Compute E-step for Two-Stage Binary Outcome Misclassification Model Estimated With the EM-Algorithm
w_j_2stage(
ystar_matrix,
ytilde_matrix,
pitilde_array,
pistar_matrix,
pi_matrix,
sample_size,
n_cat
)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.
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.
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.
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.
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.
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.
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.
The number of categorical values that the true outcome, Y,
and the observed outcomes can take.