Figure 3.

Illustration of the label switching problem. Plotted here are MCMC simulation traces for π_j using a randomly selected subset of 200 observations from the full Add Health data. We fitted a simpler model with 3 latent classes instead of 4 to show a more visible pattern. Subplots (a) – (c) are the traces for the original MCMC chain. Subplots (d) – (f) are the relabeled chains. Signs of label switching are present in (a) where the chain first hovers around π₁ ≈ 0.60 and then it drifts to the proximity of 0.15 near the 2,000th iteration. This is corroborated by (c) where π₃ drifts up to ≈ 0.60 exactly when π₁ drifts down to ≈ 0.15, an indication that π₁ and π₃ switched labels during simulation. Similarly, signs of label switching are also visible in the π₂ chain, although not as pronounced. The relabeled MCMC chains in (d) – (f) show visibly improved simulation traces.