16.8 Ordered logistic distribution
16.8.1 Probability mass function
If K∈N with K>2, c∈RK−1 such that ck<ck+1 for k∈{1,…,K−2}, and η∈R, then for k∈{1,…,K}, OrderedLogistic(k | η,c)={1−logit−1(η−c1)if k=1,logit−1(η−ck−1)−logit−1(η−ck)if 1<k<K,andlogit−1(η−cK−1)−0if k=K. The k=K case is written with the redundant subtraction of zero to illustrate the parallelism of the cases; the k=1 and k=K edge cases can be subsumed into the general definition by setting c0=−∞ and cK=+∞ with logit−1(−∞)=0 and logit−1(∞)=1.
16.8.2 Sampling statement
k ~
ordered_logistic
(eta, c)
Increment target log probability density with ordered_logistic_lupmf(k | eta, c)
.
Available since 2.0
16.8.3 Stan functions
real
ordered_logistic_lpmf
(ints k | vector eta, vectors c)
The log ordered logistic probability mass of k given linear predictors
eta
, and cutpoints c
.
Available since 2.18
real
ordered_logistic_lupmf
(ints k | vector eta, vectors c)
The log ordered logistic probability mass of k given linear predictors
eta
, and cutpoints c
dropping constant additive terms.
Available since 2.25
int
ordered_logistic_rng
(real eta, vector c)
Generate an ordered logistic variate with linear predictor eta
and
cutpoints c
; may only be used in transformed data and generated quantities blocks
Available since 2.0