Table 4.
Group-Based Dual Trajectory Model Selection Coefficients from PSID Model
| Father | Son | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| Posterior Median | 95% Credible Interval | Inclusion Probability | Posterior Median | 95% Credible Interval | Inclusion Probability | ||||
| Panel A: Trajectory Coefficients | |||||||||
| Sustained Increase | Intercept | 10.96 | [10.92, 10.99] | -- | Ultra-Rich | Intercept | 10.65 | [10.48, 10.84] | -- |
| Age | 0.05 | [0.05, 0.06] | 100.0% | Age | 0.21 | [0.14, 0.26] | 100.0% | ||
| Age^2 | 0.00 | [−0.00, −0.00] | 100.0% | Age^2 | −0.01 | [−0.01, −0.00] | 100.0% | ||
| Age^3 | 0.00 | [0.00, 0.00] | 3.2% | Age^3 | 0.00 | [0.00, 0.00] | 77.9% | ||
| Sigma | 0.25 | [0.24, 0.26] | -- | Sigma | 0.70 | [0.66, 0.74] | -- | ||
| Mid-Life Peak | Intercept | 10.68 | [10.58,10.76] | -- | Upper | Intercept | 10.96 | [10.91, 11.01] | -- |
| Age | 0.10 | [0.09,0.13] | 100.0% | Age | 0.07 | [0.05, 0.08] | 100.0% | ||
| Age^2 | 0.00 | [−0.00, −0.00] | 100.0% | Age^2 | 0.00 | [−0.00, −0.00] | 100.0% | ||
| Age^3 | 0.00 | [0.00, 0.00] | 9.6% | Age^3 | 0.00 | [0.00, 0.00] | 77.9% | ||
| Sigma | 0.68 | [0.65,0.71] | -- | Sigma | 0.28 | [0.27, 0.30] | -- | ||
| Upper Middle | Intercept | 10.76 | [10.73,10.81] | -- | Upper Middle | Intercept | 10.60 | [10.56, 10.65] | -- |
| Age | 0.05 | [0.03,0.06] | 100.0% | Age | 0.07 | [0.04, 0.08] | 100.0% | ||
| Age^2 | 0.00 | [−0.00, −0.00] | 100.0% | Age^2 | 0.00 | [−0.00, −0.00] | 100.0% | ||
| Age^3 | 0.00 | [0.00, 0.00] | 94.6% | Age^3 | 0.00 | [0.00, 0.00] | 86.7% | ||
| Sigma | 0.23 | [0.22,0.24] | -- | Sigma | 0.33 | [0.32, 0.34] | -- | ||
| Lower Middle | Intercept | 10.53 | [10.49,10.59] | -- | Lower-Middle | Intercept | 10.33 | [10.28,10.38] | |
| Age | 0.02 | [0.01,0.03] | 100.0% | Age | 0.01 | [0.01, 0.03] | 100.0% | ||
| Age^2 | 0.00 | [−0.00,−0.00] | 100.0% | Age^2 | 0.00 | [−0.00, 0.00] | 47.6% | ||
| Age^3 | 0.00 | [0.00, 0.00] | 10.2% | Age^3 | 0.00 | [0.00, 0.00] | 2.6% | ||
| Sigma | 0.37 | [0.36,0.38] | -- | Sigma | 0.39 | [0.38, 0.40] | -- | ||
| Low Earners | Intercept | 10.28 | [10.18, 10.40] | -- | Low Earners | Intercept | 9.90 | [9.77, 10.02] | -- |
| Age | 0.00 | [−0.01,0.03] | 50.0% | Age | 0.07 | [0.05, 0.09] | 100.0% | ||
| Age^2 | 0.00 | [−0.00,0.00] | 18.9% | Age^2 | 0.00 | [−0.00, −0.00] | 100.0% | ||
| Age^3 | 0.00 | [0.00, 0.00] | 0.0% | Age^3 | 0.00 | [0.00, 0.00] | 2.6% | ||
| Sigma | 1.06 | [1.03,1.08] | -- | Sigma | 1.17 | [1.13, 1.21] | -- | ||
| Panel B: Group Probabilities | |||||||||
| Sustained Increase | 15.1% | [12.8%, 17.7%] | -- | Ultra-Rich | 9.9% | [7.7%, 12.3%] | |||
| Mid-Life Peak | 15.0% | [12.6%, 17.7%] | -- | Upper | 16.4% | [13.9%, 19.2%] | |||
| Upper Middle | 21.8% | [19.0%, 24.7%] | -- | Upper Middle | 28.1% | [24.9%, 31.5%] | |||
| Lower Middle | 25.9% | [23.0%, 28.9%] | -- | Lower-Middle | 24.4% | [21.3%, 27.6%] | |||
| Low Earners | 22.0% | [19.2%, 24.9%] | -- | Low Earners | 21.1% | [18.4%, 24.0%] | |||
| Panel C: Transition Probabilities | |||||||||
| Sustained Increase | Ultra-Rich | 38.5% | [28.1%, 49.6%] | -- | Ultra-Rich | Sustained Increase | 25.1% | [17.7%, 33.6%] | |||
| Mid-Life Peak | Ultra-Rich | 25.0% | [15.4%, 35.9%] | -- | Upper | Sustained Increase | 26.6% | [19.2%, 35.1%] | |||
| Upper Middle | Ultra-Rich | 13.5% | [7.2%, 22.0%] | -- | Upper-Middle | Sustained Increase | 26.4% | [18.7%, 35.0%] | |||
| Lower Middle | Ultra-Rich | 14.4% | [7.6%, 23.2%] | -- | Lower-Middle | Sustained Increase | 9.3% | [4.2%, 16.0%] | |||
| Low Earners | Ultra-Rich | 7.5% | [2.3%, 15.4%] | -- | Low Earners | Sustained Increase | 11.7% | [6.6%, 18.4%] | |||
| Sustained Increase | Upper | 24.6% | [17.7%, 32.5%] | -- | Ultra-Rich | Mid-Life Peak | 16.4% | [9.4%, 25.0%] | |||
| Mid-Life Peak | Upper | 17.6% | [10.8%, 25.5%] | -- | Upper | Mid-Life Peak | 19.2% | [11.8%, 28.0%] | |||
| Upper Middle | Upper | 31.0% | [23.2%, 39.5%] | -- | Upper-Middle | Mid-Life Peak | 18.3% | [10.8%, 26.9%] | |||
| Lower Middle |Upper | 17.6% | [11.3%, 24.8%] | -- | Lower-Middle | Mid-Life Peak | 22.1% | [14.8%, 30.6%] | |||
| Low Earners | Upper | 8.5% | [4.2%, 14.4%] | -- | Low Earners | Mid-Life Peak | 23.1% | [16.0%, 31.2%] | |||
| Sustained Increase |Upper Middle | 14.2% | [9.8%, 19.5%] | -- | Ultra-Rich | Upper Middle | 6.1% | [3.2%, 10.2%] | |||
| Mid-Life Peak | Upper Middle | 9.8% | [5.7%, 14.8%] | -- | Upper | Upper Middle | 23.2% | [17.4%, 29.8%] | |||
| Upper Middle | Upper Middle | 25.6% | [20.0%, 31.8%] | -- | Upper-Middle | Upper Middle | 33.1% | [26.0%, 40.4%] | |||
| Lower Middle | Upper Middle | 27.7% | [22.0%, 34.1%] | -- | Lower-Middle | Upper Middle | 22.3% | [16.4%, 29.0%] | |||
| Low Earners | Upper Middle | 22.2% | [16.8%, 28.1%] | -- | Low Earners | Upper Middle | 14.8% | [10.1%, 20.4%] | |||
| Sustained Increase | Lower-Middle | 5.8% | [2.6%, 10.0%] | -- | Ultra-Rich | Lower Middle | 5.5% | [2.8%, 9.1%] | |||
| Mid-Life Peak | Lower-Middle | 13.6% | [9.1%, 19.1%] | -- | Upper | Lower Middle | 11.2% | [7.2%, 16.0%] | |||
| Upper Middle | Lower-Middle | 19.9% | [14.7%, 25.9%] | -- | Upper-Middle | Lower Middle | 30.2% | [23.9%, 37.0%] | |||
| Lower Middle | Lower-Middle | 33.6% | [27.1%, 40.6%] | -- | Lower-Middle | Lower Middle | 31.7% | [25.2%, 38.5%] | |||
| Low Earners | Lower-Middle | 26.5% | [20.4%, 33.2%] | -- | Low Earners | Lower Middle | 21.0% | [15.8%, 27.1%] | |||
| Sustained Increase | Low Earners | 8.4% | [4.7%, 13.3%] | -- | Ultra-Rich | Low Earners | 3.3% | [1.0%, 7.3%] | |||
| Mid-Life Peak | Low Earners | 16.5% | [11.3%, 22.6%] | -- | Upper | Low Earners | 6.3% | [3.1%, 10.9%] | |||
| Upper Middle | Low Earners | 15.3% | [10.4%, 21.2%] | -- | Upper-Middle | Low Earners | 28.3% | [21.5%, 35.7%] | |||
| Lower Middle | Low Earners | 25.7% | [19.6%, 32.9%] | -- | Lower-Middle | Low Earners | 29.4% | [22.6%, 36.8%] | |||
| Low Earners | Low Earners | 33.4% | [26.6%, 40.6%] | -- | Low Earners | Low Earners | 32.0% | [25.4%, 39.3%] | |||
Note: i|j refers to the conditional probability of the father (son) being in latent group j conditional on the son (father) being in latent group i. Sigma is the estimated standard deviation of the residuals. Intercepts are forced into the model and not subject to model selection.