EM_function_normalY_XM function

EM Algorithm Function for Estimation of the Misclassification Model

Function is for cases with $Y \sim Normal$ and with an interaction term in the outcome mechanism.

EM_function_normalY_XM(
  param_current,
  obs_mediator,
  obs_outcome,
  X,
  Z,
  c_matrix,
  sample_size,
  n_cat
)

Arguments

• param_current: A numeric vector of regression parameters, in the order $\beta, \gamma, \theta$. The $\gamma$ vector is obtained from the matrix form. In matrix form, the gamma parameter matrix rows correspond to parameters for the M* = 1

  observed mediator, with the dimensions of Z. In matrix form, the gamma parameter matrix columns correspond to the true mediator categories $j = 1, \dots,$ n_cat. The numeric vector gamma_v is obtained by concatenating the gamma matrix, i.e. gamma_v <- c(gamma_matrix).

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

• obs_outcome: A vector containing the outcome variables of interest. There should be no NA terms.

• X: A numeric design matrix for the true mediator mechanism.

• Z: A numeric design matrix for the observation mechanism.

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

• sample_size: An integer value specifying the number of observations in the sample. This value should be equal to the number of rows of the design matrix, X or Z.

• n_cat: The number of categorical values that the true outcome, M, and the observed outcome, M* can take.

Returns

EM_function_bernoulliY returns a numeric vector of updated parameter estimates from one iteration of the EM-algorithm.