I have a simple linear model that predicts an outcome based on a few input variables (e.g. y = a*x + b), which are based on theory (psychology). None of the variables are free parameters, meaning there is no need to fit the model. I would like to assess the (predictive) quality of the model by comparing it to the data (and possibly also to a more complex model containing a logarithmic term that I have fitted to the data first). However, since the model is not fitted, regular measures of model quality (e.g. R2, AIC, BIC) are not applicable. I calculated the RMSE, but it is not very informative as a standalone value. So here is the question:
(1) Is there a more informative way to answer the question whether the model with zero free parameters is able to predict the data well?
Similarly (2) if I want to compare the simple model with zero free parameters to the model with 1 free parameter, is there a better way than simply saying one model has a lower mean RMSE according to a cross validation? Especially as the simple model seems to be at a disadvantage because it is not fitted.