Table 5.

Childrens’ Fear Data; the rows in the upper table show the posterior distribution $\text{Pr}(K_{+}|\mathbf{y})$ of the number of clusters $K_{+}$ for various latent class models: sparse latent class models with $K=10$ (SFM) with hyper priors $e_0\sim \mathcal{G}(1,200)$ and $e_0\sim \mathcal{G}(2,4K)$ (matched to DPM), DPM with hyper priors $\alpha \sim \mathcal{G}(2,4)$ and $\alpha \sim \mathcal{G}(1,200/K)$ (matched to SFM)

$\text{Pr}(K_{+}|\mathbf{y})$	$K_{+}=1$	$K_{+}=2$	$K_{+}=3$	$K_{+}=4$	$K_{+}=5$	$K_{+}=6$	$K_{+}\ge 7$
SFM
$e_0\sim \mathcal{G}\left(1,,,200\right)$	0	0.686	0.249	0.058	0.007	0.001	0.000
Matched to DPM	0	0.128	0.267	0.280	0.201	0.090	0.033
DPM
$\alpha \sim \mathcal{G}\left(2,,,4\right)$	0	0.101	0.235	0.246	0.197	0.118	0.103
Matched to SFM	0	0.688	0.251	0.048	0.011	0.002	0.000

$log\widehat{p}(\mathbf{y}|K)$	$K=1$	$K=2$	$K=3$	$K=4$	$K=5$
FM ($e_0=4$)	$-$ 333.01	$-$ 330.46	$-$ 333.67	$-$ 337.37	$-$ 340.48

The lower table shows log marginal likelihoods, $log\widehat{p}(\mathbf{y}|K)$, estimated for a latent class model with $e_0=4$ (FM) for increasing K

The posterior mode ${\widehat{K}}_{+}$ is denoted in bold (upper table). The number of components K with the largest marginal likelihood is denoted in bold (lower table)