Quality & Quantity 36: 113–127, 2002.
© 2002 Kluwer Academic Publishers. Printed in the Netherlands.
Combining Modelling Strategies to Analyse
Teaching Styles Data
NEIL H. SPENCER
Department of Statistics, Economics, Accounting and Management Systems, University of
Hertfordshire, Hertford Campus, Mangrove Road, Hertford, SG13 8QF, UK,
Abstract. This paper combines two estimation procedures: Iterative Generalized Least Squares as
used in the software MLwiN; Gibbs Sampling as employed in the software BUGS to produce a
modelling strategy that respects the hierarchical nature of the Teaching Styles data and also allows
for the endogeneity problems encountered when examining pupil progress.
Key words: endogeneity; iterative generalized least squares; gibbs sampling.
The progress that pupils make in their academic achievement is seen as an indicator
of the quality of the education that they receive. With the possibility of sanctions
being imposed on schools and/or teachers that are seen to produce inadequate
progress, and role models being made of those schools and/or teachers that pro-
duce progress above what is generally expected, it is of prime importance that the
assessment of pupil progress is handled with care. This care must be taken in the
actual measurement of pupil achievement and also the statistical analyses to which
measures are subjected.
The role of multilevel models in the analysis of educational data is now gener-
ally accepted. Recently published papers in the ﬁeld that use them in their analyses
include Dryler (1999), Brutsaert (1999), Goldstein and Sammons (1997), Hofman
et al. (1999). Those that use multilevel analyses to examine pupil progress include
Sammons and Smees (1998), Strand (1997), Tymms et al. (1997). In the setting
of education, pupils are grouped into classes which are then grouped into schools.
In the multilevel model, each level of the hierarchy in the data has a random effect
associated with it to allow for the contribution to the response of unmeasured or un-
measureable inﬂuential factors that operate at each level. Coefﬁcients of regressors
in the model may also have random components to allow the effect of the regressors
to vary between the different groupings at the various levels of the hierarchy. It is
this respect that multilevel models give to the hierarchy of the data that have made
their use commonplace. Software speciﬁcally designed to ﬁt multilevel models
have been available since the 1980s and now include MLwiN (Goldstein et al.,