R2MLwiN (version 0.8-1)

tutorial: Exam results for six inner London Education Authorities

Description

A subset of data from a much larger dataset of examination results from six inner London Education Authorities (school boards).

source

Browne, W. J. (2012) MCMC Estimation in MLwiN Version 2.26. University of Bristol: Centre for Multilevel Modelling. Goldstein, H., Rasbash, J., Yang, M., Woodhouse, G., Pan, H., Nuttall, D., Thomas, S. (1993) A multilevel analysis of school examination results. Oxford Review of Education, 19, 425--433. Rasbash, J., Charlton, C., Browne, W.J., Healy, M. and Cameron, B. (2009) MLwiN Version 2.1. Centre for Multilevel Modelling, University of Bristol. Rasbash, J., Steele, F., Browne, W.J. and Goldstein, H. (2012) A User's Guide to MLwiN Version 2.26. Centre for Multilevel Modelling, University of Bristol.

Details

The tutorial dataset is one of the sample datasets provided with the multilevel-modelling software package MLwiN (Rasbash et al., 2009), and is a subset of data from a much larger dataset of examination results from six inner London Education Authorities (school boards). The original analysis (Goldstein et al., 1993) sought to establish whether some secondary schools had better student exam performance at 16 than others, after taking account of variations in the characteristics of students when they started secondary school; i.e., the analysis investigated the extent to which schools `added value' (with regard to exam performance), and then examined what factors might be associated with any such differences. See also Rasbash et al. (2012) and Browne (2012).

See Also

See mlmRev package for an alternative format of the same dataset.

Examples

data(tutorial, package = "R2MLwiN")

# Fit 2-level variance components model, using IGLS (default estimation method)
(VarCompModel <- runMLwiN(normexam ~ 1 + (1 | school) + (1 | student), data = tutorial))

# print variance partition coefficient (VPC)
print(VPC <- coef(VarCompModel)[["RP2_var_Intercept"]] /
             (coef(VarCompModel)[["RP1_var_Intercept"]] +
             coef(VarCompModel)[["RP2_var_Intercept"]]))

# Fit same model using MCMC
(VarCompMCMC <- runMLwiN(normexam ~ 1 + (1 | school) + (1 | student),
 estoptions = list(EstM = 1), data = tutorial))

# return diagnostics for VPC
VPC_MCMC <- VarCompMCMC@chains[,"RP2_var_Intercept"] /
            (VarCompMCMC@chains[,"RP1_var_Intercept"] +
            VarCompMCMC@chains[,"RP2_var_Intercept"])
sixway(VPC_MCMC, name = "VPC")

# Adding predictor, allowing its coefficient to vary across groups (i.e. random slopes)
(standlrtRS_MCMC <- runMLwiN(normexam ~ 1 + standlrt + (1 + standlrt | school) + (1 | student),
 estoptions = list(EstM = 1), data = tutorial))

# Example modelling complex level 1 variance
# fit log of precision at level 1 as a function of predictors
(standlrtC1V_MCMC <- runMLwiN(normexam ~ 
  1 + standlrt + (school | 1 + standlrt) + (1 + standlrt | student),
  estoptions = list(EstM = 1, mcmcMeth = list(lclo = 1)),
  data = tutorial))