a_ordaz"` - Aranda-Ordaz asymmetric (lambda \> 0) * lambda = 1: equals logit * lambda -\\> 0: approaches cloglog * `"gev"` - Generalized extreme value (shape parameter xi) * xi = 0: Gumbel (equals loglog) * xi \\< 0: Weibull (short tail) * xi \\> 0: Frechet (heavy tail) * `"sp"` - Symmetric power (r \> 0, base distribution) * r = 1: equals base distribution * 0 \\< r \\< 1: positively skewed * r \\> 1: negatively skewed * `"log_gamma"` - Log-gamma (lambda) * lambda = 0: equals probit * lambda \\> 0 or \\< 0: asymmetric * `"aep"` - Asymmetric exponential power (theta1 \> 0, theta2 \> 0) * alpha = 0.5 fixed for identifiability * theta1 = theta2: symmetric distribution * theta = 2: Gaussian kernel (but NOT equal to probit due to scaling) * theta \\< 2: heavy tails (leptokurtic) * theta \\> 2: light tails (platykurtic)1a:T5bf,clmstan supports the following link functions for cumulative link models: Standard links (no additional parameters): * `"logit"` - Logistic (proportional odds model) * `"probit"` - Normal (latent variable interpretation) * `"cloglog"` - Complementary log-log (proportional hazards) * `"loglog"` - Log-log (Gumbel minimum) * `"cauchit"` - Cauchy (heavy tails) Flexible links (with additional parameters): * `"tlink"` - Student-t (df \> 0) * df = Inf: equals probit * df \\< 3: increasingly heavy tails; df \\> 30 is nearly normal * `"aranda_ordaz"` - Aranda-Ordaz asymmetric (lambda \> 0) * lambda = 1: equals logit * lambda -\\> 0: approaches cloglog * `"gev"` - Generalized extreme value (shape parameter xi) * xi = 0: Gumbel (equals loglog) * xi \\< 0: Weibull (short tail) * xi \\> 0: Frechet (heavy tail) * `"sp"` - Symmetric power (r \> 0, base distribution) * r = 1: equals base distribution * 0 \\< r \\< 1: positively skewed * r \\> 1: negatively skewed * `"log_gamma"` - Log-gamma (lambda) * lambda = 0: equals probit * lambda \\> 0 or \\<

link_functions function