Big Gods Theory

In this paper two causal models that approximate the nearly frequency-independent cyclic behaviour of soils are analysed in detail. The study was motivated by the need to conduct time-domain viscoelastic analysis on soil structures without adopting the ad hoc assumption of Rayleigh damping. First, the causal hysteretic model is introduced in which its imaginary part is frequency independent the same way that is the imaginary part of the popular non-causal constant hysteretic model. The adoption of an imaginary part that is frequency independent even at the zero-frequency limit, in conjunction with the condition that the proposed model should be causal, yields a real part that is frequency dependent and singular at zero frequency. The paper shows that the causal hysteretic model, although pathological at the static limit, is the mathematical connection between the non-causal constant hysteretic model and the physically realizable Biot model. The mathematical structure of the two causal models is examined and it is shown that the causal hysteretic model is precisely the high-frequency limit of the Biot model. Although both models have a closed-form time-domain representation, only the Biot model is suitable for a time-domain viscoelastic analysis with commercially available computer software. The paper demonstrates that the simplest, causal and physically realizable linear hysteretic model that can approximate the cyclic behaviour of soil is the Biot model. The proposed study elucidates how the dynamic analysis of soil structures can be conducted rigorously in terms of the viscoelastic properties of the soil material and not with the ad hoc Rayleigh damping approach which occasionally has been criticized that tends to overdamp the higher vibration modes. The study concludes that under pulse-type motions the Rayleigh damping approximation tends to overestimate displacements because of the inappropriate viscous type of dissipation that is imposed. Under longer motions that induce several cycles, the concept of equivalent viscous damping is more appropriate and the Rayleigh damping approximation results to a response that is comparable to the response computed with a rigorous time-domain viscoelastic finite element analysis. Copyright © 2000 John Wiley & Sons, Ltd.

BackgroundCausal inference has seen an increasing popularity in medical research. Estimation of causal effects from observational data allows to draw conclusions from data when randomized controlled trials cannot be conducted. Although the identification of structural causal models (SCM) and the calculation of structural coefficients has received much attention, a key requirement for valid causal inference is that conclusions are drawn based on the true data-generating model.MethodsIt remains widely unknown how large the probability is to reject the true structural causal model when observational data from it is sampled. The latter probability – the causal false-positive risk – is crucial, as rejection of the true causal model can induce bias in the estimation of causal effects. In this paper, the widely used causal models of confounders and colliders are studied regarding their causal false-positive risk in linear Markovian models. A simulation study is carried out which investigates the causal false-positive risk in Gaussian linear Markovian models. Therefore, the testable implications of the DAG corresponding to confounders and colliders are analyzed from a Bayesian perspective. Furthermore, the induced bias in estimating the structural coefficients and causal effects is studied.ResultsResults show that the false-positive risk of rejecting a true SCM of even simple building blocks like confounders and colliders is substantial. Importantly, estimation of average, direct and indirect causal effects can become strongly biased if a true model is rejected. The causal false-positive risk may thus serve as an indicator or proxy for the induced bias.ConclusionWhile the identification of structural coefficients and testable implications of causal models have been studied rigorously in the literature, this paper shows that causal inference also must develop new concepts for controlling the causal false-positive risk. Although a high risk cannot be equated with a substantial bias, it is indicative of the induced bias. The latter fact calls for the development of more advanced risk measures for committing a causal type I error in causal inference.

The origins of religion and of complex societies represent evolutionary puzzles1-8. The 'moralizing gods' hypothesis offers a solution to both puzzles by proposing that belief in morally concerned supernatural agents culturally evolved to facilitate cooperation among strangers in large-scale societies9-13. Although previous research has suggested an association between the presence of moralizing gods and social complexity3,6,7,9-18, the relationship between the two is disputed9-13,19-24, and attempts to establish causality have been hampered by limitations in the availability of detailed global longitudinal data. To overcome these limitations, here we systematically coded records from 414societies that span the past 10,000years from 30regions around the world, using 51measures of social complexity and 4measures of supernatural enforcement of morality. Our analyses not only confirm the association between moralizing gods and social complexity, but also reveal that moralizing gods follow-rather than precede-large increases in social complexity. Contrary to previous predictions9,12,16,18, powerful moralizing 'big gods' and prosocial supernatural punishment tend to appear only after the emergence of 'megasocieties' with populations of more than around one million people. Moralizing gods are not a prerequisite for the evolution of social complexity, but they may help to sustain and expand complex multi-ethnic empires after they have become established. By contrast, rituals that facilitate the standardization of religious traditions across large populations25,26 generally precede the appearance of moralizing gods. This suggests that ritual practices were more important than the particular content of religious belief to the initial rise of social complexity.

ObjectiveTo define confounding bias in difference‐in‐difference studies and compare regression‐ and matching‐based estimators designed to correct bias due to observed confounders.Data sourcesWe simulated data from linear models that incorporated different confounding relationships: time‐invariant covariates with a time‐varying effect on the outcome, time‐varying covariates with a constant effect on the outcome, and time‐varying covariates with a time‐varying effect on the outcome. We considered a simple setting that is common in the applied literature: treatment is introduced at a single time point and there is no unobserved treatment effect heterogeneity.Study designWe compared the bias and root mean squared error of treatment effect estimates from six model specifications, including simple linear regression models and matching techniques.Data collectionSimulation code is provided for replication.Principal findingsConfounders in difference‐in‐differences are covariates that change differently over time in the treated and comparison group or have a time‐varying effect on the outcome. When such a confounding variable is measured, appropriately adjusting for this confounder (ie, including the confounder in a regression model that is consistent with the causal model) can provide unbiased estimates with optimal SE. However, when a time‐varying confounder is affected by treatment, recovering an unbiased causal effect using difference‐in‐differences is difficult.ConclusionsConfounding in difference‐in‐differences is more complicated than in cross‐sectional settings, from which techniques and intuition to address observed confounding cannot be imported wholesale. Instead, analysts should begin by postulating a causal model that relates covariates, both time‐varying and those with time‐varying effects on the outcome, to treatment. This causal model will then guide the specification of an appropriate analytical model (eg, using regression or matching) that can produce unbiased treatment effect estimates. We emphasize the importance of thoughtful incorporation of covariates to address confounding bias in difference‐in‐difference studies.

Finding cause-effect relationships is the central aim of many studies in the physical, behavioral, social and biological sciences. We consider two well-known mathematical causal models: Structural equation models and causal Bayesian networks. When we hypothesize a causal model, that model often imposes constraints on the statistics of the data collected. These constraints enable us to test or falsify the hypothesized causal model. The goal of our research is to develop efficient and reliable methods to test a causal model or distinguish between causal models using various types of constraints. For linear structural equation models, we investigate the problem of generating a small number of constraints in the form of zero partial correlations, providing an efficient way to test hypothesized models. We study linear structural equation models with correlated errors focusing on the graphical aspects of the models. We provide a set of local Markov properties and prove that they are equivalent to the global Markov property. For causal Bayesian networks, we study equality and inequality constraints imposed on data and investigate a way to use these constraints for model testing and selection. For equality constraints, we formulate an implicitization problem and show how we may reduce the complexity of the problem. We also study the algebraic structure of the equality constraints. For inequality constraints, we present a class of inequality constraints on both nonexperimental and interventional distributions.

Different emphases on ideological, socio-economic and technological changes have been brought to bear on the cultural variability made materially manifest in pre-Iron Age Saharan pastoral societies. The models have ranged from limited or no complexity before iron production to transient mobile elites across the Sahara, to socially complex communities from the mid-Holocene onwards in the Central Libyan Sahara, and to permanent elites with complex social structures. Here, ethnographic cultural variability is stressed, previous models detailed, and data for the Eastern and Central Sahara summarised and analysed. The emerging picture is of a mosaic of population movements, clustering and experimentation resulting in transient peaks of wealth and the potential for incipient social complexity to become temporarily or permanently manifest. Saharan social diversity serves as a warning against linear models and highlights the importance of an explanatory framework for investigating the evolution of social structures outside of permanently settled communities for North Africa.

The increasing prevalence of multiple, long time series data fuels the hope for gaining better understanding and more precise prediction of various phenomena in many domains, hence calling for the development of new methodologies in time series analysis. Two features pertinent to the practical usefulness of any time series model are sparsity and causality. A sparse time series model means that only a small subset of model parameters are non-zero, which is usually preferable to its non-sparse counterparts in terms of interpretability, robustness, parsimony and estimation variability. Causality refers to the dependence structure for which only past and present information is used. Causality is an indispensable feature for certain purposes such as prediction, and is usually desirable when modeling real-world phenomena. This dissertation devotes to the development of two time series methodologies that incorporate sparsity and causality. In the first part of the thesis, we introduce the sparse causal dynamic linear regression model. Two approaches are proposed for construction of such models. The first one utilizes the frequency domain solution of a classic two-sided dynamic linear model and augments it with a simple soft-thresholding operator. This approach is computationally efficient and enjoys good performance theoretically and empirically under the assumption that the true dynamic regression relationship is causal and sparse. The second approach constructs a sparse causal dynamic linear model by minimizing certain penalized mean squared prediction error. This approach is computationally intensive but is superior to the first approach as it does not require the causal assumption. It enjoys better empirical performance and opens up meaningful extensions. In the second part of the thesis, we introduce the sparse causal dynamic principal component analysis. This procedure also has two variants. The first one computes the principal component series as a sparse and causal linear filter of the original data. The filter is obtained by minimizing a penalized reconstruction loss functional in the frequency domain. The principal component series so obtained enjoys good performance in terms of summarizing high-dimensional data, estimating factors in dynamic factor models, and prediction. However, it is computationally intensive. The second approach imposes sparsity structure on the innovation representation of the data generating process, which leads to simpler computational algorithms. In addition, this method is of interest in its own right for certain applications in finance and econometrics.

ABSTRACTObjectives To determine the relationships between five models of primary care service delivery and quality of care indicators in an urban population. Two fee-for-service (FFS) and three alternative-funded models of primary care service delivery were studiedApproach We allocated all Manitoba residents who had at least three visits to any primary care provider (PCP) at any Winnipeg clinic between 2010-2013 to the most responsible PCP (N = 626,264). We then allocated each PCP to a model of primary care service delivery. We created general linear mixed models to describe the relationship between each model of primary care and the dominant, traditional fee-for-service model for health services use, while controlling for a variety of PCP and patient factors, including patient social complexity.Results Patient social complexity was associated with poorer crude rates for many of the indicators. There were no differences among the models for hospital readmission within 30 days or specialist referral by the assigned PCP. Hospitalizations for ACSC were higher for one alternative funded model (1.98 OR, 1.38-2.83 95% CI), while non-indicated low back X-rays were lower for a different alternative funded model (0.14 OR, 0.03-0.59 95% CI). Ambulatory care visits to any PCP were lower for all three alternative funded models than the two FFS models. The family medicine academic teaching sites had lower rates of continuity of care (p< 0.5)Conclusion Overall, no model of primary care consistently outperformed the others. FFS models had higher rates of visits, but appeared to satisfy patient needs better because they had less use of telehealth services following visits. Teaching sites appeared to sacrifice continuity of care potentially to support other academic activities. Controlling for social complexity was associated with a reduction in the differences between models in indicator outcomes.

Motivated by the real damped simple harmonic oscillator (SHO) system, in this paper, we propose a process interpretation of causality and the first-order causal process (FoCP) model for temporal causal modelling. Compared with existing causal models that are able to model feedbacks, such as the structural equation model (SEM) and the structure vector autoregressive (SVAR) model, the FoCP model entails a novel 2-stage evolution semantic for instantaneous and cross-temporal causal relations existing in many real world dynamic systems. Graphical representations are developed to illustrate the causal structure compactly. Useful properties of the new model are identified and used to develop a conditional independence based algorithm for learning the causal structure from a multivariate time series dataset. Experiments on both simulated and real data validate the feasibility of the method to discover simple while meaningful causal structures of dynamic systems.

The purpose of the study was to investigate the characteristics of fitting linear dynamic models to the impulse response of oscillatory dynamic systems using Prony analysis. Many dynamic systems exhibit oscillatory responses with multiple modes of oscillations. Although the underlying dynamics of such systems are often nonlinear, it is frequently possible and very useful to represent the system operating about some set point with a linear model. Derivation of such linear models can be done using two basic approaches: model the system using theoretical derivations and some linearization method such as a Taylor series expansion; or use a curve-fitting technique to optimally fit a linear model to specified system response data. Prony analysis belongs to the second class of system modeling because it is a method of fitting a linear model to the impulse response of a dynamic system. Its parallel formulation inherently makes it well suited for fitting models to oscillatory system data. Such oscillatory dynamic effects occur in large synchronous-generator-based power systems in the form of electromechanical oscillations. To study and characterize these oscillatory dynamics, BPA has developed computer codes to analyze system data using Prony analysis. The objective of this study was to develop a highly detailed understanding of the properties of using Prony analysis to fit models to systems with characteristics often encountered in power systems. This understanding was then extended to develop general ``rules-of-thumb`` for using Prony analysis. The general characteristics were investigated by performing fits to data from known linear models under controlled conditions. The conditions studied include various mathematical solution techniques; different parent system configurations; and a large variety of underlying noise characteristics.

We propose a method for estimating the marginal causal log-odds ratio for binary outcomes under treatment non-compliance in placebo-randomized trials. This estimation method is a marginal alternative to the causal logistic approach by Nagelkerke et al. (2000) that conditions on partially unknown compliance (that is, adherence to treatment) status, and also differs from previous approaches that estimate risk differences or ratios in subgroups defined by compliance status. The marginal causal method proposed in this paper is based on an extension of Robins' G-estimation approach for fitting linear or log-linear structural nested models to a logistic model. Comparing the marginal and conditional causal log-odds ratio estimates provides a way of assessing the magnitude of unmeasured confounding of the treatment effect due to treatment non-adherence. More specifically, we show through simulations that under weak confounding, the conditional and marginal procedures yield similar estimates, whereas under stronger confounding, they behave differently in terms of bias and confidence interval coverage. The parametric structures that represent such confounding are not identifiable. Hence, the proof of consistency of causal estimators and corresponding simulations are based on two different models that fully identify the causal effects being estimated. These models differ in the way that compliance is related to potential outcomes, and thus differ in the way that the causal effect is identified. The simulations also show that the proposed marginal causal estimation approach performs well in terms of bias under the different levels of confounding due to non-adherence and under different causal logistic models. We also provide results from the analyses of two data sets further showing how a comparison of the marginal and conditional estimators can help evaluate the magnitude of confounding due to non-adherence.

Altered-LiNGAM (ALiNGAM) for solving nonlinear causal models when data is nonlinear and noisy

34 Multivariate analysis with latent variables

SUMMARY. Self-concept theory and ethnic identity theory imply causal relations among positive parent-child relationship, ethnic pride, and psychological adjustment of children who were intercountry adopted. This study used linear measurement and structural equation models to test the plausibility of the causal model dealing with the relations among indexes of parent’s support of ethnic background, positive parent-child relationship, collective self-esteem, and psychological adjustment in a sample of 241 Korean-born adolescent adoptees. Consistent with the expectations of the self-concept theory and the ethnic identity development theory, the findings show that a more positive parent-child relationship, in which the parents support their children’s ethnic identity development and share ethnic socialization experiences, predicts better psychological adjustment of the adopted children. Policy and practice implications of the findings are discussed. [Article copies available for a fee from The Haworth Document Delivery Service: 1-800-342-9678. E-mail address: <getinfo@haworthpressinc.com > Website: < http://www.HaworthPress.com > ©2001 by The Haworth Press, Inc. All rights reserved.]

BackgroundMenopausal hormone therapy (MHT) is a risk factor for breast cancer (BC). Evidence suggests that its effect on BC risk could be partly mediated by mammographic density. The aim of this study was to investigate the relationship between MHT, mammographic density and BC risk using data from a prospective study.MethodsWe used data from a case-control study nested within the French cohort E3N including 453 cases and 453 matched controls. Measures of mammographic density, history of MHT use during follow-up and information on potential confounders were available for all women. The association between MHT and mammographic density was evaluated by linear regression models. We applied mediation modelling techniques to estimate, under the hypothesis of a causal model, the proportion of the effect of MHT on BC risk mediated by percent mammographic density (PMD) for BC overall and by hormone receptor status.ResultsAmong MHT users, 4.2% used exclusively oestrogen alone compared with 68.3% who used exclusively oestrogens plus progestogens. Mammographic density was higher in current users (for a 60-year-old woman, mean PMD 33%; 95% CI 31 to 35%) than in past (29%; 27 to 31%) and never users (24%; 22 to 26%). No statistically significant association was observed between duration of MHT and mammographic density. In past MHT users, mammographic density was negatively associated with time since last use; values similar to those of never users were observed in women who had stopped MHT at least 8 years earlier. The odds ratio of BC for current versus never MHT users, adjusted for age, year of birth, menopausal status at baseline and BMI, was 1.67 (95% CI, 1.04 to 2.68). The proportion of effect mediated by PMD was 34% for any BC and became 48% when the correlation between BMI and PMD was accounted for. These effects were limited to hormone receptor-positive BC.ConclusionsOur results suggest that, under a causal model, nearly half of the effect of MHT on hormone receptor-positive BC risk is mediated by mammographic density, which appears to be modified by MHT for up to 8 years after MHT termination.