pitilde_compute_for_chains {COMBO}

Compute Conditional Probability of Each Observed Outcome Given Each True Outcome for a given MCMC Chain, for Every Subject

Description

Compute Conditional Probability of Each Observed Outcome Given Each True Outcome for a given MCMC Chain, for Every Subject

Usage

pitilde_compute_for_chains(chain_colMeans, V, n, n_cat)

Arguments

chain_colMeans

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]).

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.