# Are these two variants of a stochastic model functionally equivalent?

I'm trying to figure out if two models of human information processing might differ in their ability to fit different data, or whether they're functionally identical.

The general framework is that information accumulates from a start point towards a threshold at a particular rate. There can be multiple accumulators, each with a different start point, accumulation rate, and threshold. The first accumulator to pass threshold "wins". The observable behaviour of the system consists of the response (which accumulator won) and response time (the time it took for the winning accumulator to reach threshold).

The system is run through multiple "trials" and across trials the accumulators vary from their mean accumulation rate according to a Normal distribution whose variance can vary from accumulator-to-accumulator.

The two variants I'm interested in comparing differ in whether the start point or the threshold are permitted to vary from trial-to-trial.

In the start-point-varying model, the threshold of each accumulator doesn't vary from that accumulator's mean threshold from trial to trial, but the start point of each accumulator varies around that accumulator's mean start point according to a uniform distribution with a range that is unique to each accumulator.

The threshold-varying model is the opposite: the start point of each accumulator doesn't vary from that accumulator's mean start point from trial to trial, but the threshold of each accumulator varies around that accumulator's mean threshold according to a uniform distribution with a range that is unique to each accumulator.

Are these two variants, start-point-varying vs threshold-varying, functionally identical, or would they yield qualitatively discriminable behaviour?

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The way I am understanding this question, we have a race, and in one situation each contestant is handicapped by a random starting line, and in the other each contestant is handicapped by a random goal line. So the situations are identical. – Dan Brumleve May 18 '11 at 2:29
Ah, I hadn't thought of that analogy, but that seems to make it pretty straight forward. – Mike Lawrence May 18 '11 at 3:07