Safeguarding against bad luck when attempting to discredit a state-trace model

Publication date: Available online 31 January 2019Source: Journal of Mathematical PsychologyAuthor(s): Donald BamberAbstractA state-trace model for a natural phenomenon proposes that there is a causal “bottleneck” that makes the joint causal effects of two independent variables look like the effect of a single independent variable. Imagine that a state-trace model has been formulated, but the model seems implausible and we wish to find empirical evidence that it is wrong. How can we do that? Given reasonable monotonicity assumptions, a state-trace model is wrong if a point on one state trace is delta-discordant with a point on another state trace. [We say that two points (x,y) and (x′,y′) in the plane are delta-discordant if Δx=x′−x and Δy=y′−y are nonzero and have opposite signs.] So, to show the model wrong, we need to find a pair of delta-discordant points lying on different state traces. One method for finding two such points is to observe multiple points on each of two state traces with the hope that, among those points, there will be a delta-discordant pair. But this approach can have bad luck and fail to find delta-discordant pairs even though they exist. A new approach to “locating” a delta-discordant pair of points, an approach that is much less dependent on luck, is formulated in this paper. In addition, the paper describes a statistical test for evaluating whether the “located” points are really delta-discordant.

Source: Journal of Mathematical Psychology - February 1, 2019 Category: Psychiatry & Psychology Source Type: research