Compute Conditional Probability of Each Second-Stage Observed Outcome Given Each True Outcome and First-Stage Observed Outcome, for Every Subject
pitilde_compute(delta, V, n, n_cat)pitilde_compute returns an array of conditional probabilities,
\(P(\tilde{Y}_i = \ell | Y^*_i = k, Y_i = j, V_i) = \frac{\text{exp}\{\delta_{\ell kj0} + \delta_{\ell kjV} V_i\}}{1 + \text{exp}\{\delta_{\ell kj0} + \delta_{\ell kjV} V_i\}}\)
for each of the \(i = 1, \dots,\)
n subjects. Rows of the matrix
correspond to each subject and second-stage observed outcome. Specifically, the probability
for subject \(i\) and observed category $1$ occurs at row \(i\). The probability
for subject \(i\) and observed category $2$ occurs at row \(i +\)
n.
Columns of the matrix correspond to the first-stage outcome categories, \(k = 1, \dots,\)
n_cat.
The third dimension of the array corresponds to the true outcome categories,
\(j = 1, \dots,\)
n_cat.
A numeric array of regression parameters for the second-stage observed
outcome mechanism, \(\tilde{Y} | Y^*, Y\)
(second-stage observed outcome, given the first-stage observed outcome and the true outcome) ~ V (misclassification
predictor matrix). Rows of the matrix correspond to parameters for the \(\tilde{Y} = 1\)
observed outcome, with the dimensions of V.
Columns of the matrix correspond to the first-stage observed outcome categories
\(k = 1, \dots,\) n_cat. The third dimension of the array
corresponds to the true outcome categories \(j = 1, \dots,\) n_cat
A numeric design matrix.
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, V.
The number of categorical values that the true outcome, Y,
and the observed outcomes can take.