. Author manuscript; available in PMC: 2012 Feb 1.

Published in final edited form as: J Sch Psychol. 2010 Oct 18;49(1):1–23. doi: 10.1016/j.jsp.2010.09.003

Table 2.

Chi-square Difference Tests for Locating the Optimal Growth Curve Model for Behavioral Engagement and Teaching Practice Separately

Model	Behavioral Engagement		Performance Practice
Model	Chi-square	Chi-square difference test	Chi-square	Chi-square difference test
Model 1	χ² _{(df = 4)} = 12.89		χ² _{(df = 6)} = 10.03
Model 2	χ² _{(df = 7)} = 27.33	χ²_{(Model 2 – Model 1)} = 14.44, df = 3, p <.01	χ² _{(df = 7)} = 13.28	χ²_{(Model 2 – Model 1)} = 3.25, df = 1, p =.07
Model 3	χ² _{(df = 5)}= 16.14	χ²_{(Model 3 – Model 1)} = 3.25, df = 1, p =.07	χ² _{(df = 7)} = 12.34	χ²_{(Model 3 – Model 1)} = 2.31, df = 1, p =.13
Model 4	χ² _{(df = 8)} = 31.20	χ²_{(Model 4 – Model 3)} = 15.05, df = 3, p <.01	χ² _{(df = 10)} = 22.68	χ²_{(Model 4 – Model 3)} = 10.34, df = 3, p =.02

Note. The likelihood-ratio (chi-square difference) tests for behavioral engagement are presented in column 3, and the likelihood-ratio tests for goal structure are presented in column 5. Model 1 = Quadratic growth model with nonconstant residual variance; Model 2 = Quadratic growth model with constant residual variance; Model 3 = Linear growth model with nonconstant residual variance; Model 4 = Linear growth model with constant residual variance. For behavioral engagement, we fixed the variance of the quadratic term and correlations related to the quadratic term to be 0. For performance practice, we fixed the variance of both the linear and quadratic term and any correlations related to them to be 0.