Objective function of the form: \(Q_{\gamma} = \sum_{i = 1}^N \Bigl[\sum_{j = 1}^2 \sum_{k = 1}^2 w_{ij} y^*_{ik} \text{log} \{ \pi^*_{ikj} \}\Bigr]\). Used to obtain estimates of \(\gamma\) parameters.
q_gamma_f(gamma_v, Z, obs_Y_matrix, w_mat, sample_size, n_cat)q_beta_f returns the negative value of the expected log-likelihood function,
\(Q_{\gamma} = \sum_{i = 1}^N \Bigl[\sum_{j = 1}^2 \sum_{k = 1}^2 w_{ij} y^*_{ik} \text{log} \{ \pi^*_{ikj} \}\Bigr]\),
at the provided inputs.
A numeric vector of regression parameters for the observed
outcome mechanism, Y* | Y
(observed outcome, given the true outcome) ~ Z (misclassification
predictor matrix). In matrix form, the gamma parameter matrix rows
correspond to parameters for the Y* = 0
observed outcome, with the dimensions of Z.
In matrix form, the gamma parameter matrix columns correspond to the true outcome categories
\(j = 1, \dots,\) n_cat. The numeric vector gamma_v is
obtained by concatenating the gamma matrix, i.e. gamma_v <- c(gamma_matrix).
A numeric design 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.
Matrix of E-step weights obtained from w_j.
An integer value specifying the number of observations in the sample.
This value should be equal to the number of rows of the design matrix, Z.
The number of categorical values that the true outcome, Y,
and the observed outcome, Y* can take.