Dialect Variation and Reading: Is Change in Nonmainstream American English Use Related to Reading Achievement in First and Second Grades?

. Author manuscript; available in PMC: 2015 Jan 21.

Published in final edited form as: J Speech Lang Hear Res. 2011 Dec 23;55(1):55–69. doi: 10.1044/1092-4388(2011/09-0257)

Growth Model – DVAR (i.e., ΔDVAR)

Level 1 Model

DVAR_ijk = Π_0jk + Π_1jk (G2_ijk) + Π_2jk (TIMEMG1G_ijk) + Π_3jk (G2 × TIME_ijk) + e_ijk

Level 2 Model

Π_0jk = θ₀ + b_00j + c_00k

Π_1jk = θ₁

Π_2jk = θ₂ + b_20j

Π_3jk = θ₃

Growth Model – Letter-Word Identification

Level 1 Model

LWID_it = Π₀ + Π₁ (Grade 1 Month) + Π₂ (Grade 2) + Π₃ (Grade 2 Month) + ε

Level 2 Model

Π₀ = β₀₀ + β₀₁ (DVAR) + r₀

Π₁ = β₁₀ + β₁₁ (DVAR) + r₁

Π₂ = β₂₀ + β₂₁ (DVAR) + r₂

Π₃ = β₃₀ + β₃₁ (DVAR) + r₃

Growth Model – Passage Comprehension

Level 1 Model

PC_it = Π₀ + Π₁ (Grade 1 Month) + Π₂ (Grade 2) + Π₃ (Grade 2 Month) + ε

Level 2 Model

Π₀ = β₀₀ + β₀₁ (DVAR)

Π₁ = β₁₀ + β₁₁ (DVAR) + r₁

Π₂ = β₂₀ + β₂₁ (DVAR)

Π₃ = β₃₀ + β₃₁ (DVAR) + r₃

Model fitting: A series of sequential models were initially tested to examine which model best fit the data: (a) fixed intercept–fixed slope, (b) random intercept–fixed slope, (c) fixed intercept–random slope, and (d) random intercept–random slope. Following this test, the better fitting model was examined for variability in intercepts and slopes. Results from the −2 log likelihood test suggest that the random intercept–random slope model improved the description of growth for letter–word identification, χ²(7) = 40.22, p < .001, whereas the fixed intercept-random slope model was a better descriptor for growth in reading, χ²(7) = 80.45, p < .001. We then entered ΔDVAR into the model at Level 2. Nonsignificant variance components were fixed to achieve greater power in model estimation.

Proportion Reduction in Variance

\frac{{\overset{⌢}{τ}}_{q q} (U C) - {\overset{⌢}{τ}}_{q q} (C)}{{\overset{⌢}{τ}}_{q q} (U C)},

where τ̑_qq (UC) represents the tau estimate for a given parameter (e.g., intercept) for the unconditional model and τ̑_qq (C) is a tau estimate for the conditional model (Raudenbush & Bryk, 2002).