Compute Conditional Probability of Each Observed Outcome Given Each True Outcome for a given MCMC Chain, for Every Subject
pistar_compute_for_chains(chain_colMeans, Z, n, n_cat)pistar_compute_for_chains returns a matrix of conditional probabilities,
\(P(Y_i^* = k | Y_i = j, Z_i) = \frac{\text{exp}\{\gamma_{kj0} + \gamma_{kjZ} Z_i\}}{1 + \text{exp}\{\gamma_{kj0} + \gamma_{kjZ} Z_i\}}\)
for each of the \(i = 1, \dots,\)
n subjects. Rows of the matrix
correspond to each subject and observed outcome. Specifically, the probability
for subject \(i\) and observed category $0$ occurs at row \(i\). The probability
for subject \(i\) and observed category $1$ occurs at row \(i +\)
n.
Columns of the matrix correspond 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 gamma[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, Z.
The number of categorical values that the true outcome, Y,
and the observed outcome, Y* can take.