To select the \(gh\)-parsimonious mixture model, i.e., with some \(g\) and/or \(h\) parameters equal to zero, conditionally on a fixed number of components \(K\).
step_fmx(
object,
test = c("BIC", "AIC"),
direction = c("forward", "backward"),
...
)Function step_fmx() returns an object of S3 class 'step_fmx',
which is a list of selected models (in reversed order) with attribute(s)
'direction' and
'test'.
The algorithm starts with quantile least Mahalanobis distance estimates of either the full mixture of Tukey \(g\)-&-\(h\) distributions model, or a constrained model (i.e., some \(g\) and/or \(h\) parameters equal to zero according to the user input). Next, each of the non-zero \(g\) and/or \(h\) parameters is tested using the likelihood ratio test. If all tested \(g\) and/or \(h\) parameters are significantly different from zero at the level 0.05 the algorithm is stopped and the initial model is considered \(gh\)-parsimonious. Otherwise, the \(g\) or \(h\) parameter with the largest p-value is constrained to zero for the next iteration of the algorithm.
The algorithm iterates until only significantly-different-from-zero \(g\) and \(h\) parameters are retained, which corresponds to \(gh\)-parsimonious Tukey \(g\)-&-\(h\) mixture model.