How to Estimate Following Model using R /MLwiN?

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• tj = Belta0j ＋ Belta1j * timetj + etj              
• Belta0j  = Gamma00 + Gamma01 * X1j + Gamma02 * X2tj + u0j   
• Belta1j  = Gamma10 + Gamma11 * X3j + u1j               
  

t and j are indexes for time and individual;

It seems that HLM does not support to include the predictor from lower-level in the higher level mode. My first questions are:Can I specify an exact model as the above in HLM so all the lower-level predictors could be included in the high level model, and How can we estimate the following model using R /MLwiN?

• Ytj = Belta0j ＋ Belta1j * timetj + β2j * X2tj +etj                  
• Belta0j  = Gamma00 + Gamma01 * X1j + u0j                                   
• Belta1j  = Gamma10 + Gamma11 * X3j + u1j                                    
• Belta1j  = Gamma20                                                               
  

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关键词：following estimate follow Using MLwiN individual following included support higher

Two Multilevel Modeling Techniques for Analyzing Comparative Longitudinal Survey Datasets

Malcolm Fairbrother

School of Geographical Sciences, University of Bristol

30 March 2013

http://seis.bris.ac.uk/~ggmhf/MHF.MLM-longit.2013.pdf

y_tj = B_0 + B_1*X_j + B_2*X_tj + B_3*time_tj + B_4*X_j*time_tj + u_1j*time_tj + u_0j + e_tj

So there's an overall intercept, slope on X_j, slope on X_tj, slope on time, slope on the interaction between X_j and time, and three random erros (residual error, a random intercept by j, and a random time slope by j).

In R, this could be fitted using: lmer(y ~ Xtj + time*Xj + (time | group), data=dat) or using other functions, such as MCMCglmm.