MORAL GODS: TEST OF A THEORY OF
ETHICAL REVIVALS RESULTING FROM
MORAL CRISIS IN TIMES OF UNEQUAL
SCARCITY AND SOCIAL INEQUALITY
This study compares two DEf models for Moral Gods, one by Brown and
Eff and the other by White, Oztan and Snarey. DEf regression, with
imputation of missing variables and correction for autocorrelation, uses
first and second-stage ols regressions, 1SLS (first stage OLS) and 2SLS.
Using the results of 2SLS, we examine the combined set of variables from
both models and then use the imputations of these variables and of Wy,
the variable that aims at control of autocorrelation. Our 3-stage
regression uses imputed independent variables and Wy in an integrated
model in which we can find the most predictive variables of each model
using the Bayesian Network library(Bnlearn). We aim to explain these
concise R codes and contribute our use of them to our XSEDE CoSSci/DEf
Science Gateway.
Douglas R. White, Bahattin Tolga Oztan, John Snarey
Outline of Slides
ABQhiGodPresentation2014.pptx
2
*p3-4 Theory: Crises of inequality in polities with exchange systems
Many such examples studied by Peter Turchin (2005 etc)
*5 Example: Han dynasty collapse & Moral crisis
*6 Defining Key Theoretical Variables (FxCmntyWages, AnimXbwealth, SuperjhWriting)
*7 Wy term regression: Model equations used in comparison Brown&Eff 2010 White et al
*8 Wy 2SLS term regression results
*9 CoSSci/DEf 2SLS modeling results for HiGods: Key theoretical & other variables
*10 3stage regression results with imputed variables: White et al. (2011) Brown & Eff (2010)
*11 3-stage model uses imputed variables & est(Wy) & allows Bayesian Network Learning
*12 Bayesian Network Graph and Cross-tabs
*13 Trestles bootstraps, alternative models, Paul Rodriguez
*14 Paul Rodriguez use of library(bootstrap) to show alternate Bayesian Networks
*15 Questions about Bayesian Networks (belongs after p.13 in longer talk)
*16 Summary: Null Hypotheses and Comparison of Results
model: Ev2007Higod4.xls
Trailing Questions
Do our results differ drastically from the usual OLS regression? Yes
Recap of 3-stage Regression with imputed variables that includes the estimated Wy and results
What is Bayesian Network Learning, a Bayesian Network, and library(bnlearn)?
False hopes; Bivariate distributions; Recap of Def 2SLS and 3-stage regression
Turchin 2005:
Dynamical
Feedbacks in
Structural
Demography
Han China shows one of many examples of exchange
system political dynamics that create MORAL CRISIS
periods. Two full cycles over 500 years are shown in
the Phase diagram to the right and in cycles below
(phase diagram is actually from another example)
Rise
+Pop-conf
Peace
-Pop-conf
Conflict
+Pop+cnf
Crash
-P+conf
Key:
3
=Innovation phases Inequality & crashes
Chinese phase diagram
p.3
p.4
4
Example: Han dynasty collapse & Moral
crisis followed by adoption of Buddhism p.5
5
Confucianism originated as an "ethical-sociopolitical teaching"
during the Spring and Autumn Period, but later developed
metaphysical and cosmological elements in the Han Dynasty.
Following the official abandonment of Legalism in China after the
Qin Dynasty, Confucianism became the official state ideology of
the Han. Nonetheless, from the Han period onward, most Chinese
emperors have used a mix of Legalism and Confucianism as their
ruling doctrine, often with the latter embellishing the former. In
other words, Confucian values were used to sugar-coat the harsh
Legalist ideas that underlie the Imperial system. The
disintegration of the Han in the second century CE opened the
way for the spiritual and otherworldly doctrines of Buddhism
and Daoism to dominate intellectual life at that time.”
Wikipedia: Confucianism.
Defining key theoretical variables p. 6
6
*FxCmtyWages= Wages x Fixed community ((v2125>1)*1)*(v61==6)*1
concept: Given wages in communities where land is owned,
inequality is amplified in extended periods of resource
scarcity. When due to overpopulation, the value of property
increases relative to oversupply of workers whose wages are
lowered, a potential context for extreme inequality.
*AnimXbwealth = (% Pastoralism v206) x (Bridewealth v208=1)
concept: (a) owner lineages of herds of camels and horses
employ suborned lineages as herders and caravan workers.
(b) In times of extreme scarcity following population
increase that outruns food supply, plentiful workers are of
lesser value (c) herd ownership is of excess value due to
scarcity, and (d) if brideprice is present, owners have a
more extreme advantages in acquiring multiple wives from
lesser lineages.
*SuperjhWriting= Superjurisdictiocal Hierarchy x Writing
v237*(1+((v149>=3)*1))
concept: In such Malthusian crises as above, taxes relative
to income pose a potential context for extreme inequality.
Wy term Regression: comparing models of
White,Oztan,Snarey and Brown and Eff p.7
7
W is a weighted sum of square zero-diagonal matrices
(inverse distance, language similarities) with row sums
normalized to 1, so that the product Wy measures
interdependencies in the dependent variable y and is thus
suitable as a control for autocorrelation in a regression
equation for the dependent variable y.
An initial regression (1sls) estimates the Wy dependent
variable using the columns of WX as predictor variables,
i.e., estimate Wy = a + WXc + υ and save the vector of
estimated scores
(1) ŷw = â + WXĉ, where ŷw is
now a suitable control variable
for autocorrelation of the dependent variable y.
DEf first imputes all variables, then estimates ŷw. Then,
a second ols regression (2), the 2SLS Dow-Eff equation
(DEf), estimates the βiXi coefficients βi and the
autocorrelation coefficient ρ (of ŷw ) that together
predict the dependent variable y.
Ŷw term 2SLS Regression Results p. 8
8
(2) y = β0 +ρŷw +β1X1 + β2X2 +…+ βKX2K +
ε
e.g. testing HiGod predictors of White etal and Brown & Eff
Slide 9 shows results of 2SLS regression for significant
variables at p < .10: six are those of White et al
(AnimXbwealth, No_Rain_Dry, Writing, Missions, bio.5, and
Distant Father, plus PCsizeSq– also significant in Brown &
Eff), and Caste is a second significant Brown & Eff
variable. FxCmtyWages, at p < 0.14 as a predictor in this
model, is not significant.
3-stage Regression Results
Slide 10 shows how imputed rather than raw variables, used
in a third ols regression, elevates the FxCmtyWages variable
to significance, as proposed from prior theory.
DEf 2SLS results for HiGods p. 9
9
3-stage regression with imputed variables:
White et al (bold or red) vs. Brown & Eff
p.10
10
Coefficients: Estimate Std. Error t value Pr(>|t|)
(Intercept)
0.006272
0.473491
0.013 0.98945
Wy
0.651359
0.136649
4.767 0.00061 ***
FxCmtyWages*
0.751684
0.259420
2.898 0.00426 **
Missions
0.334426
0.140836
2.375 0.01868 *
bio.5 (temp) -0.150861
0.079799 -1.891 0.06039 .
PCsizeSq**
-0.077855
0.041264 -1.887 0.06090 .
Writing
0.115742
0.064661
1.790 0.07524 .
Caste
0.171590
0.104619
1.640 0.10283
AnimXbwealth
0.090378
0.059296
1.524 0.12932
DistantFather -0.129960
0.087188 -1.491 0.13793
No_rain_Dry
0.120057
0.083832
1.432 0.15395
PCsize
0.102367
0.078573
1.303 0.19440
ExtWar
-0.013503
0.010783 -1.252 0.21221
AgPot
-0.053785
0.064506 -0.834 0.40556
FoodScarcity
0.018975
0.056114
0.338 0.73567
Anim
-0.006878
0.057393 -0.120 0.90476
*The FxCmtyWages variable is, as hypothesized, significant.
**Works in both models. All variables imputed for n=186
The 3-stage model uses regression-imputed variables Xh
and ŷw & facilitates Bayesian Network Learning
p.11
11
(3) y = β0 +ρŷw +β1Xh1+β2Xh2 +…+ βKXh2K + ε
A new regression model uses the imputed variables Xh:
HiGod <- h$data[,"HiGod"]
h$data[, retrieves imputed vars
AnimXbwealth <- h$data[,"AnimXbwealth"]
No_rain_Dry <- h$data[,"No_rain_Dry"]
Writing <- h$data[,"v149"]
AgPot <- h$data[,"PCAP"]
PCsizeSq <- h$data[,"PCsizeSq"], etc.
The function h$data[…] denotes imputed variables whether
data are missing or not.
A 4th-stage analysis compares the White et al and Brown and
Eff models by joint analysis of all of their 3-stage
variables and allows the use of Bayesian Network Learning
with R library(bnlearn), newly available in 2014.
Bayesian Network Learning Results using imputed data and
library(bnlearn) in comparing the two Moral Gods models p.12
AnimXbwealth
HiGod 0
1 54
2 40
3 13
4 21
1
7
6
1
2
2
6
5
4
0
3
1
0
3
9
4
0
0
1
3
5
0
0
0
1
7
0
0
1
0
8
1
0
0
3
9
0
0
0
4
HiGod
FxCmtyWages 1 2 3 4
0 43 27 11 17
1 18 11 5 23
White, Oztan & Snarey (2014)
3=neither Islam nor Christianity
4=supportive of morality
Writing & Records
HiGod 1 2 3 4 5
1 35 16 10 0 8
2 25 17 6 0 3
3 7 9 3 2 2
4 6 7 2 10 18
Brown & Eff (2010)
12
Trestles bootstraps, Paul Rodriguez p.13
13
Next, a bootstrap procedure was used to explore the distribution of possible
network models (Efron & Tishbrini, 1986). One thousand bootstrap resamples were
taken by sampling the original dataset with replacement. For each new sample
dataset, a bayes network was found using the grow-shrink algorithm (heeding
independencies in the data). The binary valued adjacency matrix for each network
was saved and then averaged across all 1000 networks, thereby producing an
expectation for the presence of every edge (Figure with graph in file named
'BNwboot_nowy_05thresh'). This approach has proved very useful in biological
network discovery (e.g. Marbach, etal. 2012). The expectation serves as a weight
on the edge, but it does not indicate what typical networks appear in the
bootstrap samples. Therefore, we also sorted and counted the adjacency
matrices, and printed out the most frequent networks.
Efron, B.; Tibshirani, R. 1993. An Introduction to the Bootstrap. Chapman & Hall/CRC.
Marbach D, Costello JC, Küffner R, Vega NM, Prill RJ, Camacho DM, Allison KR; The
DREAM5 Consortium, Kellis M, Collins JJ, Stolovitzky G. 2012. Wisdom of crowds for
robust gene network inference. Nature Methods 9(8):796-804. 58 collaborators.
Margaritis, D. and Thrun, S. 2000. Bayesian network induction via local neighborhoods. In
Advances in Neural Information Processing Systems 12. (“the bootstrap.”)
library(bootstrap)
blocLite(Rgraphviz)
14
Bioconductor.blocLite.R
library(bootstrap)
Paul Rodriguez SDSC
blocLite(Rgraphviz)
V=letters[1:10]
M=1:4
g1=randomGraph(V,M,0.2)
plot(g1)
Probabilities are generated by
bootstrap, run on SDSC
Trestles supercomputer
1695=No Scarification,
270=Class stratification
p. 13b (shown in session discussion #2)
15
Questions about Bayesian Networks
p.14
16

*Why are ab identifiable? Because there is no observed
variable or bias that significantly affect them both (KF:1024).

Does subtraction of variables alter a BN graph? No. Addition?

Only if the above* is violated (strengthened by many candidates).

If you add x and get axb will that change a BN? No. Since
.. are probabilities, their product is a probability but a to b may
have other additive probabilities from other paths. axb? Yes.

Does subsampling cases in the same time period alter a BN?
Yes. W matrices and PCs for imputing data are subsampled too.

Why do significances change between DEf and Wy Reg?
Entry of est(Wy) is an additional variable...
KF=Koller & Friedman 2009. Probabilistic Graphical Models.
SUMMARY: Null Hypotheses and Comparison of
Results
p.15
17
The null hypothesis for the pvalues in our models is that the
true value of the coefficient is zero. For Moral Gods:
The Autocorrelation regression model tells us that
that some theoretically-derived variables are significant.
The Wy term imputed variable regression also
shows an especially significant effect of FxCmntyWages
but for moral gods unconcerned with humans.
The Wy term Bayesian Network shows potential
causality of FxCmntyWages and AnimXbwealth.
The Bootstrap shows probabilistic alternative
models, several with indirect effects, each with the central
theoretical variables, FxCmntyWages and AnimXbwealth.
Questions/Discussions
18
OTHER
QUESTIONS?
Christian Brown and Anthon Eff. 2010. The State and the Supernatural: Support for
Prosocial Behavior, Structure and Dynamics: eJournal of Anthropological Sciences
4(1).
Douglas R. White, B. Tolga Oztan, Giorgio Gosti, Elliott Wagner, and John Snarey.
2010. Discovery of Hidden Variables for the Evolution of Ethical Religions. Submitted
to Scientific American.
Question: In regard to autocorrelation, i.e., Galton’s
problem, do our results differ from OLS? Yes, very much.
Estimate Std. Error t value Pr(>|t|)
19

(Intercept)
1.019415
0.729651
1.397
0.16577

dx$FxCmtyWages
0.023184
0.273012
0.085
0.93251

dx$v2006 Missions 0.457471
0.220324
2.076
0.04068 *

dx$v149 Writing
0.260651
0.104351
2.498
0.01429 *

dx$v272
0.193109
0.182208
1.060
0.29203

dx$AnimXbwealth
0.105582
0.079593
1.327
0.18798

dx$v3
-0.003290
0.072426
-0.045
0.96387

dx$No_rain_Dry
0.340791
0.126310
2.698

dx$v1650
-0.012738
0.015911
-0.801
0.42546

dx$v1685
-0.038787
0.082818
-0.468
0.64066

dx$v206
-0.008370
0.072604
-0.115
0.90848

dx$bio.5
-0.002922
0.001762
-1.659
0.10064

PCAP
0.139448
0.101782
1.370
0.17404

PCsize
0.025052
0.140601
0.178
0.85898

PCsizeSq
-0.054963
0.057641
-0.954
0.34284
0.00831 **
Recap of 3-stage Regression with imputed variables
that includes the estimated Wy and results
20


Once DEf is run, Wy is defined along with imputed
variables. A simple OLS regression can be run where
y = β0+β1Wy + βiimputed(Xi)+ ε
This model gives a total Rsq including Wy, and
somewhat different coefficients and significances.
____FxCmtyWages is the most significant variable.
AnimXbridewealth is close to significance and less
significant than in DEf. Five variables are significant. All
belong to the White et al., one shared with Brown and
Eff (2010), one exclusive to Brown and Eff.
What is Bayesian Network Learning? A
Bayesian Network, and library(bnlearn)?
21
We have compared the White et al and Brown and Eff models
by analysis of their combined variables using Bayesian
Network Learning: library(bnlearn).
A Bayesian Network has statistically significant
conditional probabilities of nonindependence (controlling
for linked variables that qualify for network membership)
in which the links among variables can be directed so as
to satisfy a directed asymmetric graph (DAG) network
structure. This entails exclusion of paths that form
cycles. The maximal DAG qualifies as a kind of path
analysis in which links are potential sources of logically
and statistically consistent causality, although not
necessarily causal.
The imputed variables in the Wy regression listed above
generate the limited Bayesian Network segments below.
22
False Hopes: That Eff-Brown variables would
have indirect effects through the core theoretical
models in White et al.


We were hoping that at least the Bayesian Network of
variables analysis would show that Brown and Eff (2010)
variables were indirect predictors operating through the
mediation of the theoretically anticipated variables of
White et al. (2014).
This was not reflected either in the DEf models or in the
Bayesian Networks.
Recap: Autocorrelation Regression (DEf) and
Theoretical Variables
23


To explicate the results in more detail, our models tell us about some
of the variables involved or not involved in the development of
Moral Gods. SuperjhWriting, FxCmtyWages, and AnimXbwealth are
theoretically grounded compound variables (White et al. 2011).
AnimXbwealth measures the potential for inequalities in herd
sizes among pastoral societies that engage in bridewealth.
____FxCmtyWages measures the potential for income inequality in
agricultural societies. These two variables are representative of
moments of economic trouble that lead to moral crises requiring the
intervention of a moral god (Alexander 1987, cited in White et al.
2011).
Both are sensitive to population pressure as it affects
resources that can increase inequality in complex societies.
____Writing, a proxy for Superjurisdictional hierarchy with writing,
which is not a significant variable, might measure the extent to which
there is a potential for dynamically unstable exchange between
government collecting taxes and citizens paying taxes.
Bivariate distribution of variables and their
correlations
24