ordered_logistic_lpmf() [2/3]

template<bool propto, typename T_y , typename T_loc , typename T_cut , require_all_not_nonscalar_prim_or_rev_kernel_expression_t< T_y, T_loc, T_cut > * = nullptr>

return_type_t< T_loc, T_cut > stan::math::ordered_logistic_lpmf	(	const T_y &	y,
		const T_loc &	lambda,
		const T_cut &	c
	)

Returns the (natural) log probability of the specified array of integers given the vector of continuous locations and specified cutpoints in an ordered logistic model.

Typically the continuous location will be the dot product of a vector of regression coefficients and a vector of predictors for the outcome

\[ \frac{\partial }{\partial \lambda} = \begin{cases}\\ -\mathrm{logit}^{-1}(\lambda - c_1) & \mbox{if } k = 1,\\ -(((1-e^{c_{k-1}-c_{k-2}})^{-1} - \mathrm{logit}^{-1}(c_{k-2}-\lambda)) + ((1-e^{c_{k-2}-c_{k-1}})^{-1} - \mathrm{logit}^{-1}(c_{k-1}-\lambda))) & \mathrm{if } 1 < k < K, \mathrm{and}\\ \mathrm{logit}^{-1}(c_{K-2}-\lambda) & \mathrm{if } k = K. \end{cases} \]

\[ \frac{\partial }{\partial \lambda} = \begin{cases} -\mathrm{logit}^{-1}(\lambda - c_1) & \text{if } k = 1,\\ -(((1-e^{c_{k-1}-c_{k-2}})^{-1} - \mathrm{logit}^{-1}(c_{k-2}-\lambda)) + ((1-e^{c_{k-2}-c_{k-1}})^{-1} - \mathrm{logit}^{-1}(c_{k-1}-\lambda))) & \text{if } 1 < k < K, \text{ and}\\ \mathrm{logit}^{-1}(c_{K-2}-\lambda) & \text{if } k = K. \end{cases} \]

Template Parameters

propto	True if calculating up to a proportion.
T_y	Y variable type (integer or array of integers).
T_loc	Location type.
T_cut	Cut-point type.

Parameters

y	Array of integers
lambda	Vector of continuous location variables.
c	Positive increasing vector of cutpoints.

Returns

Log probability of outcome given location and cutpoints.

Exceptions

std::domain_error	If the outcome is not between 1 and the number of cutpoints plus 2; if the cutpoint vector is empty; if the cutpoint vector contains a non-positive, non-finite value; or if the cutpoint vector is not sorted in ascending order.
std::invalid_argument	If y and lambda are different lengths.

Definition at line 75 of file ordered_logistic_lpmf.hpp.