Skew-normal response family

skew_normal() defines a one-response skew-normal distribution with formulas for location mu, residual standard deviation sigma, and residual slant nu.

Usage

skew_normal()

Value

A drm_family object.

Details

The implemented family is univariate: mu = eta_mu, log(sigma) = eta_sigma, and nu = eta_nu. The likelihood transforms internally to the native Azzalini location xi, scale omega, and slant alpha = nu, but user-facing methods keep the public moment parameterization: fitted() returns E[y] = mu, stats::sigma() returns SD[y] = sigma, and predict(..., dpar = "nu") returns the residual slant. Positive nu gives right-skewed residuals, negative nu gives left-skewed residuals, and nu = 0 reduces to the Gaussian location-scale likelihood.

Ordinary unlabelled random intercepts and independent numeric slopes such as (1 | id) and (0 + x | id) may enter mu. Correlated or labelled mu slopes, sigma or nu random effects, sd(group) scale formulas, structured effects, known sampling covariance, bivariate skew-normal models, residual rho12, and latent skew(id) syntax remain unsupported.

Examples

skew_normal()
#> $name
#> [1] "skew_normal"
#> 
#> $family
#> [1] "skew_normal"
#> 
#> $n_response
#> [1] 1
#> 
#> $dpars
#> [1] "mu"    "sigma" "nu"   
#> 
#> $links
#>         mu      sigma         nu 
#> "identity"      "log" "identity" 
#> 
#> attr(,"class")
#> [1] "drm_family"