In practice, different latent class analysis models are fitted by attributing different values to \(G\), usually ranging from 1 to \(G_{max}\). However, for a set of variables, not all the models corresponding to increasing values of \(G\) are identifiable. Indeed, a necessary (but not sufficient) condition for a latent class analysis model to be identifiable is:
$$\prod_{j=1}^M C_j > G\Biggl(\, \sum_{j=1}^M C_j - M + 1\Biggr)$$
where \(C_j\) denotes the number of categories of variable \(j\), \(j=1,...,M\), and \(M\) is the number of variables in the data Y. Another condition requires the number of observed distinct configurations of the variables in the data to be greater than the number of parameters of the model. The function returns the subset of values of vector Gvec such that both the above conditions are satisfied.