COMBO_EM_algorithm function

EM-Algorithm Estimation of the Binary Outcome Misclassification Model

Jointly estimate $\beta$ and $\gamma$ parameters from the true outcome and observation mechanisms, respectively, in a binary outcome misclassification model.

COMBO_EM_algorithm(
  Ystar,
  x_matrix,
  z_matrix,
  beta_start,
  gamma_start,
  tolerance = 1e-07,
  max_em_iterations = 1500,
  em_method = "squarem"
)

Arguments

• Ystar: A numeric vector of indicator variables (1, 2) for the observed outcome Y*. There should be no NA terms. The reference category is 2.

• x_matrix: A numeric matrix of covariates in the true outcome mechanism. x_matrix should not contain an intercept and no values should be NA.

• z_matrix: A numeric matrix of covariates in the observation mechanism. z_matrix should not contain an intercept and no values should be NA.

• beta_start: A numeric vector or column matrix of starting values for the $\beta$

  parameters in the true outcome mechanism. The number of elements in beta_start

  should be equal to the number of columns of x_matrix plus 1.

• gamma_start: A numeric vector or matrix of starting values for the $\gamma$

  parameters in the observation mechanism. In matrix form, the gamma_start matrix rows correspond to parameters for the Y* = 1

  observed outcome, with the dimensions of z_matrix plus 1, and the gamma parameter matrix columns correspond to the true outcome categories $M \in \{1, 2\}$. A numeric vector for gamma_start is obtained by concatenating the gamma matrix, i.e. gamma_start <- c(gamma_matrix).

• tolerance: A numeric value specifying when to stop estimation, based on the difference of subsequent log-likelihood estimates. The default is 1e-7.

• max_em_iterations: An integer specifying the maximum number of iterations of the EM algorithm. The default is 1500.

• em_method: A character string specifying which EM algorithm will be applied. Options are "em", "squarem", or "pem". The default and recommended option is "squarem".

Returns

COMBO_EM_algorithm returns a data frame containing four columns. The first column, Parameter, represents a unique parameter value for each row. The next column contains the parameter Estimates, followed by the standard error estimates, SE. The final column, Convergence, reports whether or not the algorithm converged for a given parameter estimate.