Compute Conditional Probability of Each Observed Outcome Given Each True Outcome for a given MCMC Chain, for Every Subject
pitilde_compute_for_chains(chain_colMeans, V, n, n_cat)pitilde_compute_for_chains returns a matrix of conditional probabilities,
\(P(\tilde{Y}_i = \ell | Y^*_i = k, Y_i = j, V_i) = \frac{\text{exp}\{\delta_{\ell kj0} + \delta_{\ell kjV} V_i\}}{1 + \text{exp}\{\delta_{\ell kj0} + \delta_{\ell kjV} V_i\}}\)
corresponding to each subject and observed outcome. Specifically, the probability for subject \(i\) and second-stage observed category $1$ occurs at row \(i\). The probability for subject \(i\) and second-stage observed category $2$ occurs at row \(i +\)
n.
Columns of the matrix correspond to the first-stage outcome categories \(j = 1, \dots,\)
n_cat.
The third dimension of the array corresponds to the true outcome categories,
\(j = 1, \dots,\)
n_cat.
A numeric vector containing the posterior means for all
sampled parameters in a given MCMC chain. chain_colMeans must be a named
object (i.e. each parameter must be named as delta[l,k,j,p]).
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, \(Y\), the first-stage observed outcome, \(Y^*\), and the second-stage observed outcome, \(\tilde{Y}\),\ can take.