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).
.calc_alpha_star(params, param_scales, vcov = NULL, base = c("e", "10"))A list with elements:
Numeric scalar; the alpha_star value, or NA.
Numeric scalar; delta-method SE, or NA.
Character or NULL; diagnostic message if alpha_star
could not be computed.
Named list of parameter values. Must contain entries matchable
to alpha and k (e.g., alpha, log_alpha, log10_alpha).
Named list indicating the scale of each parameter in
params: "natural", "log", or "log10".
Optional. Either a variance--covariance matrix with named rows/columns, or a named numeric vector of standard errors for the alpha and k parameters.
Character; the logarithmic base: "e" (natural log, used
by hurdle models) or "10" (log10, used by HS/Koff equations).
Standard errors are obtained via the delta method when a variance--covariance matrix (or SE vector) is supplied.
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.