theta_optim_XM function

Likelihood Function for Normal Outcome Mechanism with a Binary Mediator and an Interaction Term

theta_optim_XM(param_start, m, x, c_matrix, outcome, sample_size, n_cat)

Arguments

• param_start: A numeric vector or column matrix of starting values for the $\theta$

  parameters in the outcome mechanism and $\sigma$ parameter. The number of elements in param_start

  should be equal to the number of columns of x_matrix and c_matrix plus 2 (if interaction_indicator is FALSE) or 3 (if interaction_indicator is TRUE). Starting values should be provided in the following order: intercept, slope coefficient for the x_matrix term, slope coefficient for the mediator m term, slope coefficient for first column of the c_matrix, ..., slope coefficient for the final column of the c_matrix, and, optionally, slope coefficient for xm). The final entry should be the starting value for $\sigma$.

• m: vector or column matrix containing the true binary mediator or the E-step weight (with values between 0 and 1). There should be no NA terms.

• x: A vector or column matrix of the predictor or exposure of interest. There should be no NA terms.

• 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.

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

• 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

theta_optim_XM returns a numeric value of the (negative) log-likelihood function.