## Description

`bpr_gradient` computes the gradient w.r.t the coefficients w of the Binomial distributed Probit regression log likelihood function.

## Usage

 `1` ```bpr_gradient(w, H, data, is_NLL = FALSE) ```

## Arguments

 `w` A vector of parameters (i.e. coefficients of the basis functions) `H` The `L x M` matrix design matrix, where L is the number of observations and M the number of basis functions. `data` An `L x 2` matrix containing in the 1st column the total number of trials and in the 2nd the number of successes. Each row corresponds to each row of the design matrix. `is_NLL` Logical, indicating if the Negative Log Likelihood should be returned.

## Value

the gradient vector of the log likelihood w.r.t the vector of coefficients w

## Mathematical formula

The gradient of the Binomial distributed Probit regression log likelihood function w.r.t to w is computed by the following formula:

log p(y | f, w) = ∑_{l=1}^{L} log Binom(m_{l} | t_{l}, Φ(w^{t}h(x_{l})))

`bpr_likelihood`, `design_matrix`
 ```1 2 3 4 5 6 7``` ```obj <- polynomial.object(M=2) obs <- c(0,.2,.5) des_mat <- design_matrix(obj, obs) H <- des_mat\$H w <- c(.1,.1,.1) data <- matrix(c(10,12,15,7,9,8), ncol=2) gr <- bpr_gradient(w, H, data) ```