Variance matters: the shape of a datum

Area of Science:

• Quantitative Psychology
• Behavioral Analysis
• Mathematical Psychology

Background:

• Behavioral choice data are typically analyzed using logarithmic transforms of response and reinforcer ratios.
• The generalized-matching relation is a common framework for analyzing these choice data.
• Ordinary linear regression is the standard method for assessing the relationship between log choice and log reinforcer ratios.

Purpose of the Study:

• To identify limitations of ordinary linear regression in analyzing behavioral choice data.
• To propose an alternative analytical approach that addresses the inherent variance in log reinforcer ratios.
• To improve the accuracy of parameter estimates in models of hyperbolic and exponential decay processes.

Main Methods:

• Critique of ordinary linear regression assumptions (normality, equal variance, fixed x-values).
• Argument for the non-normal and skewed distribution of log reinforcer ratios due to binomial processes.
• Description of an alternative approach for analyzing choice data when variance in choice is measured.

Main Results:

• Ordinary linear regression systematically underestimates generalized-matching sensitivity.
• Faulty parameter estimates arise from non-linear regression applied to hyperbolic and exponential decay processes.
• Model comparisons are compromised by the assumption of normally distributed error around each data point.

Conclusions:

• The variance in log reinforcer ratios necessitates an analytical approach beyond ordinary linear regression.
• Accurate quantitative analysis of behavior requires methods that account for the true distribution of choice data.
• The proposed alternative approach offers improved accuracy for parameter estimation and model comparison in behavioral research.