We are working on three substantive research projects:
Goldstein and Noden (2003: Oxford Review of Education 29, 225-237) introduced a new model-based approach to the measurement of diversity by considering a multilevel model where the main focus of interest was the modelling of variation. In the case of schooling, eligibility for free school meals has been the focus of much interest. These authors used the proportion of such children in a school as their response variable in a 3-level model which explicitly included school and local education authority (LEA) effects. Thus the between-school and between-LEA variances are model parameters. In essence these parameters capture the diversity among schools and LEAs and functions of the estimates of them will correspond to different indexes that have been put forward in the literature. There are several advantages to such a modelling approach. The first is that the models can be elaborated to include covariates and also to allow, for example, different variances for different types of schools or LEAs and to incorporate trend terms that allow the study of changes in variation across time. The second is that the model parameters are not functions of the size of school, which affects the traditional indexes. The third advantage is that since underlying processes are being modelled this allows inferences to a superpopulation of interest and readily provides interval estimates and significance tests.
Further work (Leckie et al., 2011) has developed the argument for a multilevel modelling approach by first describing and expanding upon its notable advantages. They then propose a major extension to this approach by introducing a simple simulation method that allows traditional descriptive indices to be reformulated within a modelling framework. The multilevel approach and the simulation method are illustrated with an application that models recent social segregation among schools in London.
In February 2009, LEMMA (jointly with the NCRM ADMIN node) participated in a 2-day workshop on measuring segregation which attracted 50 participants. Rebecca Pillinger's presentation explored some of the weaknesses of descriptive segregation indices, which mostly stem from their measuring unevenness due to chance as well as to systematic sorting (i.e. their failure to recognise that observed data is drawn from a superpopulation). Goldstein and Noden's approach was extended to handle the case where the characteristic of interest has multiple categories. This is then applied to PLASC data to examine ethnic segregation in England between 2002 and 2008. LEA level segregation is found to be greater than school level segregation for both Black pupils compared to White and Asian pupils compared to White. A more complex model is then fitted which allows for segregation by Free School Meal status as well as ethnicity, and it is found that ethnic segregation exists over and above segregation by Free School Meals status. The workshop included a practical session on modelling segregation in MLwiN, which has been converted to online training materials.
Leckie G.B., Pillinger R.J., Jones K. and Goldstein H. (2011) Multilevel modelling of social segregation. Journal of Educational and Behavioral Statistics. Forthcoming.
There are two strands to this project:
School effectiveness analyses have largely ignored the role of the family as an important source of variation for children's educational progress. Sibling analyses in developmental psychology and behavioural genetics have largely ignored sources of shared environmental variation beyond the immediate family. Rasbash et al. (2010) formulate a multilevel cross-classified model that examines variation in children's progress during secondary schooling and partitions this variability into pupil, family, primary school, secondary school, local education authority and residential area. Their results suggest that about 50% of what has been labelled as pupil variation in school effectiveness models is really between-family variation and that about 22% of the total variance is due to shared environments beyond the immediate family.
This work has been selected as the best JRSSA paper of the year, and will be presented in the "Best of the Society Journal Papers" session at the 2010 RSS conference. An article has also been written for the RSS magazine Significance (Leckie et al., 2010).
This work extends and applies methods developed under the correlated random classifications project (Browne and Goldstein, 2010). Using data from the Avon Longitudinal Study of Parents and Children (ALSPAC) linked to national pupil attainment data, we allow for correlation between random effects for primary schools with overlapping catchment areas in an analysis of Key Stage 2 attainment. Preliminary work was presented at the International Multilevel Modelling conference in 2009 (Clarke et al., 2009) and further developments were presented at the 2010 NCRM Research Methods Festival.
See also Correlated random classifications
It is well established that risky behaviours in families cluster together (e.g. Jenkins et al. 2005: Child Development 76, 24-39) and that the causal relationships between these behaviours is not well understood. We will examine the directionality of relationships between parental depression, child behaviour, marital difficulties and family type (single parent, nuclear, step) in a multiprocess model. Family data provide a particularly challenging set of issues for multiprocess models because of the complex structure of families: individuals are multiple members of dyads and dyads are nested within families.
Three papers have been submitted to journals. Jenkins et al. (2010) considers maternal depression as a shared family effect, Jenkins et al. (2009) develop a cross-classified multilevel model with complex covariance structure to examine changes in the quality of sibling relationships over time. Steele et al. (2010) propose a multilevel simultaneous equations model for joint estimation of reciprocal parent-child effects and sibling effects, with an application to maternal depression and child delinquency using ALSPAC data.
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