Dubrovnik 2005 Presentation
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Dubrovnik 2005 Presentation
- 1. Explaining Causal Modelling Federica Russo Institut Supérieur de Philosophie – UCL Centre for Philosophy of Natural and Social Science - LSE
- 3. What is a causal model? X 1 age X 2 education X 3 age at marriage Y number of children 1 2 12 13 23 3
Editor's Notes
- INTRODUCTION [attention getter] [need] causality & explanation closely connected; several attempts to provide accounts of expl, caus, caus expl.; just recall knock down objection raised debate still open [task] fascinated by explanation, my PhD on causality, in part. causal modelling in soc sc. Don’t deal with expl directly in PhD, it pops up now&then. Submitted last week, eventually had time to relax & think about it (expl), in part. expl & causal modelling [main message] take home message – let me be bold …- came to conclusion (very tentative) : causal modelling is a model of expl
- My starting point: CM in soc sc. Phil literature not paid extensive attention – however attempts in Suppes 1982, Irzik&Meyer 1985 ( CM gives new directions for stat expl). MY point: CM new directions for causal expl. Recently Woodward 2003 analyzes CM to develop counterfactual account of causal expl. Tell u what I understood causal model are, what they do (how CM works) and what they’re designed for. Go deeper: analysis of struc eq show how its language employs expl in number of ways. However not sophisticated conceptualization of expl Go through case study in demography: Caldwell’s classical model of M’s ed& Ch surv. in developing countries OSS: let me ask u to take this as “informal” first thoughts on expl & CM. kind of first intuitions that may subsequently become a path of research interested in comments and feedbacks
- Explain ex: fertility survey; var X1, X2, X3 are observed; relations btw var expressed mathematically as in the eq, pictorially as in the graph. CM= Set of equation associated with a graph. In the graph: nodes, arrows In the equations: variables, parameters Causal interpretation of graph and equations controversial. E.g in Bayes Nets, debate on validity of CMC supposed to grant causal iterpretation; probl of det – indet in structural eq. BUT this is the top of iceberg … causal models, made of: number of assumptions (statistical – e.g. linearity, normality of distributions, causal – e.g. correlation -var, stability, invariance, metaphysical – e.g. direction of time, asymmetry, causal priority), in model building stage background theories, causal context, -- this guide formulation of: conceptual hypothesis, choice of variables testing stage: hypothetico-deductive methodology
- Causal models model properties of a social system* model relations btw these properties, represented by variables. *soc. System= roughly, a given population – e.g. in fertility survey before, a given pop in developing countries Causal models statistically model causal relations statistical causality To model its properties = to give a scheme, a skeleton of how these properties or characteristics (Education, #children, age …) relate. Possibility: think the graph = scheme of underlying causal mechanism that governs the soc system. BUT this causal mech is NOT modelled in terms of spatio-temporal processes and interactions (Salmon) – it is statistically modelled** **Stat Modelled = by means of statistical concepts of correlation, constant conjunction, screening-off … Structural models (designed for causal analysis) uncover stable relations btw properties CM aims at detecting causal rel brw properties, explain the dynamic of the system through its causes. WHY? bcz knowledge of causes allows us to explain, predict, intervene on society. Hence CM MODEL OF EXPL OSS: not in D-N sense; closer to S-R; it is H-D H-D structure* of expl (?) structure: given by graph & eq logic of testing to confirm/disconfirm causal hypothesis OSS: good/successful expl = confirmed model* (also, see later coefficient of determination * Confirmed model = conceptual hyp (=hypothesized causal link) is accepted (int validity) OSS: background theories & knowledge give the context expl is context-relative probl of generalizing (ext validity) (pragmatics of expl?)
- Typical form of str eq. Y,X called in varieties of ways depending on sc discipline. e.g. endogenous – exogenous Y – response var Xs – explanatory var Xs explain Y OSS: in sc literature NO explication of this use of explanatory, explanation, explain Best guess: intuitively “account for” Xs are relevant causal factors in the causal mechanism, formalized by struc eq + graph, that produce Y N.B. unsophisticated use of expl, nevertheless, intuitively clear. Let’s set aside for time being “what” is expl focus on what this expl consists of
- Goal: explain variability in Y: Variations in Xs explain variations in Y as Xs vary, so Y does Variations in Xs produce variability in Y as long as we can control variations in Xs we can also predict how Y will accordingly vary s quantify “causal impact” of each of the Xs. BUT: how is expl “quantify” – how good is expl? coeff of det r 2 r 2 = square of correlation coeff r. r= -1 r +1 ; 0 r 2 +1 r 2 = statistic used to determine how well a regression fits r 2 represents the fraction of variability in Y that can be explained by variability in Xs r 2 indicates how much of the total variation in Y can be accounted for by the regression function r 2 gives the proportion of the variance of Y that is predictable from the Xs. It’s a measure that allows to determine how certain we can be in making predictions from a certain model r 2 is the ration of the explained variation to the total variation OSS my theoretical arguments end here – don’t have clear ideas on how all these remarks should be “organized” and deepened in order to give a new account of expl Now I’ll go through a case study to show why - seems to me – a causal model gives a causal expl
- Introduce case study: 1979 article in Pop Studies. developing countries, in part rural & urban area in Nigeria; objective= understand factors that influence child mortality; former studies: focus on sanitary, medical, social, political factors. evidence gathered in other studies. In analyzing impact of public health service, Caldwell notices that many socio-ec factors provide little expl of mortality rates. INSTEAD, mother’s education is of surprising importance design a study focused on mother’s ed. Explain graph. E = child mortality measured by age of child at death Y ; C1 = mother’s education measured by years of schooling of mother X1 ; C2 = socio-economic status, operationally defined by X1 , by income X2 and by years of schooling of father X3 . Arrows = causal relationships; pointed-dashed lines = indicators C1 , C2 , E are measured from the variables X1 , X2 , X3 , Y ; the straight line = indicators C1 and C2 are correlated.
- (i) What is the social system under inquiry? The analysis concerns populations of developing countries, in particular, data refer to the city of Ibadan (Nigeria). (ii) What properties or characteristics of the social system does Caldwell take into account? In his study, Caldwell especially takes into account mother’s education, because former studies focussed only on socio-economic influence and on medical or technological influence. Caldwell is mainly interested in child mortality, related to maternal education and other socio-economic factors. (iii) What does it mean to model these properties? Modelling the properties of the systems means to study the relations between variables – causal modelling will try to establish what relations are causal . (iv) What is Caldwell’s result? Mother’s education is a significant determinant in child mortality and it must be examined as an important force on its own, since maternal education cannot be employed as a proxy for general social and economic change. Let me go back to 2 questions of previous slide: The graph tells a causal story Bcz the whole statistical set-up is built and evaluated within a causal context we want to quantify the causal impact of some variables on other variables – this can be done thanks to causal modelling (rember the quite rich structure of a causal model
- The causal models accounts for – spells out (causal) relations btw variables of interest. unveil a causal mechanism Modelling + background theory & knowledge allows to dare the following: maternal education does have causal impact on child survival. – modelling allows step forward: why it is so? why has maternal education a causal impact on child mortality? Education serves two roles: (i) it increases skills and knowledge, as well as the ability to deal with new ideas, and (ii) it provides a vehicle for the import of a different culture. [this comes from knowledge of causal context] Educated women are less “fatalistic” about illness, and adopt many of the alternatives in child care and therapeutics that become available. Educated women are more likely to be listened to by doctors and nurses. In West African households, education of women greatly changes the traditional balance of familiar relationships with significant effect on child care. OSS: knowledge of causal context allows us to go beyond the mere mechanism depicted in the graph and formalized in the equations
- CM aims at explaining soc system by modelling structural (=stable) relations – i.e. stable causal relations btw properties of the system Structural eq make use of expl vocabulary – for the variables, for their role, for the interpretation of coeff of determinantion Caldwell explains child survival through its cause(s)
- OSS: that expl-caus are related is not new. First attempts to valorize CM in Irzik&Meyer BUT for stat expl. Also, Woodward builds counterfactual account of caus expl on CM … improvement, although counterfactual approach challenged (Dawid) Since CM uses expl vocabulary in a complete unsophisticated way, seems to me, there is a lot of work to be done for philosophers CM seems to be a model of expl. It has H-D structure, accompanied by struc eq formalization and graphical representation of the causal mechanism. It incorporates knowledge of the causal context and background theories (pragmatics of expl)
- Let me be bold … although I’m not going to subscribe completely this slogan – just want to propose a insight and see what happens OK, maybe this is passing the buck. Bcz now have to say what is a model … this still is a hot topic in phil of sc. However, topic less controversial if we think of stat models rather than, say, physical model of pendulum. There’s +or- consensus on what a stat model is (= set of probability distributions). Probl: causal model is much more than this … maybe philosophical analysis of features of causal models is the right path to understand what causal expl is.