COMBO (version 1.1.0)

misclassification_prob: 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)

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.

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.

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)