scott rifkin
2006-Dec-28 21:05 UTC
[R] lmer: Interpreting random effects contrasts and model formulation
I'm trying to fit a nested mixed model using lmer and have some questions about the output and my model formulations. I have replicate measures on Lines which are strictly nested within Populations. (a) So if I want to fit a model where Line is a random effect and Populations are fixed and the random Line effect is constant across Populations, I have: measure_ijk = mu + P_i + L_ij + e_ijk where L ~ N(0,s_L) measure ~ 1 + Population + (1|Population:Line) (b) If instead I want to allow the random Line effect to be Population specific, I put: measure_ijk = mu + P_i + L_ij + e_ijk where L_i ~ N(0,s_L_i) measure ~ 1 + Population + (Population | Population:Line) (c) Question 1: if instead, I put: measure ~ 1 + Population + (1 | Population:Line) + (Population | Population:Line) would the model be: measure_ijk = mu + P_i + L_ij + e_ijk where L_i ~ N(0,s_L_i)+N(0,s_L) ? (d) Question 2: in (b) above, the part of the output from summary(model) corresponding to (Population | Population:Line) is: Random effects: Groups Name Variance Std.Dev. Corr pop:line (Intercept) 52.1214951 7.219522 popP1 39.5706524 6.290521 0.995 popP2 24.8629456 4.986276 0.994 0.986 popP3 0.6350483 0.796899 0.993 0.985 0.982 popP4 1.4422308 1.200929 0.992 0.986 0.985 0.980 Residual 0.0025377 0.050375 How do I interpret these contrasts? If it were fixed effects, it would be treatment contrasts which I understand. Is it a similar thing here where the Variance of 39.57 for popP1 is actually: Variance(popP0 - popP1) = Variance(popP0) + Variance(popP1) - 2*Corr(popP0,popP1)*StdDev(popP0)*StdDev(popP1) => 39.57 = 52.12 + StdDev(popP1)^2 - 2*0.995*7.219522*StdDev(popP1) (e) Question 3: For the model (c), there is another line at the top of the results with the intercept corresponding to (1|Population:Line). Random effects: Groups Name Variance Std.Dev. Corr pop:line (Intercept) 3.2490952 1.802525 pop:line (Intercept) 47.1995788 6.870195 e popP1 44.6401379 6.681328 0.995 popP2 34.1298102 5.842072 0.994 0.980 popP3 0.8056185 0.897563 0.991 0.983 0.983 popP4 2.5663700 1.601989 0.993 0.985 0.985 0.983 Residual 0.0025374 0.050372 How does this play into the estimates? (I suspect this will become clear when I understand the answer to question d) Thanks much, Scott Rifkin