Page 189 - Second language development of newly arrived migrant kindergarteners - Frederike Groothoff
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cases) as well as the Comparison Model GISI: β0ijcons a GISII: GISI + β1Age1ij GISIII: GISII + e1iAge1ij GISIV: GISIII + u10jAge1ij GISV: GISIV + β2Age2ij GISDEF: GISI + β1jAge1ij a In addition to the intercept, variance individuals are estimated. The influence of the school learning environment 189 Guiraud Index Score (GIS) From the comparison between the consecutive models (see Table 8.13) it is apparent that a model for GIS with a fixed linear component – allowing for differences in Age – fit the data better than a model with only an intercept (ΔΧ2 (GISII) = 57.07; df = 1; p < .001). The variance within individuals did not depend on the age of participants (GISIII). However, the variance between individuals is a function of Age (GISIV). Adding Age2 to the model did not improve the fit significantly (GISIV). Hence, in the final model (GISDEF) a fixed effect of Age, as well as a variance between pupils component which depends on Age needs to be included, and with this model we continued the analysis. Table 8.13: Fit of Different Polynomials (-2LL) for Changes in Guiraud Index Score (162 of Consecutive Models. Comparison Models GISI vs GISII GISII vs GISIII GISIII vs GISIV GISIV vs GISV ΔΧ2 Δdf 57.07 1 2.16 2 6.25 2 1.17 1 p <.001 .34ns .04 .28ns     -2LL 414.70 357.63 355.47 349.22 348.05 349.52                   components for differences within and between        Based on this General Development Model we constructed Figure 8.9, in which both the average development of Guiraud Index Score as well as the differences within and between individuals are represented (see Table 6.8 in Appendix 6 for the parameter estimates). The average GIS at an age of 73 months was estimated as 3.66. Each month a child grew older, his GIS increased by 0.04. 

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