Can I reduce the AICc penalty for multiple variables, when some variables should be grouped? I have a data set of mean trait values for each of 18 populations, and want to test whether several ecological variables are related to variation in traits. I'm using the corrected Akaike information criterion to evaluate which ecological model fits best. 
One of the models uses distance-based Moran eigenvector maps (dbMEMs) based on geographic distance (following Legendre et al 2015 Methods in Ecology & Evolution, and earlier work). In generating the dbMEMs, I recovered 4 significant and positive dbMEMs. My understanding is that these 4 synthetic variables should be used together in subsequent analyses, to evaluate unmeasured spatially-structured ecological variation.
A model of the mean trait values that includes all 4 dbMEMs has a strong adjusted-R2 value compared to some other models (e.g., PC1 from a PCA on various ecological variables expected to be important). The other models appear to be a weak fit. But, the AICc value is high for the dbMEMs model because it is penalized for having 4 variables. 
Because these 4 variables 'travel' together and are used together, it seems reasonable to me to treat them as 1 variable, and to therefore calculate AICc with a k value that is 3 less than the original value. 
For example, I can calculate AICc with k = 3, rather than k = 6 (accounting for the intercept, error, and 4 dbMEM variables). The AICc is naturally lower then and reflects how the model actually seems to fit the data relative to other models. 
Is it valid to 'correct' the penalty for extra variables in this way? I can't find a reference for it.
 A: If these 3 variables were identical then there'd be only 1 parameter (but then you would not include them all in the model). As they are different, there is the possibility of overfitting due to each one and AICc needs to be penalized to reflect this. As I do not understand exactly what goes on with the "dbMEMs", it may or may not be that the effective number of parameters is less than 3 for these, but it certainly would not be 1 (much more likely to be close to 3 or exactly 3). One case, where there is a way of accounting for a smaller effective number of parameters is the deviance information criterion for hierarchical models. However, I am not aware of an applicable approach that could be easily transferred to all kinds of general situations.
Also, in my response above I assume that the creation of the "dbMEMs" does not make use of the outcome data you are trying to model. If you have used it, then there is a further problem that likely invalidates the AICc in your subsequent modeling.
