Temporalization In Causal Modeling. Jonathan Livengood & Karen Zwier TaCitS 06/07/2017

Transcription

1 Temporalization In Causal Modeling Jonathan Livengood & Karen Zwier TaCitS 06/07/2017

2 Temporalization In Causal Modeling Jonathan Livengood & Karen Zwier TaCitS 06/07/2017

3 Introduction Causal influence, as it is modeled and discussed in the social sciences, is widely agreed to require time to propagate. Causes precede their effects in time. This is a common-sense view: a platitude.

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13 Introduction Social scientists and statisticians talking about methodology agree that causes precede their effects. In their theoretical remarks, they express a commitment to the common sense idea that causation does not run backward through time.

14 Warren Miller One way or another, any causal explanation of some dependent occurrence must include the fact that the cause of an effect preceded the effect.

15 To reasonably infer that X is a cause of Y, there must be time precedence; that is, X precedes Y in time. Rex Kline

16 James Davis The great principle of causal order [is this]: after cannot cause before.

17 For a relationship to admit a causal interpretation, we require that Hume s criterion of temporal succession be met. Michael Sobel

18 Paul Holland The role of time now becomes important because of the fact that when a unit is exposed to a cause this must occur at some specific time or within a specific time period. Response variables must fall into the post-exposure class.

19 Introduction Philosophers and methodologists have also endorsed the commonsense idea that causes precede effects, and some have suggested using information about time-ordering for selecting or constructing appropriate causal models.

20 Clark Glymour Knowledge of time order permits decisions about causal dependence that outweigh strength of association and other factors.

21 Clark Glymour If one observes A occurring before B and B before C, the fact that C is more strongly associated with B than is A does not lead one to think that C is the more likely, or stronger, cause of B; instead, one concludes that C is no cause at all of B.

22 Clark Glymour In typical social studies, time order often provides the only reliable information negative information, at that about cause and effect.

23 Introduction But ordinary practice is often neither explicit nor careful about the relationship between causation and time. An area of special concern is the widespread use of cross-sectional data to construct time-free models.

24 Introduction Two time-free causal models. Dawes et al. (2015) Livengood et al. (2010)

25 Introduction In our paper, Karen and I propose the following Temporalization Criterion of Admissibility for causal models: A causal model is admissible if and only if there is at least one temporalized version of the model that is responsible to the data and preserves a common-sense temporal ordering of causes and effects.

26 Introduction In our paper, Karen and I propose the following Temporalization Criterion of Admissibility for causal models: A causal model is admissible if and only if there is at least one temporalized version of the model that is responsible to the data and preserves a common-sense temporal ordering of causes and effects. Is the criterion trivial?

27 Introduction The rest of my talk today is organized around making the Temporalization Criterion of Admissibility clear and defending the claim that such a weak, necessary condition is nonetheless non-trivial. Temporal Ordering Temporalization Responsible Modeling

28 Temporal Ordering According to common sense, causes precede their effects in time. And we ve seen several social scientists, statisticians, and philosophers endorsing that common-sense idea. Can we give a precise articulation to the platitude that is suitable for social scientific work?

29 Temporal Ordering Here is a first attempt, which we call the Naïve Causal Temporality Principle: For any two variables X and Y, if X occurs at time t and Y occurs at time t* and X is a cause of Y, then t < t*.

30 Temporal Ordering At first blush, the Naïve CTP looks pretty good. It s basically what Kline said in the pull quote we saw earlier.

31 Temporal Ordering At first blush, the Naïve CTP looks pretty good. It s basically what Kline said in the pull quote we saw earlier. But let us be philosophers and ask, What does it mean for a variable to occur?

32 Temporal Ordering At first blush, the Naïve CTP looks pretty good. It s basically what Kline said in the pull quote we saw earlier. But let us be philosophers and ask, What does it mean for a variable to occur? From a mathematical point of view, a variable is just a set of ordered pairs. But is a set the sort of thing that can occur?

33 Temporal Ordering Maybe a variable represents something that occurs. But the most plausible thing (at least, relative to the notation) for a variable to represent is a property universal. And property universals also don t seem to be the sorts of things that occur.

34 Temporal Ordering Let s try revising the Naïve CTP in order to avoid having to think about variables occurring. Here is a proposal, which we call the Revised Causal Temporality Principle: For any two variables X t and Y t*, where the indices t and t* indicate the respective times at which X and Y are measured for the same unit u: if X t is a cause of Y t*, then t < t*.

35 Temporal Ordering The Revised CTP is an improvement in some respects, and it is very similar to instructions that Spirtes, Glymour, and Scheines (2000) give for adding temporal information to their graphical search procedures. But it is too strict.

36 Temporal Ordering Consider the system whose outputs look like the time trace below. In this system, B causes A. But if we measure in the way suggested in the time traces here and apply the Revised CTP, we will say that A causes B.

37 Temporal Ordering Hence, we need at least one more revision. Perhaps this principle also fails, but so far, we are happy with it, so we call it simply the Causal Temporality Principle: For any two variables X t and Y t*, where the indices t and t* indicate the times at which X and Y take on their respective values for the same unit u: if X t is a cause of Y t*, then t < t*.

38 Temporalization Given the CTP, we may restate the Temporalization Criterion of Admissibility as follows: A causal model is admissible if and only if there is at least one temporalized version of the model that is responsible to the data and satisfies the CTP.

39 Temporalization Let s turn now to the question of what it means to temporalize a causal model. First pass: Give the variables in the model a partial ordering representing their temporal relations. Dawes et al. (2015)

40 Temporalization Let s turn now to the question of what it means to temporalize a causal model. t A < t B < t C < t D t A t B t C t D First pass: Give the variables in the model a partial ordering representing their temporal relations. Dawes et al. (2015)

41 Temporalization Let s turn now to the question of what it means to temporalize a causal model. t A < t B < t C < t D t A t B t D Of course, the order we put on the temporal indices need not reflect the causal order. t C Dawes et al. (2015)

42 Temporalization Alternatively, we could focus on the causal processes themselves and specify how long they take. L=1 L=3 L=2 Second pass: Give the lag times for each edge in the graph. L=2 L=1 L=1 Dawes et al. (2015)

43 Temporalization Alternatively, we could focus on the causal processes themselves and specify how long they take. L=1 L=2 L=3 L=2 L=1 L=1 As with ordering time indices, the lag times need not match the causal order. Dawes et al. (2015)

44 Temporalization Finally, we might break up a variable into indexed time-slices and draw a new causal graph, which we call a time-slice temporalization.

45 Temporalization I think that requiring time-slice temporalization is not unreasonable. But a weaker notion might be substituted. Regardless of the version of temporalization one endorses, temporalizing a time-free graph introduces an enormous amount of under-determination.

46 Responsible Modeling Given the amount of freedom we have in temporalizing a time-free causal model, one might be skeptical that the Temporalization Criterion of Admissibility places any constraints at all on practice.

47 Responsible Modeling In this section of the talk, I argue that there are real, concrete cases in the social science literature that do not satisfy the Temporalization Criterion of Admissibility. Simons et al. on religiosity and risky sexual behavior Timberlake and Williams on foreign investment and repression Beilock et al. on teacher math anxiety and student success

48 Responsible Modeling In this section of the talk, I argue that there are real, concrete cases in the social science literature that do not satisfy the Temporalization Criterion of Admissibility. Simons et al. on religiosity and risky sexual behavior Timberlake and Williams on foreign investment and repression Beilock et al. on teacher math anxiety and student success

49 Responsible Modeling A temporalization is responsible to the data only if it satisfies the following requirements: First, it assigns time indices to variables in a manner that is consistent with the temporal features of the data as they were generated or collected. Second, when temporalization yields a redrawn graph, the redrawn graph accurately represents the statistical features of the data.

50 Responsible Modeling Simons, Burt, and Peterson (2009) used pencil and paper surveys to collect data on 2,108 undergraduates enrolled in sociology courses in They measured (or attempted to measure) a number of features relevant to religiosity and risky sexual behavior, including feelings about first intercourse, age at first intercourse, attitudes about sexual permissiveness, and number of sexual partners.

51 Responsible Modeling They drew the following graph for males (and a similar one for females): Commitment Religiosity Permissiveness Feelings Num Partners Debut Age

52 Responsible Modeling The question they used to measure Religiosity was What is the influence of religion in your life? But in order for their causal model to be responsible to the data, the variable would need to capture respondents religiosity for the time leading up to their first intercourse.

53 Responsible Modeling Similarly, their measure of attitudes about sexual permissiveness did not specify the time at which those permissive attitudes were held by the respondents. But given the wording, the most likely property being measured was the current attitudes of the respondents.

54 Responsible Modeling And some questions were themselves temporally ambiguous. They asked, With whom did you first have sexual intercourse? And they offered the response choices never had sexual intercourse, spouse after marriage, fiancé, steadily dating partner, and casual acquaintance. In order for the temporal properties to be clear, the respondents would need to specify their relationship at the time of first intercourse. The question does not make this adequately clear.

55 Responsible Modeling The upshot is a dilemma: either apply the CTP to constrain the timeordering of the variables in the model and have a model without adequate empirical support or accept the temporal properties of the variables as given in the time-free model and reject the CTP.

56 Responsible Modeling Beilock, Gunderson, Ramirez, and Levine (2010) investigated the influence that the math anxiety of elementary educators has on their students. They measured the math ability of 117 boys and girls in firstand second-grade classes some time in the first three months and then again in the last two months of the school year.

57 Responsible Modeling They also measured the children s gender ability beliefs at the beginning and end of the school year. And they measured the teachers math ability and math anxiety some time in the last two months of the school year.

58 Responsible Modeling Beilock et al. found no association between teacher anxiety (measured only once, recall, at the end of the year) and student achievement at the beginning of the year. But

59 Regression analysis established that teachers math anxiety had a significant negative effect on girls [but not boys ] math achievement at the end of the school year. Sian Beilock

60 Responsible Modeling They also found that when gender ability beliefs were included in the statistical model, the association between math achievement and teacher anxiety became non-significant.

61 In early elementary school, where the teachers are almost all female, teachers math anxiety carries consequences for girls math achievement by influencing girls beliefs about who is good at math. Sian Beilock

62 Responsible Modeling The causal models Beilock et al. drew are time-free. But the measurements they made were temporally ordered.

63 Responsible Modeling If we try to build in the temporal relations in a natural way that retains the statistical properties of the original graph, we obtain:

64 Responsible Modeling But this model violates the CTP, since there are causal relations between variables that have the same time index.

65 Responsible Modeling One might hope that a more fine-grained temporalization will help. Thinking about the physical system, one might try:

66 Responsible Modeling But unlike the simple model, this more complicated model does not entail that TMA(f) and GMA(f) are independent conditional on GAB(f).

67 Responsible Modeling But unlike the simple model, this more complicated model does not entail that TMA(f) and GMA(f) are independent conditional on GAB(f).

68 Responsible Modeling Hence, the original model is inadmissible, since its temporalized versions either violate the CTP or fail to be responsible to the data. And so, the Temporalization Criterion of Admissibility puts a non-trivial constraint on causal modeling.

69 Summing Up I began this talk by observing that according to ordinary common sense, causes precede their effects in time. And I gave examples of social scientists, statisticians, and philosophers endorsing that view.

70 Summing Up I proposed a weak, necessary condition on causal modeling: the Temporalization Criterion of Admissibility. I sharpened up some of the moving parts of the criterion, and then I argued that the criterion places non-trivial constraints on the practice of causal modeling in the social sciences by considering a couple of concrete examples.

71 Thank you for your attention.