Likelihood Function for Normal Outcome Mechanism with a Binary Mediator
theta_optim(param_start, m, x, c_matrix, outcome, sample_size, n_cat)theta_optim returns a numeric value of the (negative) log-likelihood function.
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 \(\sigma\).
A 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.
A vector or column matrix of the predictor or exposure of interest. There
should be no NA terms.
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.
A vector containing the outcome variables of interest. There
should be no NA terms.
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.
The number of categorical values that the true outcome, M,
and the observed outcome, M* can take.