. Author manuscript; available in PMC: 2013 Jan 17.

Published in final edited form as: J Educ Psychol. 2012 Aug;104(3):603–621. doi: 10.1037/a0027571

Table 7.

A. Models Including Intervention Effects for WJ Math
Term	Model 4	Model 5	Model 6	Model 7
Fixed Effects
Intercept	459.41^*	458.71^*	458.10^*	459.46^*
Linear	15.47^*	15.81^*	16.54^*	16.51^*
Quadratic	−1.15^*	−1.14^*	−1.31^*	−1.30^*
Retention Grade 1	1.28	3.62^*	5.51^*	4.48^*
Retention 1 × linear	--------	−1.18^*	−3.62^*	−3.52^*
Retention 1 × quadratic	--------	--------	0.54^*	0.51^*
Retention Grades 2–4	--------	--------	--------	−7.51^*
Variance Components
Intercept (L2)	26.21^*	26.04^*	25.89^*	26.77^*
Linear (L2)	14.44^*	13.47^*	11.94^*	11.98^*
Quadratic (L2)	.31	0.31	0.26^*	0.26^*
Intercept (L3)	86.21^*	85.96^*	85.63^*	78.24^*
Residual (L1)	30.16^*	29.71^*	29.66^*	29.64^*
Covariance Components
Intercept and Slope	−21.60^*	−20.52^*	−19.70^*	−19.33^*
Intercept and Quadratic	3.36^*	3.2^*	3.07^*	2.91^*
Slope and Quadratic	−2.06^*	−1.99^*	−1.70^*	−1.70^*

B. Models Including Intervention Effects for WJ Reading
Term	Model 4	Model 5	Model 6	Model 8
Fixed Effects
Intercept	426.65^*	424.06^*	423.22^*	424.88^*
Linear	31.42^*	32.45^*	33.81^*	33.79^*
Quadratic	−3.54	−3.54^*	−3.82^*	−3.82^*
Retention Grade 1	3.53	11.59^*	14.52^*	13.11^*
Retention 1 × linear	--------	−3.36^*	−8.02^*	−8.03^*
Retention 1 × quadratic	--------	--------	1.00^*	1.00^*
Retention Grades 2–4	--------	--------	--------	−8.78^*
Variance Components
Intercept (L2)	60.04^*	74.79^*	82.55^*	48.43^*
Linear (L2)	14.04^*	13.41^*	14.00^*	14.03^*
Quadratic (L2)	0	0	0	0
Intercept (L3)	198.54^*	197.62^*	198.33^*	191.04^*
Residual (L1)	99.45^*	94.81^*	93.85^*	93.83^*
Covariance Components
Intercept and Slope	−15.33	−17.57	−23.97^*	−23.70^*
Intercept and Quadratic	1.10	0.94	2.22	2.21
Slope and Quadratic	−1.34^*	−1.26^*	−1.32^*	−1.33^*

Note. Model 4 estimates the effect of retention in grade 1 on the intercept. Model 5 estimates the effect of retention in grade 1 on the intercept and linear slope. Model 6 estimates the effect of retention on the intercept, linear slope, and quadratic acceleration. Model 7 estimates the effect of retention at grade 1 on the intercept, linear slope, and quadratic acceleration, plus the effect of retention in grades 2–4 on the level. All models estimate the corresponding random variance and covariance components for the intercept, slope, and quadratic acceleration at level 2. These components are conditional on the specific grade retention effects included in the model. All models estimate a random intercept variance component for the intercept at level 3 to account for the matching.

p < .05. Time was coded as years and tenths of years elapsed since the initial measurement in first grade (November) which was coded as 0. Tests of fixed effects are two-tailed; tests of variance components are one-tailed since variances must be positive or zero. L1 = level 1, L2 = level 2, L3 = level 3.