Compute E-step for Two-Stage Binary Outcome Misclassification Model Estimated With the EM-Algorithm

Usage

w_j_2stage(
  ystar_matrix,
  ytilde_matrix,
  pitilde_array,
  pistar_matrix,
  pi_matrix,
  sample_size,
  n_cat
)

Arguments

ystar_matrix: A numeric matrix of indicator variables (0, 1) for the observed outcome Y*. Rows of the matrix correspond to each subject. Columns of the matrix correspond to each observed outcome category. Each row should contain exactly one 0 entry and exactly one 1 entry.
ytilde_matrix: A numeric matrix of indicator variables (0, 1) for the observed outcome \(\tilde{Y}\). Rows of the matrix correspond to each subject. Columns of the matrix correspond to each observed outcome category. Each row should contain exactly one 0 entry and exactly one 1 entry.
pitilde_array: A numeric array of conditional probabilities obtained from the internal function pitilde_compute. Rows of the matrices correspond to each subject and to each second-stage observed outcome category. Columns of the matrix correspond to each first-stage observed outcome category. The third dimension of the array corresponds to each true, latent outcome category.
pistar_matrix: A numeric matrix of conditional probabilities obtained from the internal function pistar_compute. Rows of the matrix correspond to each subject and to each first-stage observed outcome category. Columns of the matrix correspond to each true, latent outcome category.
pi_matrix: A numeric matrix of probabilities obtained from the internal function pi_compute. Rows of the matrix correspond to each subject. Columns of the matrix correspond to each true, latent outcome category.
sample_size: An integer value specifying the number of observations in the sample. This value should be equal to the number of rows of the observed outcome matrices, ystar_matrix and ytilde_matrix.
n_cat: The number of categorical values that the true outcome, Y, and the observed outcomes can take.

Value

w_j returns a matrix of E-step weights for the EM-algorithm, computed as follows: \(\sum_{k = 1}^2 \sum_{\ell = 1}^2 \frac{y^*_{ik} \tilde{y}_{i \ell} \tilde{\pi}_{i \ell kj} \pi^*_{ikj} \pi_{ij}}{\sum_{h = 1}^2 \tilde{\pi}_{i \ell kh} \pi^*_{ikh} \pi_{ih}}\). Rows of the matrix correspond to each subject. Columns of the matrix correspond to the true outcome categories \(j = 1, \dots,\) n_cat.