TABLE 1.

Likelihood ratio chi-square tests comparing models

	Unconditional model	Linear model with random intercept and fixed linear slope	Linear model with random intercept and random linear slope	Quadratic model with random intercept, random linear slope, and fixed quadratic slope	Quadratic model with random intercept, random linear slope, and random quadratic slope
Log likelihood	−2390.541	−1831.260	−1827.688	−1790.110	−1780.979
χ2		1118.562	7.144	75.156	18.262
df		1	2	1	3
P		<.001	.028	<.001	<.001

Each model except for the unconditional model is compared to the preceding model.