Table 3.
Group-Based Dual Trajectory Model Selection Coefficients from Simulated Data, with Three Latent Groups
| Series A | Series B | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| True Parameter | Estimated Median of the Posterior Distribution | 95% Credible Interval | Inclusion Probability | True Parameter | Estimated Median of the Posterior Distribution | 95% Credible Interval | Inclusion Probability | ||
| Panel A: Trajectory Coefficients | |||||||||
| Latent Group 1 | Intercept | 80 | 80.18 | [79.42, 80.93] | -- | 50 | 49.71 | [48.23, 50.60] | -- |
| Age | −1 | −1.04 | [−1.44, −0.65] | 100% | 1 | 1.20 | [0.79, 2.58] | 100% | |
| Age^2 | 0.5 | 0.50 | [0.45, 0.55] | 100% | −0.5 | −0.52 | [−0.85, −0.48] | 100% | |
| Age^3 | 0 | 0.00 | [0.00, 0.00] | 2% | 0 | 0.00 | [0.00, 0.02] | 9% | |
| Sigma | 4 | 3.97 | [3.96, 4.10] | -- | 6 | 6.16 | [5.99, 6.33] | -- | |
| Latent Group 2 | Intercept | 120 | 119.97 | [119.17, 120.66] | -- | 90 | 90.21 | [89.81, 90.65 | -- |
| Age | 20 | 19.90 | [19.55, 20.45] | 100% | 0.03 | 0.36 | [0.28, 0.44] | 100% | |
| Age^2 | −2 | −1.99 | [−2.13, −1.95] | 100% | 0 | 0.00 | [0.00, 0.00] | 2% | |
| Age^3 | 0 | 0.00 | [0.00, 0.01] | 4% | 0 | 0.00 | [0.00, 0.00] | 0% | |
| Sigma | 4 | 4.06 | [3.94, 4.18] | -- | 6 | 5.93 | [5.79, 6.06] | -- | |
| Latent Group 3 | Intercept | 100 | 100.43 | [99.55, 101.27] | -- | 100 | 101.40 | [99.84, 102.92] | -- |
| Age | 10 | 9.57 | [8.78, 10.37] | 100% | −30 | −31.00 | [−32.24, −29.75] | 100% | |
| Age^2 | −0.5 | −0.38 | [−0.59, −0.19] | 100% | 3 | 3.19 | [2.91, 3.47] | 100% | |
| Age^3 | 0.1 | 0.09 | [0.08, 0.11] | 100% | −0.3 | −0.31 | [−0.33, −0.29] | 100% | |
| Sigma | 4 | 3.99 | [3.91, 4.08] | -- | 6 | 6.08 | [5.92, 6.23] | -- | |
| Panel B: Group Probabilities | |||||||||
| 1 | 20% | 21.7% | [19.2%, 24.3%] | -- | 31% | 30.9% | [28.1%, 33.8%] | ||
| 2 | 30% | 28.0% | [25.2%, 30.8%] | -- | 40% | 40.5% | [37.5%, 43.6%] | ||
| 3 | 50% | 50.3% | [47.2$, 53.4%] | -- | 29% | 28.5% | [25.8%, 31.4%] | ||
| Panel C: Transition Probabilities | |||||||||
| 1 | 1 | 32.2% | 33.2% | [28.2%, 38.7%] | -- | 50% | 47.3% | [30.8%, 53.8%] | ||
| 2 | 1 | 19.4% | 17.8% | [13.8%, 22.3%] | -- | 20% | 25.3% | [19.8%, 31.5%] | ||
| 3 | 1 | 48.4% | 48.9% | [43.5%, 54.3%] | -- | 30% | 27.2% | [21.6%, 33.3%] | ||
| 1 | 2 | 10.0% | 13.6% | [10.4%, 17.1%] | -- | 20% | 19.7% | [15.4%, 24.6%] | ||
| 2 | 2 | 52.5% | 48.6% | [43.7%, 53.4%] | -- | 70% | 70.4% | [64.9%, 75.5%] | ||
| 3 | 2 | 37.5% | 37.8% | [33.2%, 42.6%] | -- | 10% | 9.8% | [6.7%, 13.6%] | ||
| 1 | 3 | 20.7% | 20.7% | [16.2%, 25.6%] | -- | 30% | 30.0% | [26.1%, 34.2%] | ||
| 2 | 3 | 10.3% | 9.6% | [6.5%, 13.3%] | -- | 30% | 30.4% | [26.5%, 34.6%] | ||
| 3 | 3 | 69.0% | 69.6% | [64.1%, 74.8%] | -- | 40% | 39.5% | [35.4%, 43.8%] | ||
Note: pi_k refers to the marginal probability of latent group k in Series A. pi_i_j refers to the conditional probability of being in latent group j in Series B conditional on being in latent group i in Series A. Sigma is the estimated standard deviation of the residual. Intercepts are forced into the model and not subject to model selection.