## From association to causation via regression (1997)

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Venue: | Indiana: University of Notre Dame |

Citations: | 16 - 6 self |

### BibTeX

@INPROCEEDINGS{Freedman97fromassociation,

author = {David A. Freedman},

title = {From association to causation via regression},

booktitle = {Indiana: University of Notre Dame},

year = {1997},

pages = {113--161},

publisher = {Press}

}

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### Abstract

For nearly a century, investigators in the social sciences have used regression models to deduce cause-and-effect relationships from patterns of association. Path models and automated search procedures are more recent developments. In my view, this enterprise has not been successful. The models tend to neglect the difficulties in establishing causal relations, and the mathematical complexities tend to obscure rather than clarify the assumptions on which the analysis is based. Formal statistical inference is, by its nature, conditional. If maintained hypotheses A, B, C,... hold, then H can be tested against the data. However, if A, B, C,... remain in doubt, so must inferences about H. Careful scrutiny of maintained hypotheses should therefore be a critical part of empirical work-- a principle honored more often in the breach than the observance.

### Citations

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Citation Context ...edged even by the modelers: Formally speaking, probabilistic analysis is indeed sensitive only to covariations, so it can never distinguish genuine causal dependencies from spurious correlations.... (=-=Pearl 1988-=-, 396) 10sSuch admissions-- like Yule’s footnote 25-- are fatal to the enterprise. Of course, Pearl does not give up. For instance, he goes on to say that experiments just provide the opportunity to o... |

496 |
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Citation Context ...; without this assumption (SGS p. 45; CG p. 4), the program output is uninformative. Therefore, I told BUILD to make the assumption; I believe that is what SGS did for the Rindfuss example. Also see (=-=Spirtes et al. 1993-=-, 13-15). I told BUILD that ED and AGE could not cause the remaining variables, following (SGS p. 139). However, SGS actually made the stronger assumption that (i) FEC, ED and AGE could not cause YCIG... |

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Citation Context ...4. Other literature There is an extensive literature on the evaluation of models, going back at least to the Keynes-Tinbergen exchange (Keynes 1939 and 1940, Tinbergen 1940). Also see (Liu 1960) and (=-=Lucas 1976-=-). For more recent discussions, with other citations to the literature, see (Freedman 1987 and 1991). Many authors have tried to explain the basis for inferring causation by using regression. See, for... |

407 | Maximum Likelihood Estimation of Misspecified Dynamic Models - White - 1984 |

373 | Fusion, Propagation and Structuring in Belief Networks
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Citation Context ...here is a connection between the theory of "Directed Acyclic Graphs" (DAGs) and conditional independence of random variables. (See Darroch et al. 1980, Kiiveri and Speed 1982, Speed and Kiiveri 1986; =-=Pearl 1986-=-, Pearl 1988, Verma and Pearl 1990, Geiger 1990, Pearl and Verma 1991.) Much of this work is reviewed in SGS and CG. However, the mathematics of nonlinear causal diagrams seems to be irrelevant to the... |

304 |
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Citation Context ...s to the literature, see (Freedman 1987 and 1991). Many authors have tried to explain the basis for inferring causation by using regression. See, for example, (Pratt and Schlaifer 1984 and 1988), or (=-=Holland 1986-=- and 1988). Of enthusiastic views on social-science modeling, there is no shortage; see, for instance, (Smelser and Gerstein 1986) or (Bartels and Brady 1993). For a recent discussion of causal modeli... |

205 | A theory of inferred causation
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Citation Context ...c Graphs" (DAGs) and conditional independence of random variables. (See Darroch et al. 1980, Kiiveri and Speed 1982, Speed and Kiiveri 1986; Pearl 1986, Pearl 1988, Verma and Pearl 1990, Geiger 1990, =-=Pearl and Verma 1991-=-.) Much of this work is reviewed in SGS and CG. However, the mathematics of nonlinear causal diagrams seems to be irrelevant to the big question: how do we infer causation from association? Most the a... |

169 | The American Occupational Structure - Blau, Duncan - 1967 |

146 |
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Citation Context ...esults as intervening to set X = x. 39There are tests for exogeneity in the literature, as well as model specification tests. However, these have limited relevance to causal inference. For example, (=-=Hausman 1978-=-) assumes that certain variables are known a priori to be exogenous, and then tests whether other variables are exogenous; he interprets exogeneity as orthogonality to disturbance terms. He also has a... |

118 |
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Citation Context ...new matrix is still positive definite, so it is a legitimate correlation matrix. Section 12.1 discusses the connection between the Timberlake-Williams model and the faithfulness assumption. Also see (=-=Cartwright 1989-=-, 79-84). 38s11. Some mathematical issues Sections 11 and 12 address by mathematical example two questions: (i) To what extent can correlational methods recover an underlying path diagram? (ii) When c... |

96 | Causal networks: semantics and expressiveness
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Citation Context ...ween the theory of "Directed Acyclic Graphs" (DAGs) and conditional independence of random variables. (See Darroch et al. 1980, Kiiveri and Speed 1982, Speed and Kiiveri 1986; Pearl 1986, Pearl 1988, =-=Verma and Pearl 1990-=-, Geiger 1990, Pearl and Verma 1991.) Much of this work is reviewed in SGS and CG. However, the mathematics of nonlinear causal diagrams seems to be irrelevant to the big question: how do we infer cau... |

95 | Comment: Graphical models, causality, and intervention
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Citation Context ...tion of autonomy (i.e., that each parameter can be perturbed without altering the others), the model cannot predict the effect of interventions or other changes.... [personal communication] Also see (=-=Pearl 1993-=-; Pearl and Wermuth 1993). 64s14. Other literature There is an extensive literature on the evaluation of models, going back at least to the Keynes-Tinbergen exchange (Keynes 1939 and 1940, Tinbergen 1... |

91 |
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Citation Context ...ated. 4 (Meehl 1954) provides some well-known examples. Predictive validity is best demonstrated by making real ex ante forecasts in several different contexts (Ehrenberg and Bound 1993). 5 Also see (=-=Manski 1993-=-). 6sAt this remove, the flaws in Yule’s argument may be apparent. For example, there seem to be some important variables missing from the equation, including variables that measure economic activity.... |

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Citation Context ...h consistent with that matrix. 49s11.5 Methodological contributions There is a connection between the theory of "Directed Acyclic Graphs" (DAGs) and conditional independence of random variables. (See =-=Darroch et al. 1980-=-, Kiiveri and Speed 1982, Speed and Kiiveri 1986; Pearl 1986, Pearl 1988, Verma and Pearl 1990, Geiger 1990, Pearl and Verma 1991.) Much of this work is reviewed in SGS and CG. However, the mathematic... |

70 |
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(Show Context)
Citation Context ... the stratification model of Blau and Duncan (1964). SGS (pp. 142-5) and CG (pp. 21-22) seem to be quite critical of this model; their current position is almost diametrically opposite to the one in (=-=Glymour et al. 1987-=-, 33-9). Like SGS, I do not believe that the Blau-Duncan regressions are a satisfactory causal model. On the other hand, as descriptions of the data, the equations can tell us something important abou... |

70 |
Clinical versus Statistical Prediction: a Theoretical Analysis and a Review of the Evidence
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- 1954
(Show Context)
Citation Context ...causal inference, it is the individual coefficients that do the trick. In equation (1), for example, it is b that should tell you what happens to pauperism when the outrelief ratio is manipulated. 4 (=-=Meehl 1954-=-) provides some well-known examples. Predictive validity is best demonstrated by making real ex ante forecasts in several different contexts (Ehrenberg and Bound 1993). 5 Also see (Manski 1993). 6sAt ... |

70 |
Gaussian Markov distributions over finite graphs
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- 1986
(Show Context)
Citation Context ...ological contributions There is a connection between the theory of "Directed Acyclic Graphs" (DAGs) and conditional independence of random variables. (See Darroch et al. 1980, Kiiveri and Speed 1982, =-=Speed and Kiiveri 1986-=-; Pearl 1986, Pearl 1988, Verma and Pearl 1990, Geiger 1990, Pearl and Verma 1991.) Much of this work is reviewed in SGS and CG. However, the mathematics of nonlinear causal diagrams seems to be irrel... |

68 | Causal inference, path analysis, and recursive structural equation models - Holland - 1988 |

66 |
Introduction to structural equation models
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- 1975
(Show Context)
Citation Context ...(b) U V Y X Y Z Notes: In panel (a), X and Z are assumed to be independent. In panel (b), U and V are assumed to be independent; it may be shown in consequence that X and Z are independent. Also see (=-=Duncan 1975-=-, 113-27). 11s4. Two ideas of conditional probabilities The distinction between the two ideas of conditioning-selecting subjects with X = x, or intervening to set X = x-seems fundamental. A concrete e... |

60 | Linear Statistical Inference and its Applications, 2nd ed - Rao - 1973 |

43 |
The history of statistics
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(Show Context)
Citation Context ...ssociation. This is a bold claim, which does not survive examination. 1 Gauss was fitting orbits to astronomical observations, with least squares to estimate the elements of the orbits (Gauss 1809). (=-=Stigler 1986-=-, 145-46) awards priority to (Legendre 1805). 2sThe balance of this paper is organized as follows. Section 2 discusses Yule’s work. Sections 3 and 4 explain the critical idea of "exogeneity." Section ... |

41 |
Linear dependencies represented by chain graphs
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(Show Context)
Citation Context ...). Of enthusiastic views on social-science modeling, there is no shortage; see, for instance, (Smelser and Gerstein 1986) or (Bartels and Brady 1993). For a recent discussion of causal modeling, see (=-=Cox and Wermuth 1993-=-). 15. Conclusions SGS have not succeeded in clarifying the circumstances under which causal inferences can be drawn from observed associations, nor have they invented a reliable engine for performing... |

39 | Nouvelles méthodes pour la détermination des orbites des cometes - Legendre |

34 | On the Interpretation and Observation of Laws - Pratt, Schlaiffer - 1988 |

30 |
Structural analysis of multivariate data: a review. Sociological Methodology
- Kiiveri, Speed
- 1982
(Show Context)
Citation Context ...t matrix. 49s11.5 Methodological contributions There is a connection between the theory of "Directed Acyclic Graphs" (DAGs) and conditional independence of random variables. (See Darroch et al. 1980, =-=Kiiveri and Speed 1982-=-, Speed and Kiiveri 1986; Pearl 1986, Pearl 1988, Verma and Pearl 1990, Geiger 1990, Pearl and Verma 1991.) Much of this work is reviewed in SGS and CG. However, the mathematics of nonlinear causal di... |

29 |
Graphoids: a qualitative framework for probabilistic inference
- Geiger
- 1990
(Show Context)
Citation Context ...rected Acyclic Graphs" (DAGs) and conditional independence of random variables. (See Darroch et al. 1980, Kiiveri and Speed 1982, Speed and Kiiveri 1986; Pearl 1986, Pearl 1988, Verma and Pearl 1990, =-=Geiger 1990-=-, Pearl and Verma 1991.) Much of this work is reviewed in SGS and CG. However, the mathematics of nonlinear causal diagrams seems to be irrelevant to the big question: how do we infer causation from a... |

27 |
Professor Tinbergen’s Method
- KEYNES
- 1939
(Show Context)
Citation Context ...mmunication] Also see (Pearl 1993; Pearl and Wermuth 1993). 64s14. Other literature There is an extensive literature on the evaluation of models, going back at least to the Keynes-Tinbergen exchange (=-=Keynes 1939-=- and 1940, Tinbergen 1940). Also see (Liu 1960) and (Lucas 1976). For more recent discussions, with other citations to the literature, see (Freedman 1987 and 1991). Many authors have tried to explain ... |

26 | The logic of influence diagrams - Pearl, Geiger, et al. |

25 |
Vector Autoregressions for Causal Inference
- Leamer
- 1985
(Show Context)
Citation Context ...ut only "super" exogeneity permits estimating the effects of interventions. Examples are given to illustrate the definitions (Engle, Hendry, and Richard 1983, 287-94). There is further discussion in (=-=Leamer 1985-=-). 40s11.1 The basic statistical problem Suppose you have n random variables with a jointly normal distribution; all the variables have mean 0, and you know the covariance matrix, which is positive de... |

19 |
Introduction to Econometrics, 2nd ed
- Maddala
- 1992
(Show Context)
Citation Context ...measured on Duncan’s scale, combining information on education and income; missing values were imputed at the overall mean. SGS (p. 139) give the wrong definitions for NOSIB and ADOLF. 10 See, e.g., (=-=Maddala 1992-=-); for discussion, see (Daggett and Freedman 1985). 17sIf looked at coldly, the argument may seem implausible. A critique can be given along the following lines. (i) Statistical assumptions. Just why ... |

17 |
1992a) As others see us: a case study in path analysis
- Freedman
(Show Context)
Citation Context ...eir effects. I have discussed such models elsewhere, and do not believe they offer much help in deducing causation from association, because there is little evidence to support the basic assumptions (=-=Freedman 1987-=-). To pursue the discussion here, a slightly more explicit definition of the models may be in order. Definition. A "path model" starts with variables at "level 0," which are exogenous in the minimal s... |

16 | Statistical models and shoe leather - Freedman - 1991 |

16 |
Specification tests in econometrics," Econometrica 46
- Hausman
- 1978
(Show Context)
Citation Context ...esults as intervening to set X = x. 39sThere are tests for exogeneity in the literature, as well as model specification tests. However, these have limited relevance to causal inference. For example, (=-=Hausman 1978-=-) assumes that certain variables are known a priori to be exogenous, and then tests whether other variables are exogenous; he interprets exogeneity as orthogonality to disturbance terms. He also has a... |

14 |
Underidentification, structural estimation, and forecasting
- Liu
- 1960
(Show Context)
Citation Context ...uth 1993). 64s14. Other literature There is an extensive literature on the evaluation of models, going back at least to the Keynes-Tinbergen exchange (Keynes 1939 and 1940, Tinbergen 1940). Also see (=-=Liu 1960-=-) and (Lucas 1976). For more recent discussions, with other citations to the literature, see (Freedman 1987 and 1991). Many authors have tried to explain the basis for inferring causation by using reg... |

14 | Education and fertility: implications for the roles women occupy - John - 1980 |

12 |
1997) The regression method of causal inference and a dilemma confronting this method
- Clogg, Haritou
(Show Context)
Citation Context ...section, as will the idea of "structural" equations. 11 The solution to the "omitted variable" problem may seem easy-- just throw some more variables into the model. The difficulties are explored in (=-=Clogg and Haritou 1994-=-). Also see (Freedman 1983). 18s5.1 A thought experiment Figure 4. A simpler version of the model. DADSOCC FEC A simpler version of the model restricts attention to a more homogenous group of women, w... |

12 |
Dependence, political exclusion, and government repression: Some cross-national evidence
- Timberlake, Williams
- 1984
(Show Context)
Citation Context ...ts are shown in the first three columns of Table 7. The estimated coefficient of FI is significantly positive, and is interpreted as measuring the effect of foreign investment on political exclusion (=-=Timberlake and Williams 1984-=-, 143). 36sTable 7. The Timberlake and Williams model. Political exclusion (PO) is regressed on foreign investment (FI), energy development (EN), and civil liberties (CV). The first three columns show... |

10 |
On the nature and discovery of structure
- Pratt, Schlaifer
- 1984
(Show Context)
Citation Context ... recent discussions, with other citations to the literature, see (Freedman 1987 and 1991). Many authors have tried to explain the basis for inferring causation by using regression. See, for example, (=-=Pratt and Schlaifer 1984-=- and 1988), or (Holland 1986 and 1988). Of enthusiastic views on social-science modeling, there is no shortage; see, for instance, (Smelser and Gerstein 1986) or (Bartels and Brady 1993). For a recent... |

9 |
Cancer: Science and
- Cairns
- 1978
(Show Context)
Citation Context ... births set the conditions under which other roles are assumed.... Education is another prime factor conditioning female roles. [p. 431, footnote omitted] 8 For a discussion of the epidemiology, see (=-=Cairns 1978-=-, Peto and zur Hausen 1986, Sherman et al. 1991, Hakama et al. 1993). 9 I use this example because it is discussed by SGS pp. 139-40; also see CG pp. 14-15. 14sThe overall relationship between educati... |

9 | Maximum Likelihood Estimation of Misspecified Models - unknown authors - 1982 |

8 |
Predictability and Prediction
- Ehrenberg, Bound
- 1993
(Show Context)
Citation Context ...ism when the outrelief ratio is manipulated. 4 (Meehl 1954) provides some well-known examples. Predictive validity is best demonstrated by making real ex ante forecasts in several different contexts (=-=Ehrenberg and Bound 1993-=-). 5 Also see (Manski 1993). 6sAt this remove, the flaws in Yule’s argument may be apparent. For example, there seem to be some important variables missing from the equation, including variables that ... |

8 |
Early Childbearing and Later Economic WellBeing, American Sociological Review
- Hofferth, Moore
- 1979
(Show Context)
Citation Context ...om association. Their theory is summarized in (Glymour 1993), cited as CG. For present purposes, a "path model" is a recursive system of regression equations, in which the dependent variables 13 See (=-=Hofferth and Moore 1979-=-, Moore and Hofferth 1980). An "instrument" is an exogenous variable, used as part of the two-stage least squares estimation procedure. Some investigators may draw a terminological distinction: an "in... |

8 |
Reply to Keynes
- Tinbergen
- 1940
(Show Context)
Citation Context ...(Pearl 1993; Pearl and Wermuth 1993). 64s14. Other literature There is an extensive literature on the evaluation of models, going back at least to the Keynes-Tinbergen exchange (Keynes 1939 and 1940, =-=Tinbergen 1940-=-). Also see (Liu 1960) and (Lucas 1976). For more recent discussions, with other citations to the literature, see (Freedman 1987 and 1991). Many authors have tried to explain the basis for inferring c... |

7 |
Instrumental and ‘Quasi-Instrumental’ Variables
- Bartels
- 1991
(Show Context)
Citation Context ...er. (Rindfuss et al. 1984, 981-82). In short, results can depend quite strongly on assumptions of exogeneity, and there is no good way to justify one set of assumptions rather than another. Also see (=-=Bartels 1991-=-), who comments on the impact of exogeneity assumptions, and the difficulty of verification. 6. Automated searches for causality SGS (Spirtes, Glymour, and Scheines 1992) have computerized algorithms ... |

7 |
A review of recent work on the foundations of causal inference
- Glymour
- 1997
(Show Context)
Citation Context ...plications of regression techniques to social science is (Yule 1899). Recent examples will be found in (Spirtes, Glymour, and Scheines 1992), to be cited here as SGS. (The SGS theory is summarized in =-=Glymour 1993-=-, cited as CG.) SGS have attracted considerable attention in the philosophy of science, because they have developed computerized algorithms that search for path models. With their algorithms, SGS clai... |

7 |
A Note on Screening Regression Equations.” The American Statistician 37(2
- Freedman
- 1983
(Show Context)
Citation Context ...tural" equations. 11 The solution to the "omitted variable" problem may seem easy-- just throw some more variables into the model. The difficulties are explored in (Clogg and Haritou 1994). Also see (=-=Freedman 1983-=-). 185.1 A thought experiment Figure 4. A simpler version of the model. DADSOCC ED *** FEC AGE A simpler version of the model restricts attention to a more homogenous group of women, where the only r... |

6 |
Twins, smoking and mortality: a 12-year prospective study of smoking-discordant twin pairs
- Kaprio, Koskenvuo
- 1989
(Show Context)
Citation Context ...sumptions. Instead, they studied the matter empirically, using data from twin studies. For a recent report on the Swedish twin registry, see (Floderus et al. 1988). On the Finnish twin registry, see (=-=Kaprio and Koskenvuo 1989-=-). Data on the Danish twin registry are fragmentary. There are forthcoming data on the U.S. twin registry, which are quite strong (Dorit Carmelli, personal communication). The numbers on lung cancer a... |

4 |
The State of Quantitative Political Methodology
- Bartels, Brady
- 1993
(Show Context)
Citation Context ...or example, (Pratt and Schlaifer 1984 and 1988), or (Holland 1986 and 1988). Of enthusiastic views on social-science modeling, there is no shortage; see, for instance, (Smelser and Gerstein 1986) or (=-=Bartels and Brady 1993-=-). For a recent discussion of causal modeling, see (Cox and Wermuth 1993). 15. Conclusions SGS have not succeeded in clarifying the circumstances under which causal inferences can be drawn from observ... |

4 |
On the identification of nonparametric structural equations
- Pearl
- 1994
(Show Context)
Citation Context ...ting others from continuing their education.) Group II. Daughters are randomized to the various levels of AGE, and ED is observed as the response. (More gedanken intervention is needed.) 12 Also see (=-=Pearl 1994-=-ab). 19sThe statistical model can now be translated. For the women in Group I, AGE should not depend on DADSOCC-- the "no arrow" assumption; however, AGE should depend linearly on ED. For the women in... |

4 |
1993]: TETRAD II: Documentation for Version 2.2
- Spirtes, Scheines, et al.
(Show Context)
Citation Context ...; without this assumption (SGS p. 45; CG p. 4), the program output is uninformative. Therefore, I told BUILD to make the assumption; I believe that is what SGS did for the Rindfuss example. Also see (=-=Spirtes et al. 1993-=-, 13-15). I told BUILD that ED and AGE could not cause the remaining variables, following (SGS p. 139). However, SGS actually made the stronger assumption that (i) FEC, ED and AGE could not cause YCIG... |