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Why use arbitrary points scores?: ordered categories in models of educational progress

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Much statistical modelling of random effects on ordered responses, particularly of grades in educational research, continues to use linear models and to treat the responses through arbitrary scores. Methodological and software developments now facilitate the proper treatment of such situations through more realistic generalized random-effects models. This paper reviews some methodological comparisons of these approaches. It highlights the flexibility offered by the macro facilities of the multilevel random-effects software MLwiN. It considers applications to an analysis of primary school educational progress from reception to England and Wales national curriculum key stage 1 mathematics. By contrasting the results from generalized modelling and scoring approaches it draws some conclusions about the theoretical, methodological and practical options that are available. It also considers that results of generalized random-model estimation may be more intelligible to users of analytical results.

Keywords: Extra-multinomial Variation; Generalized linear models; Iterative generalized least squares; MLwiN; Multilevel; National curriculum assessment; Ordered responses; Primary education; Random effects; School effects; Scoring ordered categories

Document Type: Research Article

Affiliations: University of Birmingham and Institute of Education, London, UK

Publication date: 1999-03-01

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