Feedback and Mediation in Causal Inference Illustrated by Stochastic Process Models

The concept of causality is naturally related to processes developing over time. Central ideas of causal inference like time‐dependent confounding (feedback) and mediation should be viewed as dynamic concepts. We shall study these concepts in the context of simple dynamic systems. Time‐dependent confounding and its implications are illustrated in a Markov model. We emphasize the distinction between average treatment effect, ATE, and treatment effect of the treated, ATT. These effects could be quite different, and we discuss the relationship between them. Mediation is studied in a stochastic differential equation model. A type of natural direct and indirect effects is considered for this model. Mediation analysis of discrete measurements from such processes may give misleading results, and one needs to consider the underlying continuous process. The dynamic and time‐continuous view of causality and mediation is an essential feature, and more attention should be payed to the time aspect in causal inference.     

Econometric methodology and the philosophy of science

Econometricians have generally used the term ‘methodology’ to be synonymous with ‘methods’ and, consequently, the field of econometric methodology has been dominated by the discussion of econometric techniques. The purpose of this paper is to present an alternative perspective on econometric methodology by relating it to the more general field of economic methodology, particularly through the use of concepts drawn from the philosophy of science. Definitional and conceptual issues surrounding the term ‘methodology’ are clarified. Three methodologies, representing abstractions from the actual approaches found within econometrics, are identified. First, an ‘a priorist’ methodology, which tends to accord axiomatic status to economic theory, is outlined, and the philosophical foundations of this approach are explored with reference to the interpretive strand within the philosophy of the social sciences. A second approach is an ‘instrumentalist’ one emphasising prediction as the primary goal of econometrics, and a third methodology is ‘falsificationism’, which attempts to test economic theories. These are critically evaluated by introducing relevant issues from the philosophy of science, so that the taxonomy presented here can serve as a framework for future discussions of econometric methodology.     

Joint models for mixed categorical outcomes: a study of HIV risk perception and disease status in Mozambique

Two types of bivariate models for categorical response variables are introduced to deal with special categories such as ‘unsure’ or ‘unknown’ in combination with other ordinal categories, while taking additional hierarchical data structures into account. The latter is achieved by the use of different covariance structures for a trivariate random effect. The models are applied to data from the INSIDA survey, where interest goes to the effect of covariates on the association between HIV risk perception (quadrinomial with an ‘unknown risk’ category) and HIV infection status (binary). The final model combines continuation-ratio with cumulative link logits for the risk perception, together with partly correlated and partly shared trivariate random effects for the household level. The results indicate that only age has a significant effect on the association between HIV risk perception and infection status. The proposed models may be useful in various fields of application such as social and biomedical sciences, epidemiology and public health.     

Path analysis and determining the distribution of indirect effects via simulation

The difference between a path analysis and the other multivariate analyses is that the path analysis has the ability to compute the indirect effects apart from the direct effects. The aim of this study is to investigate the distribution of indirect effects that is one of the components of path analysis via generated data. To realize this, a simulation study has been conducted with four different sample sizes, three different numbers of explanatory variables and with three different correlation matrices. A replication of 1000 has been applied for every single combination. According to the results obtained, it is found that irrespective of the sample size path coefficients tend to be stable. Moreover, path coefficients are not affected by correlation types either. Since the replication number is 1000, which is fairly large, the indirect effects from the path models have been treated as normal and their confidence intervals have been presented as well. It is also found that the path analysis should not be used with three explanatory variables. We think that this study would help scientists who are working in both natural and social sciences to determine sample size and different number of variables in the path analysis.     

Exact parametric causal mediation analysis for a binary outcome with a binary mediator

Statistical Methods & Applications - With reference to causal mediation analysis, a parametric expression for natural direct and indirect effects is derived for the setting of a binary outcome...     

A general definition of influence between stochastic processes

We extend the study of weak local conditional independence (WCLI) based on a measurability condition made by (Commenges and Gégout-Petit J R Stat Soc B 71:1–18) to a larger class of processes that we call D￠{\bf {\mathcal{D}'}}. We also give a definition related to the same concept based on certain likelihood processes, using the Girsanov theorem. Under certain conditions, the two definitions coincide on D￠{\bf {\mathcal{D}'}}. These results may be used in causal models in that we define what may be the largest class of processes in which influences of one component of a stochastic process on another can be described without ambiguity. From WCLI we can construct a concept of strong local conditional independence (SCLI). When WCLI does not hold, there is a direct influence while when SCLI does not hold there is direct or indirect influence. We investigate whether WCLI and SCLI can be defined via conventional independence conditions and find that this is the case for the latter but not for the former. Finally we recall that causal interpretation does not follow from mere mathematical definitions, but requires working with a good system and with the true probability.     

Model selection information criteria in latent class models with missing data and contingency question

Latent class analysis (LCA) has been found to have important applications in social and behavioural sciences for modelling categorical response variables, and non-response is typical when collecting data. In this study, the non-response mainly included ‘contingency questions’ and real ‘missing data’. The primary objective of this study was to evaluate the effects of some potential factors on model selection indices in LCA with non-response data. We simulated missing data with contingency question and evaluated the accuracy rates of eight information criteria for selecting the correct models. The results showed that the main factors are latent class proportions, conditional probabilities, sample size, the number of items, the missing data rate and the contingency data rate. Interactions of the conditional probabilities with class proportions, sample size and the number of items are also significant. From our simulation results, the impact of missing data and contingency questions can be amended by increasing the sample size or the number of items.     

Estimation of causal effects in observational studies with interference between units

Causal effects are usually estimated under the assumption of no interference between individuals. This assumption means that the potential outcomes for one individual are unaffected by the treatments received by other individuals. In many situations, this is not reasonable to assume. Moreover, not taking interference into account could result in misleading conclusions about the effect of a treatment. For two-stage observational studies, where treatment assigment is randomized in the first stage but not in the second stage, we propose IPW estimators of direct and indirect causal effects as defined by Hudgens and Halloran (J Am Stat Assoc 103(482):832–842, 2008) for two-stage randomized studies. We illustrate the use of these estimators in an evaluation study of an implementation of Triple P (a parenting support program) within preschools in Uppsala, Sweden.     

Further properties of generalized residual designs

The concept of ‘residuation’ is extended so that all ‘generalized residual designs’ (in the sense of Shrinkhande and Singhi) are in fact ‘residual’ with respect to the extended type of residuation. A measure of departure from the usual type of residuation is given in general, and stronger estimates of this measure are given for affine designs.     

The analysis of ordinal time-series data via a transition (Markov) model

While standard techniques are available for the analysis of time-series (longitudinal) data, and for ordinal (rating) data, not much is available for the combination of the two, at least in a readily-usable form. However, this data type is common place in the natural and health sciences where repeated ratings are recorded on the same subject. To analyse these data, this paper considers a transition (Markov) model where the rating of a subject at one time depends explicitly on the observed rating at the previous point of time by incorporating the previous rating as a predictor variable. Complications arise with adequate handling of data at the first observation (t=1), as there is no prior observation to use as a predictor. To overcome this, it is postulated the existence of a rating at time t=0; however it is treated as ‘missing data’ and the expectation–maximisation algorithm used to accommodate this. The particular benefits of this method are shown for shorter time series.     

A simpler approach for mediation analysis for dichotomous mediators in logistic regression

Mediation is a hypothesized causal chain among three variables. Mediation analysis for continuous response variables is well developed in the literature, and it can be shown that the indirect effect is equal to the total effect minus the direct effect. However, mediation analysis for categorical responses is still not fully developed. The purpose of this article is to propose a simpler method of analysing the mediation effect among three variables when the dependent and mediator variables are both dichotomous. We propose using the latent variable technique which in turn will adjust for the necessary condition that indirect effect is equal to the total effect minus the direct effect. An intensive simulation study is conducted to compare the proposed method with other methods in the literature. Our theoretical derivation and simulation study show that the proposed approach is simpler to use and at least as good as other approaches provided in the literature. We illustrate our approach to test for the potential mediators on the relationship between depression and obesity among children and adolescents compared to the method in Winship and Mare using National children health survey data 2011–2012.     

Learning causal structure from mixed data with missing values using Gaussian copula models

We consider the problem of causal structure learning from data with missing values, assumed to be drawn from a Gaussian copula model. First, we extend the ‘Rank PC’ algorithm, designed for Gaussian copula models with purely continuous data (so-called nonparanormal models), to incomplete data by applying rank correlation to pairwise complete observations and replacing the sample size with an effective sample size in the conditional independence tests to account for the information loss from missing values. When the data are missing completely at random (MCAR), we provide an error bound on the accuracy of ‘Rank PC’ and show its high-dimensional consistency. However, when the data are missing at random (MAR), ‘Rank PC’ fails dramatically. Therefore, we propose a Gibbs sampling procedure to draw correlation matrix samples from mixed data that still works correctly under MAR. These samples are translated into an average correlation matrix and an effective sample size, resulting in the ‘Copula PC’ algorithm for incomplete data. Simulation study shows that: (1) ‘Copula PC’ estimates a more accurate correlation matrix and causal structure than ‘Rank PC’ under MCAR and, even more so, under MAR and (2) the usage of the effective sample size significantly improves the performance of ‘Rank PC’ and ‘Copula PC.’ We illustrate our methods on two real-world datasets: riboflavin production data and chronic fatigue syndrome data.

     

中国非正规经济的就业效应研究———基于投入产出模型

随着我国经济由高速增长向高质量发展转型,非正规经济在促进我国劳动就业方面的作用不断凸显。本文通过编制2002-2017年包含非正规经济部门的投入产出序列表,采用投入产出模型,定量测度制造业、建筑业、批发零售住宿餐饮业、交通运输仓储邮政业、居民服务其他服务业等5个行业非正规部门发展对我国劳动就业的直接和间接效应。研究结果显示:①各行业非正规部门对就业的直接贡献均高于同期同行业的正规部门,而且以批发零售住宿餐饮业为主的第三产业非正规部门的就业效应高于以制造业、建筑业为主的第二产业非正规部门;②由于制造业和建筑业两个行业非正规部门均存在较强的后向关联效应,因而对就业的间接贡献高于以批发零售住宿餐饮业为代表的第三产业非正规部门;③各行业非正规部门产出变化对就业的间接贡献主要集中于农林牧渔业、制造业、批发零售住宿餐饮业、租赁和商务服务业等行业,在建筑业、交通运输仓储邮政业、居民服务其他服务业等行业的表现不容乐观; ④动态来看,样本期内5个行业非正规部门产出变化对就业的直接和间接贡献均呈下降态势。     

Direct and Indirect Effects Based on Difference-in-Differences With an Application to Political Preferences Following the Vietnam Draft Lottery

Abstract

We propose a difference-in-differences approach for disentangling a total treatment effect within specific subpopulations into a direct effect and an indirect effect operating through a binary mediating variable. Random treatment assignment along with specific common trend and effect homogeneity assumptions identify the direct effects on the always and never takers, whose mediator is not affected by the treatment, as well as the direct and indirect effects on the compliers, whose mediator reacts to the treatment. In our empirical application, we analyze the impact of the Vietnam draft lottery on political preferences. The results suggest that a high draft risk due to the draft lottery outcome leads to an increase in mild preferences for the Republican Party, but has no effect on strong preferences for either party or on specific political attitudes. The increase in Republican support is mostly driven by the direct effect not operating through the mediator that is military service.     

资本技能互补与技术进步的技能偏向决定

本文基于三要素双层嵌套式CES生产函数和质量阶梯型技术创新模型，通过对企业行为的理论分析，揭示了决定技术进步方向的各种因素，发现技术进步的方向取决于技术进步的直接效应、资本技能互补的间接效应和劳动力市场内部的规模效应。其中，资本技能互补效应引致技术进步偏向于技能的机制有二：一是通过体现于资本的技术水平提高偏向于技能劳动，二是通过资本规模的扩大偏向于技能劳动。运用贝叶斯参数估计方法对中国1991-2016年期间技术进步技能偏向指数的实证测算结果表明，资本技能互补效应对于决定技术进步的技能偏向作用巨大，尽管在此期间直接效应偏向于非技能劳动，但是由于资本技能互补的间接效应和要素配置的规模效应偏向于技能劳动，且二者的作用强度均大于直接效应，从而使得中国的技术整体呈现出技能劳动偏向。     

Stochastic geometry models in high-level vision

We survey the use of Markov models from stochastic geometry as priors in ‘high-level’ computer vision, in direct analogy with the use of discrete Markov random fields in ‘low-level’ vision. There are analogues of the Gibbs sampler, ICM and simulated annealing, and connections with existing methods in computer vision.     

我国城镇居民收入分配机会不平等因何而生

本文借鉴Roemer的环境和努力二元因素分析框架,采用CHIP数据,构建相对全面的环境集,然后借助事前法构造的反事实收入来间接测度我国城镇居民收入分配机会不平等程度及其具体生成渠道,并选取年龄、性别和地区三大环境因素,进一步剖析城镇居民收入分配机会不平等的异质性特征。结果发现：（1）城镇居民收入不平等中的23.2%是由环境因素所引致的机会不平等。城镇机会不平等程度随年龄增加而逐步积累,但在51-60岁时有所缓和,呈现倒U型特征;女性的机会不平等程度高于男性;机会不平等程度在东部、中部、西部地区依次递减。（2）从生成渠道来看,机会不平等中的78.3%源于环境因素的直接渠道影响,剩余21.7%为环境因素的间接渠道影响。两种渠道的相对程度在不同年龄间差异明显,间接渠道对女性机会不平等的解释力是男性的2倍以上,间接渠道相对程度在东部、中部、西部地区依次递减。旨在缩小机会不平等的政策应致力于补偿年龄、性别和地区等环境因素差异,尽可能使所有人的同等努力得到同等回报。     

CAUSAL GRAPHICAL MODELS IN SYSTEMS GENETICS: A UNIFIED FRAMEWORK FOR JOINT INFERENCE OF CAUSAL NETWORK AND GENETIC ARCHITECTURE FOR CORRELATED PHENOTYPES

Causal inference approaches in systems genetics exploit quantitative trait loci (QTL) genotypes to infer causal relationships among phenotypes. The genetic architecture of each phenotype may be complex, and poorly estimated genetic architectures may compromise the inference of causal relationships among phenotypes. Existing methods assume QTLs are known or inferred without regard to the phenotype network structure. In this paper we develop a QTL-driven phenotype network method (QTLnet) to jointly infer a causal phenotype network and associated genetic architecture for sets of correlated phenotypes. Randomization of alleles during meiosis and the unidirectional influence of genotype on phenotype allow the inference of QTLs causal to phenotypes. Causal relationships among phenotypes can be inferred using these QTL nodes, enabling us to distinguish among phenotype networks that would otherwise be distribution equivalent. We jointly model phenotypes and QTLs using homogeneous conditional Gaussian regression models, and we derive a graphical criterion for distribution equivalence. We validate the QTLnet approach in a simulation study. Finally, we illustrate with simulated data and a real example how QTLnet can be used to infer both direct and indirect effects of QTLs and phenotypes that co-map to a genomic region.     

The k-sample problem in a multi-state model and testing transition probability matrices

The choice of multi-state models is natural in analysis of survival data, e.g., when the subjects in a study pass through different states like ‘healthy’, ‘in a state of remission’, ‘relapse’ or ‘dead’ in a health related quality of life study. Competing risks is another common instance of the use of multi-state models. Statistical inference for such event history data can be carried out by assuming a stochastic process model. Under such a setting, comparison of the event history data generated by two different treatments calls for testing equality of the corresponding transition probability matrices. The present paper proposes solution to this class of problems by assuming a non-homogeneous Markov process to describe the transitions among the health states. A class of test statistics are derived for comparison of \(k\) treatments by using a ‘weight process’. This class, in particular, yields generalisations of the log-rank, Gehan, Peto–Peto and Harrington–Fleming tests. For an intrinsic comparison of the treatments, the ‘leave-one-out’ jackknife method is employed for identifying influential observations. The proposed methods are then used to develop the Kolmogorov–Smirnov type supremum tests corresponding to the various extended tests. To demonstrate the usefulness of the test procedures developed, a simulation study was carried out and an application to the Trial V data provided by International Breast Cancer Study Group is discussed.