M-Step Expected Log-Likelihood with respect to Beta

Objective function of the form: \( Q_\beta = \sum_{i = 1}^N \Bigl[ \sum_{j = 0}^1 w_{ij} \text{log} \{ \pi_{ij} \}\Bigr]\). Used to obtain estimates of \(\beta\) parameters.

Usage

q_beta_f(beta, X, w_mat, sample_size, n_cat)

Arguments

beta

A numeric vector of regression parameters for the Y (true outcome) ~ X (predictor matrix of interest).

X

A numeric design matrix.

w_mat

Matrix of E-step weights obtained from w_j.

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.

n_cat

The number of categorical values that the true outcome, Y, can take.

Value

q_beta_f returns the negative value of the expected log-likelihood function, \( Q_\beta = \sum_{i = 1}^N \Bigl[ \sum_{j = 1}^2 w_{ij} \text{log} \{ \pi_{ij} \}\Bigr]\), at the provided inputs.