create_synthetic_mirt_dichotomous

def create_synthetic_mirt_dichotomous(difficulty, discrimination, thetas,
                                      seed=None):
    """ Creates dichotomous multidimensional synthetic IRT data.

    Assumes the model
        P(theta) = 1.0 / (1 + exp(-1 * (dot(discrimination,theta) + difficulty)))

    Args:
        difficulty: [array, M] of difficulty parameters
        discrimination:  [2-D array, MxN] of discrimination parameters
        thetas: [2-D array, NxP] of person abilities
        seed: Optional setting to reproduce results

    Returns:
        synthetic_data: (2d array) realization of possible response given parameters


    Example:
        n_factors = 3
        n_items = 15
        n_people = 500
        difficulty = np.linspace(-2.5, 2.5, n_items)
        discrimination = np.random.randn(n_items, n_factors)
        thetas = np.random.randn(n_factors, n_people)

        synthetic_data = create_synthetic_mirt_dichotomous(difficulty, discrimination, thetas)
    """
    if seed:
        np.random.seed(seed)

    # If the input is just a vector of discriminations
    if (np.ndim(discrimination) == 1) or (discrimination.shape[0] == 1):
        discrimination = np.vstack((discrimination,) * difficulty.shape[0])

    # Inline computation of the logistic kernel
    kernel_terms = discrimination @ thetas
    kernel_terms += difficulty[:, None]
    continuous_output = 1.0 / (1.0 + np.exp(-kernel_terms))

    # convert to binary based on probability
    random_compare = np.random.rand(*continuous_output.shape)

    return random_compare <= continuous_output