pistar_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

pistar_compute_for_chains(chain_colMeans, Z, 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 gamma[k,j,p]).

Z

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, Z.

n_cat

The number of categorical values that the true outcome, Y, and the observed outcome, Y* can take.

Value

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.