It's difficult to compare raw group means against the intercept or coefficients in this type of regression with an unbalanced design and multiple predictors. To illustrate, compare your model with only the categorical variables against the overall means for your 3 species. The intercept of 7.42 is already somewhat below the group mean of 8.05 for the reference O.annularis
. The difference of 3.17 in raw group means between O.faveolata
and O.annularis
is very close to the coefficient of 3.29 for O.faveolata
, but the difference of -1.52 between group means of O.franksi
and O.annularis
is quite different from the O.franksi
coefficient of -0.09. These discrepancies presumably represent different associations of the 3 species with the other categorical predictors.
This problem will be exacerbated in your model that includes the continuous predictors, as small differences among the species in values of the continuous predictors, near their observed non-zero values, will be magnified in the extrapolation down to values of 0 for the continuous predictors that are required to provide the intercept in this formulation of the problem. You could presumably examine the relations of all continuous predictors to the individual species to understand the detailed reasons why the intercept seems to be so high to you, but that might not be worth the effort. Try instead expressing each value of a continuous predictor as its difference from its overall mean value; I suspect that your distress over the apparent discrepancies will be greatly alleviated.
Finally, please get further expert guidance on how best to deal with your Time
variable. A 6th-order non-orthogonal polynomial is probably not the best way to proceed, and it's not clear from the limited data description here how Time
and Season
would best be considered together for your model.
O. faveolata
(the value in theEstimate
column) is the predicted difference inBiomass
when the species isO. faveolata
relative to when the species isO. annularis
, with all other variables held fixed. That coefficient (and all the other coefficients) will in general be different between your two models because the first model controls for many more variables than the second model. $\endgroup$ – eipi10 Mar 16 '17 at 20:11