Treatments for undefined log ratios in matching analyses

Caron (2024) ran a computer simulation. The goal was to find the cleanest way to handle zero rates in matching-law data.

When a child never picks the left bin, the reinforcer rate for that bin is zero. Taking the log of zero gives infinity, so the ratio is undefined.

Five fixes were compared: adding 0.5, adding 1/10, dropping the point, or two kinds of full-information maximum likelihood (FIML).

Dropping the undefined point worked best. FIML came in second. Both kept bias near zero and gave the tightest estimates.

Adding small constants looked easy, but the simulation showed they tilted the slope. The tilt was small, yet it was still wrong.

Nakamura et al. (1986) showed the matching law usually fits pigeon and human data. Caron assumes that classic picture is true; the new paper just keeps the math clean when zeros show up.

Villarreal et al. (2019) offered Bayesian graphs as another way to estimate matching parameters. Caron stays in the frequentist world, yet both papers push analysts past the old "add a constant" habit.

Falligant et al. (2020) also used simulation to warn that ad-hoc rules can inflate false positives. Caron echoes that warning for matching ratios: quick fixes often sneak bias into your slope.

Next time you graph a concurrent-schedule session, skip the "add 0.5" cheat. Drop the zero point or use the FIML script your stats package already has. Your sensitivity to reinforcement shifts will stay honest—and your treatment decisions will rest on cleaner data.