Page 115 - Second language development of newly arrived migrant kindergarteners - Frederike Groothoff

Development of narrative ability 115 component – allowing for differences in Age – fit the data better than a model with only an intercept (ΔΧ2 (MLR1) = 21.74; df = 1; p < .001). The variance within individuals depends on the age of participants (ΔΧ2 (MLR2) = 59.20; df = 2; p < .001). The variance between individuals is a (linear) function of age as well (ΔΧ2 (MLR3) = 14.64; df = 1; p < .001). Finally, adding Age2 to the model improved the fit significantly (ΔΧ2 (MLR4) = 7.34; df = 1; p = .01). Hence, in the final model (MLR4) a fixed effect of Age1 and Age2, as well as variance within and between pupils components which depends on Age needs to be included, and with this model we continued the analysis. Table 5.13: Fit of Different Models (-2LL) for Changes in Measure of Lexical Richness (168 cases) as well as the Comparison of Consecutive Models. Comparison -2LL Models ΔΧ2 Δdf p Model MLR0: β0ijcons a 759.14 MLR1: MLR0 + β1Age1ij MLR2: MLR1 + e1ijAge1ij MLR3: MLR2 + u10jAge1ij MLR4: MLR3 + β2Age2ij MLR5: MLR4 + e2ijAge2ij MLR6: MLR5 + u20jAge2ijc a In addition to the intercept, variance components for differences within and between individuals are estimated b Only the covariance-coefficient between the intercept- and the age-residuals was estimated. c No convergence within 250 iterations. Based on this General Development Model we constructed Figure 5.8, in which both the average development and the differences within and between individuals are represented (see Table 2.3 in Appendix 2 for the parameter estimates). The average MLR score at 73 months was 2.25. Each month a pupil grew older his or her MLR score increased by .07, but the quadratic function of age decreased the score by .003 (since this is a small effect it is not visible in Figure 5.8). 737.41 MLR0 vs MLR1 678.20 MLR1 vs MLR2 663.56 MLR2 vs MLR3 656.21 MLR3 vs MLR4 649.31 MLR4 vs MLR5 21.74 59.20 14.64 7.34 2.74 1 <.001 2 <.001 1b <.001 1 0.01 3 .08ns