  We introduce a novel statistical significance-based approach for clustering
hierarchical data using semi-parametric linear mixed-effects models designed
for responses with laws in the exponential family (e.g., Poisson and
Bernoulli). Within the family of semi-parametric mixed-effects models, a latent
clustering structure of the highest-level units can be identified by assuming
the random effects to follow a discrete distribution with an unknown number of
support points. We achieve this by computing {\alpha}-level confidence regions
of the estimated support point and identifying statistically different
clusters. At each iteration of a tailored Expectation Maximization algorithm,
the two closest estimated support points for which the confidence regions
overlap collapse. Unlike the related state-of-the-art methods that rely on
arbitrary thresholds to determine the merging of close discrete masses, the
proposed approach relies on conventional statistical confidence levels, thereby
avoiding the use of discretionary tuning parameters. To demonstrate the
effectiveness of our approach, we apply it to data from the Programme for
International Student Assessment (PISA - OECD) to cluster countries based on
the rate of innumeracy levels in schools. Additionally, a simulation study and
comparison with classical parametric and state-of-the-art models are provided
and discussed.
