Page 78 - Second language development of newly arrived migrant kindergarteners - Frederike Groothoff
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78 Chapter 4 (2008). Normally, raw scores are adjusted for different ages however, newly arrived migrant kindergarteners could have the same amount of exposure to Dutch even though their ages differ, and thus standard scores adjusted for age will put older children at a greater disadvantage (see also Jacobs, 2016). Our measurements are nested within pupils, and observations of the same pupil are of course more alike than observations of different pupils. Due to these dependencies, the most appropriate method of analysis is considered multilevel modeling (see Quené & van den Bergh, 2004). Our 42 participants provided us with 168 data points. For this purpose, multilevel modeling of repeated measures data procedures (MLwiN software version 2.36; Rasbash, Charlton, Browne, Healy, & Cameron, 2016) was carried out. The mean development of PPVT scores was modelled by fitting different polynomial functions to the data. In the first model it was assumed there is no growth, in the second model it is assumed that scores change (on average) linearly with age, and in the third model it is assumed that the relation between scores and age deviates from linearity. In addition to these differences in mean scores, we also modelled the variance within and between pupils. Multilevel modeling allows for heteroscedasticy of variances at each level, therefore the variance within and between pupils was modelled in a series of subsequent models. In general polynomials are very flexible functions and can take almost any shape, depending on the number of parameters. In the models, both the fixed and random components increased in complexity. If yij is the score on the ith age (the age in months) of the jth individual, then a polynimial can be written as: yij = fj (ageij). This function can be written as a regression model, which assumes that the latencies depend on powers of age: yij = β0ij + β1*Age1ij + β2*Age2ij + ... It is an empirical matter to determine which order a polynominal will take in a given data set. Generally, the most parsimonious is chosen (Van den Bergh, Schmittmann, Hofman, & van der Maas, 2015), the model that explains the variation in outcome scores the best. The development of our receptive vocabulary score was tested with a maximum of 7 models. Model 0 was the basic null model in which the PPVT score was allowed to vary within and between pupils. In Model 1, Age at testing was added as a fixed main effect to test whether avarage scores differed over time. Whether the differences within and between pupils depend on Age was tested in respectively Model 2 and 3. Model 4 tested the main effect of Age2 and Model 5 and 6 tested whether there was variance within or between pupils in the exponential effect of Age. Finally one of the seven models was assigned as the best fit and seen as the General Development Model. Each score of the fit of each model, along with the difference 


































































































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