A Penalized h-Likelihood Variable Selection Algorithm for Generalized Linear Regression Models with Random Effects

Algorithm 1

[(Step 1)] (initialization).
(i)	Assume a partial linear model excluding variable selection. Express in a parametric way. For example, a cubic regression spline can be expressed by using the truncated power basis:
	where the 5 knots are percentiles of , are the associated coefficients, and , are the numbers corresponding to the cubic regression spline representation.
(ii)	Initialize the fixed effects , where is the h-likelihood estimates by treating in a parametrical way. Then, we have
(iii)	Denote the estimates by :
	where are the h-likelihood estimates.
(iv)	Determine initial value for random effects using
	with and .
[(Step 2)] (loop).
(i)	Use and to get
(ii)	For the iteration, set the estimator from the iteration and update by
(iii)	For , set if , for a small cutoff value c.
(iv)	Compute and compare to a small predetermined value . If is smaller than , stop the loop.