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Table 3 List of estimated parameters for each individual model

From: Modelling subject-specific childhood growth using linear mixed-effect models with cubic regression splines

Parameter Variable Ordinary least squares Random effects Random effects and CAR(1)
\(\beta_{0}\) Intercept 48.17 (47.43, 48.90) 48.07 (47.66, 48.49) 47.97 (47.56, 48.38)
\(\beta_{1}\) \(t_{ij}\) 4.47 (3.39, 5.55) 4.53 (4.21, 4.84) 4.65 (4.33, 4.96)
\(\beta_{2}\) \(t_{ij}^{2}\) −0.28 (−0.75, 0.18) −0.29 (−0.42, −0.15) −0.32 (−0.47, −0.18)
\(\beta_{3}\) \(t_{ij}^{3}\) 0.0015 (−0.061, 0.058) −0.0014 (−0.019, 0.016) 0.0021 (−0.017, 0.021)
\(\beta_{4}\) \(\left( {t_{ij} - 3} \right)_{ + }^{3}\) 0.026 (−0.044, 0.096) 0.026 (0.0062, 0.047) 0.023 (−0.00037, 0.046)
\(\beta_{5}\) \(\left( {t_{ij} - 6} \right)_{ + }^{3}\) −0.021 (−0.035, −0.0069) −0.022 (−0.026, −0.018) −0.022 (−0.028, −0.016)
\(\beta_{6}\) \(\left( {t_{ij} - 12} \right)_{ + }^{3}\) −0.0021 (−0.0063, 0.0020) −0.0025 (−0.0037, −0.0013) −0.0030 (−0.0050, −0.00097)
\(\beta_{7}\) \(\left( {t_{ij} - 18} \right)_{ + }^{3}\) −0.0018 (−0.0050, 0.0013) −0.0011 (−0.0020, −0.00016) −0.00056 (−0.0020, 0.00090)
\(\beta_{8}\) \(\left( {t_{ij} - 24} \right)_{ + }^{3}\) 0.00092 (−0.00085, 0.0027) 0.00047 (−0.000038, 0.00098) 0.00032 (−0.00050, 0.0011)
\(\beta_{9}\) \(\left( {t_{ij} - 40} \right)_{ + }^{3}\) −0.019 (−0.040, 0.0030) 0.00019 (−0.0062, 0.0066) −0.0029 (−0.011, 0.0048)
\(\beta_{10}\) \(I\left( {t_{ij} > 24} \right)\) −1.20 (−1.63, −0.77) −0.91 (−1.03, −0.78) −0.72 (−0.84, −0.60)
\(\beta_{11}\) \(I\left( {male} \right)\) 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)
\(\rho\) Correlation 0.66 (0.64, 0.68)
\(\sigma^{2}\) Unexplained variance 7.34 (−7.05, 21.76) 0.60 (0.59, 0.62) 0.81 (0.75, 0.87)