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

Much statistical modelling of random effects on ordered responses, particul arly of grades in educational research, continues to use linear models and to treat the responses through arbitrary scores. Methodological and softwar e developments now facilitate the proper treatment of such situations throu gh more realistic generalized random-effects models. This paper reviews som e methodological comparisons of these approaches. It highlights the flexibi lity offered by the macro facilities of the multilevel random-effects softw are MLwiN. It considers applications to an analysis of primary school educa tional 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, me thodological and practical options that are available. It also considers th at results of generalized random-model estimation may be more intelligible to users of analytical results.