misclassification_prob {COMBO}

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

Description

Compute the conditional probability of observing outcome Y^* \in \{1, 2 \} given the latent true outcome Y \in \{1, 2 \} as \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.

Usage

misclassification_prob(gamma_matrix, z_matrix)

Arguments

gamma_matrix

A numeric matrix of estimated regression parameters for the observation 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_matrix. Columns of the matrix correspond to the true outcome categories j = 1, \dots, n_cat. The matrix should be obtained by COMBO_EM or COMBO_MCMC.

z_matrix

A numeric matrix of covariates in the observation mechanism. z_matrix should not contain an intercept.

Value

misclassification_prob returns a dataframe containing four columns. The first column, Subject, represents the subject ID, from 1 to n, where n is the sample size, or equivalently, the number of rows in z_matrix. The second column, Y, represents a true, latent outcome category Y \in \{1, 2 \}. The third column, Ystar, represents an observed outcome category Y^* \in \{1, 2 \}. The last column, Probability, is the value of the equation \frac{\text{exp}\{\gamma_{kj0} + \gamma_{kjZ} Z_i\}}{1 + \text{exp}\{\gamma_{kj0} + \gamma_{kjZ} Z_i\}} computed for each subject, observed outcome category, and true, latent outcome category.

Examples

set.seed(123)
sample_size <- 1000
cov1 <- rnorm(sample_size)
cov2 <- rnorm(sample_size, 1, 2)
z_matrix <- matrix(c(cov1, cov2), nrow = sample_size, byrow = FALSE)
estimated_gammas <- matrix(c(1, -1, .5, .2, -.6, 1.5), ncol = 2)
P_Ystar_Y <- misclassification_prob(estimated_gammas, z_matrix)
head(P_Ystar_Y)