misclassification_prob function

Compute Conditional Probability of Observed Mediator Given True Mediator, for Every Subject

Compute the conditional probability of observing mediator $M^* \in \{1, 2 \}$ given the latent true mediator $M \in \{1, 2 \}$ 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.

misclassification_prob(gamma_matrix, z_matrix)

Arguments

• gamma_matrix: A numeric matrix of estimated regression parameters for the observation mechanism, M* | M (observed mediator, given the true mediator) ~ Z (misclassification predictor matrix). Rows of the matrix correspond to parameters for the M* = 1 observed mediator, with the dimensions of z_matrix. Columns of the matrix correspond to the true mediator categories $j = 1, \dots,$ n_cat. The matrix should be obtained by COMMA_EM, COMMA_PVW, or COMMA_OLS.
• z_matrix: A numeric matrix of covariates in the observation mechanism. z_matrix should not contain an intercept.

Returns

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, M, represents a true, latent mediator category $M \in \{1, 2 \}$. The third column, Mstar, represents an observed outcome category $M^* \in \{1, 2 \}$. 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 mediator category, and true, latent mediator 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_M <- misclassification_prob(estimated_gammas, z_matrix)
head(P_Ystar_M)