[R-sig-ME] interpreting random intercepts when no fixed intercept present

[John.Morrongiello at csiro.au]

Hi list

I was wondering how I interpret random effect intercepts in a model with no fixed intercept? Take for example the following model, based on those presented in Weisberg etal (2010):

M1<-lmer(growth~0+Age+(1|ID)+(1|Year)

Where growth is a repeatedly measured continuous variable, Age is a factor with 10 ordered levels (2:11) corresponding to each growth observation, ID and year are crossed random effects and represent individual animals (100) and the years in which they were sampled. This model provides a separate coefficient for each age; are the random effects deviations from just the Age2 (first) coefficient, or from the Age term in general? Each ID random effect has only one value, so they are obviously not unique deviations from each level of Age. Or are the random intercepts reflective of differences in average growth among individuals and years after the effect of age is 'accounted' for (i.e. not Age dependent)?

Furthermore, if M1 was extended to include harvest (factor with three levels) to which the population was exposed (some to just one level, others all three):

M2<-lmer(growth~0+Age+harvest+(1|ID)+(1|Year)

Is the interpretation of random effects now different to that in M1 in that they now include some harvest 'information'?

Thank you

John

Weisberg, S., Spangler, G., and Richmond, L.S. (2010). Mixed effects models for fish growth. Canadian Journal of Fisheries and Aquatic Sciences 67, 269-277.