pistar_compute {COMBO}

Compute Conditional Probability of Each Observed Outcome Given Each True Outcome, for Every Subject

Description

Compute Conditional Probability of Each Observed Outcome Given Each True Outcome, for Every Subject

Usage

pistar_compute(gamma, Z, n, n_cat)

Arguments

gamma

A numeric matrix of regression parameters for the observed outcome mechanism, Y* | Y (observed outcome, given the true outcome) ~ Z (misclassification predictor matrix). Rows of the matrix correspond to parameters for the Y* = 1 observed outcome, with the dimensions of Z. Columns of the matrix correspond to the true outcome categories j = 1, \dots, n_cat.

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 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 $1$ occurs at row i. The probability for subject i and observed category $2$ occurs at row i + n. Columns of the matrix correspond to the true outcome categories j = 1, \dots, n_cat.