P.Mean: Elbow model for accrual (created 2012-12-31). News: Sign up for "The Monthly Mean," the newsletter that dares to call itself average, www.pmean.com/news.

I was working on some elbow models for accrual. An elbow model is a linear regression model with a kink in it. The kink is a location where the slope changes, but the line is still continuous. I wanted to look at a particular elbow model for accrual where the accrual rate increases during a period of time, and then levels off. The increasing portion represents a "learning curve" where accrual is slower than the final rate.

This is a diagram of the elbow model. The actual formula for this model is a bit tricky. For values beyond the elbow, the line is flat (rate=alpha), but prior to the elbow, the rate is increasing linearly from an initial rate that is a fraction of the final rate.

The code was

lambda[i] <- alpha+step(elbow-i)*beta*(i-elbow)/elbow

but it should be

lambda[i] <- alpha+step(elbow-i)*alpha*(1-beta)*(i-elbow)/elbow

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