad clan

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

NOTE the circum-Mediterranean overlap with Evil eye (previous slide)

Paired visual comparison of spatial distributions nomad clan

v1189 Belief in evil eye

v245 Milked animals nomad clan

NOTE the circum-Mediterranean overlap with Evil eye (previous slide)

v1189 Belief in evil eye nomad clan

R2=0.513; N=186;

10 imputations; standard errors 00R2 adjusted for two-stage least squares. Language non-significant (p > .33). No effect of Islam or Christianity.

v1189 Belief in evil eye nomad clan

Some nonlinear relationships

No additional variables

Error terms homoskedastic

- " " not normally distributed
- no " " cultural lag
- no " " spatial lag

R nomad clan2=0.490; N=186;

- 10 imputations; standard errors 00R2 adjusted for two-stage least squares. Distance(p > .00002) & language significant (p > .003).

v155 Money

No nonlinear relationships nomad clan

Some additional variables

Error terms homoskedastic

- " " normally distributed
- no " " cultural lag
- no " " spatial lag

v155 Money

v238 Moral gods nomad clan

R2=0.504; N=186;

- 10 imputations; standard errors 00R2 adjusted for two-stage least squares. Distance(p < .00001) & language insignificant (p > .15).

v238 Moral gods nomad clan

No nonlinear relationships

No additional variables

Error terms ~homoskedastic

- " " not normally distributed
- no " " cultural lag
- no " " spatial lag

Transmission effects (Galton’s problem): Spatial nomad clan and cultural

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 (value < 0.15) for societies with Moral gods.

- Excluding peer effects: Causal nomad clangraph with multiple triangular 000regression coefficients - numbers are the regression coefficients

Causal graph total effects and regression slopes

THESE CAUSALITIES A-E-D-B-C ARE TRANSITIVE, all significant or nearly so, and completely ordered but the arrow from A to B is NEGATIVE

A Milked domestic animals

E Caste stratification

D Moral gods (to money only p <.15)

B Money

C Evil eye

A 2-slide example for two time periods is next, if time allows

(package*Rccs* applies to time series, includes multiplicative interactions as well)

R2 = .672 allows

Data source:

Maximizing in Jajmaniland: A Model of Caste Relations. 1968. MARTIN ORANS. American Anthropologist 70(5): 875–897.

R2 = .623

Correct time 2 predictions match causal inferences

P=.067

P=.055

P=.05

p=.067

R2 = .747

Peer effect regression time 1

(Temporal predictions about changes are even stronger)

Causal graphs may incorporate multiplicative or interaction effects, which are used by Martin Orans in his 1968 article. These are diagrammed

Jajmani system

Power concentration

Power concentration

Isolation Power concentration

Ritual-secular

Isolation correlation

Jajmani

Isolation system

None of these models were significant, however, compared to the simple linear additive effects that we tested and found significant (Ren Feng, T. Oztan, D. White)

Further slides, if time allows, effects, which are used by Martin Orans in his 1968 article. These are diagrammedshow different kinds of analysis than that of *Rccs*

Other kinds of cross-cultural effects, which are used by Martin Orans in his 1968 article. These are diagrammed 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 genealogy
- For each society these will define new variables such as
- 1) sidedness, reciprocal marriage to opposites.
- 2) structurally endogamous groups
- 3) marriage-type census as against random simulation
- 4) distribution of structural features over generations
- Multilevel analysis e.g. regional or world system effects on local societies.

Fig. 3 effects, which are used by Martin Orans in his 1968 article. These are diagrammed: An exact world entailment digraph for the sexual division of labor

Late Task A Early Task B

Female Female

Male Male

Fig. 3 effects, which are used by Martin Orans in his 1968 article. These are diagrammed: 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.

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.

5 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.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).

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.

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.

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