2 Analyzing the Direction of Causation

Students of elementary statistics have long been made to recite ``correlation does not imply causation'' and rightly so, because a premature assignment of causality to a mere statistical association could waste scientific resources and do actual harm if treatment were to be based upon it. However, one of the goals of science is to analyze complex systems into elementary processes which are thought to be causal or more fundamental and, when actual experimental intervention is difficult, it may be necessary to look to the nexus of intercorrelations among measures for clues about causality.

The claim that correlation does not imply causality comes from a fundamental indeterminacy of any general model for the correlation between a single pair of variables. Put simply, if we observe a correlation between $A$ and $B$, it can arise from one or all of three processes: $A$ causing $B$ (denoted $A\longrightarrow B$), $B$ causing $A$, or latent variable $C$ causing $A$ and $B$. A general model for the correlation between $A$ and $B$ would need constants to account for the strength of the causal connections between $A$ and $B$, $B$ and $A$, $C$ and $A$, $C$ and $B$. Clearly, a single correlation cannot be used to determine four unknown parameters.

When we have more than two variables, however, matters may look a little different. It may now become possible to exclude some causal hypotheses as clearly inconsistent with the data. Whether or not this can be done will depend on the complexity of the causal nexus being analyzed. For example, a pattern of correlations of the form $r_{AC} = r_{AB} \times r_{BC}$ would support one or other of the causal sequences $A\longrightarrow B\longrightarrow C$ or $C\longrightarrow B\longrightarrow A$ in preference to orders that place A or C in the middle.

The fact that causality implies temporal priority has been used in some applications to advocate a longitudinal strategy for its analysis. One approach is the cross-lagged panel study in which the variables A and B are measured at two points in time, $t_0$ and $t_1$. If the correlation of A at $t_0$ with B at $t_1$ is greater than the correlation of B at $t_0$ with A at $t_1$, we might give some credence to the causal priority of A over B. Methods for the statistical assessment of such relative priorities are known as ``cross-lagged panel analysis'' [] and may assessed within structural equation models [].

The cross-lagged approach, though strongly suggestive of causality in some circumstances, is not entirely foolproof. With this fact in view, researchers are always on the look-out for other approaches that can be used to test hypotheses about causality in correlational data. It has recently become clear that the cross-sectional twin study, in which multiple measures are made only on one occasion, may, under some circumstances, allow us to test hypotheses about direction of causality without the necessity of longitudinal data. The potential contribution of twin studies to resolving alternative models of causation will be discussed in Chapter . At this stage, however, it is sufficient to give a simple insight about one set of circumstances which might lead us to prefer one causal hypothesis over another.

Consider the ambiguous relationship between exercise and body weight. In free-living populations, there is a significant correlation between exercise and body weight. How much of that association is due to the fact that people who exercise use up more calories and how much to the fact that fat people don't like jogging? In the simplest possible case, suppose that we found variation in exercise to be purely environmental (i.e., having no genetic component) and variation in weight to be partly genetic. Then there is no way that the direction of causation can go from body weight to exercise because, if this were the case, some of the genetic effects on body weight would create genetic variation in exercise. In practice, things are seldom that simple. Data are nearly always more ambiguous and hypotheses more complex. But this simple example illustrates that the genetic studies, notably the twin study, may sometimes yield valuable insight about the causal relationships between multiple variables.