Table 3.

List of estimated parameters for each individual model

Parameter	Variable	Ordinary least squares	Random effects	Random effects and CAR(1)
${\mathit{\beta }}_0$	Intercept	48.17 (47.43, 48.90)	48.07 (47.66, 48.49)	47.97 (47.56, 48.38)
${\mathit{\beta }}_1$	$t_{ij}$	4.47 (3.39, 5.55)	4.53 (4.21, 4.84)	4.65 (4.33, 4.96)
${\mathit{\beta }}_2$	$t_{ij}^2$	−0.28 (−0.75, 0.18)	−0.29 (−0.42, −0.15)	−0.32 (−0.47, −0.18)
${\mathit{\beta }}_3$	$t_{ij}^3$	0.0015 (−0.061, 0.058)	−0.0014 (−0.019, 0.016)	0.0021 (−0.017, 0.021)
${\mathit{\beta }}_4$	${\left(t_{ij}-3\right)}_{+}^3$	0.026 (−0.044, 0.096)	0.026 (0.0062, 0.047)	0.023 (−0.00037, 0.046)
${\mathit{\beta }}_5$	${\left(t_{ij}-6\right)}_{+}^3$	−0.021 (−0.035, −0.0069)	−0.022 (−0.026, −0.018)	−0.022 (−0.028, −0.016)
${\mathit{\beta }}_6$	${\left(t_{ij}-12\right)}_{+}^3$	−0.0021 (−0.0063, 0.0020)	−0.0025 (−0.0037, −0.0013)	−0.0030 (−0.0050, −0.00097)
${\mathit{\beta }}_7$	${\left(t_{ij}-18\right)}_{+}^3$	−0.0018 (−0.0050, 0.0013)	−0.0011 (−0.0020, −0.00016)	−0.00056 (−0.0020, 0.00090)
${\mathit{\beta }}_8$	${\left(t_{ij}-24\right)}_{+}^3$	0.00092 (−0.00085, 0.0027)	0.00047 (−0.000038, 0.00098)	0.00032 (−0.00050, 0.0011)
${\mathit{\beta }}_9$	${\left(t_{ij}-40\right)}_{+}^3$	−0.019 (−0.040, 0.0030)	0.00019 (−0.0062, 0.0066)	−0.0029 (−0.011, 0.0048)
${\mathit{\beta }}_{10}$	$I\left(t_{ij}>24\right)$	−1.20 (−1.63, −0.77)	−0.91 (−1.03, −0.78)	−0.72 (−0.84, −0.60)
${\mathit{\beta }}_{11}$	$I\left(male\right)$	1.64 (1.54, 1.74)	1.61 (1.11, 2.12)	1.51 (0.99, 2.02)
$g_{11}$	$\text{var}\left(\text{Intercept}\right)$	–	3.60 (2.97, 4.36)	3.37 (2.73, 4.16)
$g_{22}$	$\text{var}\left(t_{ij}\right)$	–	0.0091 (0.0075, 0.011)	0.0067 (0.0054, 0.0084)
$g_{12}$	$\text{var}\left(\text{Intercept},t_{ij}\right)$	–	0.019 (−0.0059, 0.044)	0.036 (0.013, 0.059)
$\mathit{\rho }$	Correlation	–	–	0.66 (0.64, 0.68)
${\mathit{\sigma }}^2$	Unexplained variance	7.34 (−7.05, 21.76)	0.60 (0.59, 0.62)	0.81 (0.75, 0.87)