normal_mix_llike: Penalized MOUTHWASH likelihood when using a mixture of...
In dcgerard/vicar: Various Ideas for Confounder Adjustment in Regression

Penalized MOUTHWASH likelihood when using a mixture of normals.

normal_mix_llike(
  pi_vals,
  z2,
  xi,
  betahat_ols,
  S_diag,
  alpha_tilde,
  tau2_seq,
  lambda_seq,
  var_inflate_pen = 0
)

`pi_vals`	The current values of the mixing proportions.
`z2`	The current value of the unobserved confounders corresponding to the covariates of interest.
`xi`	The current value of the variance inflation parameter.
`betahat_ols`	A vector of numerics. The OLS estimates of the coefficients of interest.
`S_diag`	A vector of positive numerics. The estimated standard errors.
`alpha_tilde`	A matrix. The number of rows should be equal the length of betahat_ols. The number of columns should equal the number of hidden confounders.
`tau2_seq`	The grid of variances. This is the same thing as grid_seq in `mouthwash_second_step` if `likelihood = "normal"`.
`lambda_seq`	A numeric vector with elements all greater than or equal to 1. These are the tuning parameters for the mixing proportions.
`var_inflate_pen`	The penalty to apply on the variance inflation parameter. Defaults to 0, but should be something non-zero when `alpha = 1` and `scale_var = TRUE`.