Compute Probability of Each True Outcome, for Every Subject
true_classification_prob.RdCompute the probability of the latent true outcome \(Y \in \{1, 2 \}\) as
\(P(Y_i = j | X_i) = \frac{\exp(X_i \beta)}{1 + \exp(X_i \beta)}\)
for each of the \(i = 1, \dots,\) n subjects.
Arguments
- beta_matrix
A numeric column matrix of estimated regression parameters for the true outcome mechanism,
Y(true outcome) ~X(predictor matrix of interest), obtained fromCOMBO_EMorCOMBO_MCMC.- x_matrix
A numeric matrix of covariates in the true outcome mechanism.
x_matrixshould not contain an intercept.
Value
true_classification_prob returns a dataframe containing three 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 x_matrix.
The second column, Y, represents a true, latent outcome category \(Y \in \{1, 2 \}\).
The last column, Probability, is the value of the equation
\(P(Y_i = j | X_i) = \frac{\exp(X_i \beta)}{1 + \exp(X_i \beta)}\) computed
for each subject and true, latent outcome category.
Examples
set.seed(123)
sample_size <- 1000
cov1 <- rnorm(sample_size)
cov2 <- rnorm(sample_size, 1, 2)
x_matrix <- matrix(c(cov1, cov2), nrow = sample_size, byrow = FALSE)
estimated_betas <- matrix(c(1, -1, .5), ncol = 1)
P_Y <- true_classification_prob(estimated_betas, x_matrix)
head(P_Y)
#> Subject Y Probability
#> 1 1 1 0.7435833
#> 2 2 1 0.6660164
#> 3 3 1 0.4808373
#> 4 4 1 0.7853830
#> 5 5 1 0.2352985
#> 6 6 1 0.6954044