dot-calc_alpha_star: Compute Normalized Alpha (Alpha Star) via the Delta Method

In beezdemand: Behavioral Economic Easy Demand

Compute Normalized Alpha (Alpha Star) via the Delta Method

Description

Implements Strategy B normalization of the demand elasticity parameter \alpha so that values are comparable across different k values (Rzeszutek et al., 2025). The formula is \alpha^* = -\alpha / \ln(1 - 1/(k \cdot \ln(b))) where b is the logarithmic base used by the demand equation (10 for HS/Koff, e for hurdle models).

Usage

.calc_alpha_star(params, param_scales, vcov = NULL, base = c("e", "10"))

Arguments

params	Named list of parameter values. Must contain entries matchable to alpha and k (e.g., alpha, log_alpha, log10_alpha).
param_scales	Named list indicating the scale of each parameter in params: "natural", "log", or "log10".
vcov	Optional. Either a variance–covariance matrix with named rows/columns, or a named numeric vector of standard errors for the alpha and k parameters.
base	Character; the logarithmic base: "e" (natural log, used by hurdle models) or "10" (log10, used by HS/Koff equations).

Details

Standard errors are obtained via the delta method when a variance–covariance matrix (or SE vector) is supplied.

Value

A list with elements:

estimate

Numeric scalar; the alpha_star value, or NA.

se

Numeric scalar; delta-method SE, or NA.

note

Character or NULL; diagnostic message if alpha_star could not be computed.

References

Rzeszutek, M. J., Regnier, S. D., Franck, C. T., & Koffarnus, M. N. (2025). Overviewing the exponential model of demand and introducing a simplification that solves issues of span, scale, and zeros. Experimental and Clinical Psychopharmacology.

beezdemand documentation built on March 3, 2026, 9:07 a.m.