How to Estimate Following Model using R /MLwiN?

SPSSCHEN

1536

收藏 2014-01-08

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

Thank you again!

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SPSSCHEN

2014-1-8 11:25:03

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

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SPSSCHEN

2014-1-8 11:31:53

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.

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