Compute Conditional Probability of Each Observed Outcome Given Each True Outcome for a given MCMC Chain, for Every Subject
pitilde_compute_for_chains.RdCompute Conditional Probability of Each Observed Outcome Given Each True Outcome for a given MCMC Chain, for Every Subject
Arguments
- chain_colMeans
A numeric vector containing the posterior means for all sampled parameters in a given MCMC chain.
chain_colMeansmust be a named object (i.e. each parameter must be named asdelta[l,k,j,p]).- V
A numeric design matrix.
- n
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.- n_cat
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.
Value
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.