Instability of Parameter Estimates in flexmix R Package: Seeking Insights on Unstable Results with Two-Component Data

Question

I am trying to analyse a data set with flexmix (version 2.3-19.), where I know (based on theoretical considerations and a visual analysis) that there are 2 components. When I run the model with its specifications (similar to what Grün and Leisch do in their paper) the parameters are instable. If I run it 5 times, I get 5 different results, some significant, some non-significant. My two questions are: Why are the results this unstable? How can I mend this or what or how do I report (this) in my paper?

A reproducible example based on Grün and Leisch (see here, subsection 3.3)

data("bioChemists", package = "flexmix")
Model1 <- FLXMRglm(family = "poisson")
ff_1 <- stepFlexmix(art ~ ., data = bioChemists, k = 1:3, model = Model1)

Model2 <- FLXMRglmfix(family = "poisson", fixed = ~ kid5 + mar + ment)
ff_2 <- flexmix(art ~ fem + phd, data = bioChemists, cluster = posterior(ff_1), model = Model2)

summary(ff_2)
summary(refit(ff_2))

The model prediction is stable, meaning when I run it several times the result remains the same.

When I however, instead of "cluster" use "k = 2" (which is the number of clusters in their data, based on their prior analysis), i. e. change the model to the following set-up:

ff_3 <- flexmix(art ~ fem + phd, data = bioChemists, k = 2, model = Model2)

summary(ff_3)
summary(refit(ff_3))

The parameters somehow become instable. Even though based on what is described in the paper relating to the package, the two - "cluster" and "k" - should be substitutable.

The way Grün and Leisch write the following limitation in their paper: "However, it has to be noted that in the course of the procedure these confidence intervals will not be correct any more because the specific fitted models have already been determined using the same data." (p. 18) As I understand this, I cannot use their two-step method to stabilize the results in my analysis, as I most certainly want to interpret the confidence interval or p-value of the second step.