Hi Nicola and David, This is a great question. I have seen a couple ways to succinctly represent hierarchical models while staying true to the idea of representing the stochastic and systematic parts of our model (although of course here, what was once the systematic part know has stochastic elements so things become a little jumbled). For one type of representation, see the Zelig manual: http://gking.harvard.edu/zelig/docs/ls.mixed.pdf The other thing I have seen involves essentially merging the systematic component into the stochastic component, for the distribution of Y; the write out the stochastic component with systematic component merged in for random parameters; then write out the stochastic component with merged systematic component for the next random parameters. No matter how you slice, that's a lot of latex. By the way, a lot of these models are in Zelig for those who want to try out some of these models. Iain On Wed, Mar 24, 2010 at 2:18 PM, Nicola Bretscher <nicolabretscher at gmail.com <mailto:nicolabretscher at gmail.com>> wrote: Dear all, How do you specify the systematic and stochastic components of a model in Gary's notation if you are using a multilevel/hierarchical/mixed effects model? The model we want to use has a three level structure, comprising both fixed and random effects. Our independent variables are linear ability, quadratic ability and school-average ability and dependent variable is maths self-concept. In standard notation our model is defined as follows: Y_ijk = alpha_jk + beta_rjk*X_rijk + epsilon_ijk where alpha_jk = gamma_00 + u_0j + v_0jk (intercept) beta_rjk = gamma_r0 + u_rj + v_rjk (slope) gamma's represent the fixed component of the intercept and slope. u's represent the random component of the intercept and slope at the second level. u~N(0, SIGMA_u) v's represent the random component of the intercept and slope at the third level. v~N(0, SIGMA_v) epsilon is the error in the model as a whole. epsilon~N(0, SIGMA_e) Note SIGMA is a covariance matrix. Many thanks, Nicola and David _______________________________________________ gov2001-l mailing list gov2001-l at lists.fas.harvard.edu <mailto:gov2001-l at lists.fas.harvard.edu> http://lists.fas.harvard.edu/mailman/listinfo/gov2001-l ------------------------------------------------------------------------ _______________________________________________ gov2001-l mailing list gov2001-l at lists.fas.harvard.edu http://lists.fas.harvard.edu/mailman/listinfo/gov2001-l

Hi Iain, Are there any resources you would suggest explaining MLM? The stuff I've found online hasn't quite done it for me. I understand that MLM involves accounting for variance at different levels, but I'm not sure I quite understand how it looks. Does the following seem right for a three-level model of normally distributed outcomes? Y ~ N(a_jk+BX_ijk,sigma_y2) a ~ N(gamma_o0 + u_oj,sigma_a2) B ~ N(gamma_r0 + u_rj, sigma_B2) Thanks, Jason Iain Osgood wrote: Hi Nicola and David, This is a great question. I have seen a couple ways to succinctly represent hierarchical models while staying true to the idea of representing the stochastic and systematic parts of our model (although of course here, what was once the systematic part know has stochastic elements so things become a little jumbled). For one type of representation, see the Zelig manual: http://gking.harvard.edu/zelig/docs/ls.mixed.pdf The other thing I have seen involves essentially merging the systematic component into the stochastic component, for the distribution of Y; the write out the stochastic component with systematic component merged in for random parameters; then write out the stochastic component with merged systematic component for the next random parameters. No matter how you slice, that's a lot of latex. By the way, a lot of these models are in Zelig for those who want to try out some of these models. Iain On Wed, Mar 24, 2010 at 2:18 PM, Nicola Bretscher < nicolabretscher at gmail.com> wrote: ------------------------------ _______________________________________________ gov2001-l mailing listgov2001-l at lists.fas.harvard.eduhttp://lists.fas.harvard.edu/mailman/listinfo/gov2001-l _______________________________________________ gov2001-l mailing list gov2001-l at lists.fas.harvard.edu http://lists.fas.harvard.edu/mailman/listinfo/gov2001-l