Article

Subject-specific odds ratios in binomial GLMMs with continuous response

Statistical Methods and Applications (Impact Factor: 0.57). 02/2008; 17(3):309-320. DOI: 10.1007/s10260-007-0060-x
Source: RePEc

ABSTRACT In a regression context, the dichotomization of a continuous outcome variable is often motivated by the need to express results
in terms of the odds ratio, as a measure of association between the response and one or more risk factors. Starting from the
recent work of Moser and Coombs (Stat Med 23:1843–1860, 2004) in this article we explore in a mixed model framework the possibility
of obtaining odds ratio estimates from a regression linear model without the need of dichotomizing the response variable.
It is shown that the odds ratio estimators derived from a linear mixed model outperform those from a binomial generalized
linear mixed model, especially when the data exhibit high levels of heterogeneity.

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    ABSTRACT: In his keynote address to the National Council of Teachers of Mathematics research pre-session, Sloane (2006b) challenged mathematics education researchers to ‘quantify qualitative insights’. This quasi-experimental study used blended methods to investigate the development of two-digit addition and subtraction strategies. Concurrent classroom teaching experiments were conducted in two intact first grade classrooms (n = 41) in a mid-Atlantic American public school. From a pragmatic emergent perspective, design research (Gravemeijer & Cobb, 2006) was used to develop local instructional theory. An amplified theoretical framework for early base-ten strategies is explicated. Multilevel modelling for repeated measures was used to evaluate the differences in strategy usage between classes across occasions and the association of particular pedagogical practices with the emergence of incrementing and decrementing by ten (N10) or decomposition (1010) strategies (Beishuizen, Felix, & Beishuizen, 1990).The two matched classes were not different in terms of gender, poverty, race, pre-assessment performance, and special education services. After the first unit of instruction with differentiated pedagogical tools, the collection class was significantly (p = .001) more likely to use 1010 than the linear class. No difference was demonstrated during the post-assessment. Students in both classes were more likely to use N10 during the last structured interview than in the first (p < .0001). Furthermore, there was no difference between the two classes in using any advanced strategy; however, students in both classes were more likely to use an advanced strategy at the conclusion of the study than they were initially (p = .033). The order of emergence of 1010 and N10 was not associated with the ability to develop both strategies, but there was an association (p < .001) between use of an advanced strategy and success on a district-mandated written assessment of two-digit addition and subtraction.Two original instructional sequences of contextually-based investigations are presented. Protocols transcribed from videotaped lessons and dynamic assessment interviews are presented to illuminate specific constructs detected and to illustrate the pedagogical techniques. An amplified framework for early place value constructs is proposed. Recommendations for future studies, curricular changes, and the need of early intervention are discussed.

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