COMBO (version 1.1.0)

misclassification_prob2: Compute Conditional Probability of Each Second-Stage Observed Outcome Given Each True Outcome and First-Stage Observed Outcome, for Every Subject

Description

Compute the conditional probability of observing second-stage outcome \(Y^{*(2)} \in \{1, 2 \}\) given the latent true outcome \(Y \in \{1, 2 \}\) and the first-stage outcome \(Y^{*(1)} \in \{1, 2\}\) as \(\frac{\text{exp}\{\gamma^{(2)}_{\ell kj0} + \gamma^{(2)}_{\ell kjZ^{(2)}} Z^{(2)}\}}{1 + \text{exp}\{\gamma^{(2)}_{\ell kj0} + \gamma^{(2)}_{\ell kjZ^{(2)}} Z^{(2)}_i\}}\) for each of the \(i = 1, \dots,\) \(n\) subjects.

Usage

misclassification_prob2(gamma2_array, z2_matrix)

Value

misclassification_prob2 returns a dataframe containing five 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 z2_matrix. The second column, Y, represents a true, latent outcome category \(Y \in \{1, 2 \}\). The third column, Ystar1, represents a first-stage observed outcome category \(Y^{*(1)} \in \{1, 2 \}\). The fourth column, Ystar2, represents a second-stage observed outcome category \(Y^{*(2)} \in \{1, 2 \}\). The last column, Probability, is the value of the equation \(\frac{\text{exp}\{\gamma^{(2)}_{\ell kj0} + \gamma^{(2)}_{\ell kjZ^{(2)}} Z^{(2)}\}}{1 + \text{exp}\{\gamma^{(2)}_{\ell kj0} + \gamma^{(2)}_{\ell kjZ^{(2)}} Z^{(2)}_i\}}\)

computed for each subject, first-stage observed outcome category, second-stage observed outcome category, and true, latent outcome category.

Arguments

gamma2_array

A numeric array of estimated regression parameters for the observation mechanism, \(Y^{*(2)}| Y^{*(1)}, Y\) (second-stage observed outcome, given the first-stage observed outcome and the true outcome) ~ \(Z^{(2)}\) (second-stage misclassification predictor matrix). Rows of the array correspond to parameters for the \(Y^{*(2)} = 1\) observed outcome, with the dimensions of z2_matrix. Columns of the array correspond to the first-stage outcome categories \(k = 1, \dots,\) n_cat. The third stage of the array corresponds to the true outcome categories \(j = 1, \dots,\) n_cat. The array should be obtained by COMBO_EM or COMBO_MCMC.

z2_matrix

A numeric matrix of covariates in the second-stage observation mechanism. z2_matrix should not contain an intercept.

Examples

set.seed(123)
sample_size <- 1000
cov1 <- rnorm(sample_size)
cov2 <- rnorm(sample_size, 1, 2)
z2_matrix <- matrix(c(cov1, cov2), nrow = sample_size, byrow = FALSE)
estimated_gamma2 <- array(c(1, -1, .5, .2, -.6, 1.5,
                            -1, .5, -1, -.5, -1, -.5), dim = c(3,2,2))
P_Ystar2_Ystar1_Y <- misclassification_prob2(estimated_gamma2, z2_matrix)
head(P_Ystar2_Ystar1_Y)