Is it possible to compare between these two types of model? I have a set of data that involves 6 independent variables and 1 dependent variable. It is based of a questionnaire for social science students. I ran the assumption tests for linear regression and the linearity shows vague results, but somehow passes as a linear model. Thus, I would like to propose that fitting it into a modified Gompertz model gives a better fit and better predictions. I calculated the RMSE for both the linear and nonlinear model, and results shows that the Gompertz model has a smaller RMSE. Is this acceptable or is this impossible even to begin with?
I presume the Gompertz model you fitted has more parameters than the linear model (you should be explicit about the exact model, since there's more than one model I might call a Gompertz model).
1) If that's the case you would expect the model with more degrees of freedom to have smaller RMSE.
2) It looks like the form of the nonlinear model was chosen after seeing the data. Even if the number of parameters were the same, you would expect it to have smaller RMSE.
So I wouldn't recommend RMSE for either of those reasons.
If you hadn't seen the data before choosing to fit the Gompertz model, you might compare AIC, or BIC or some similar criterion, but this would still have an issue of model selection which can impact your inference.
You might look to assessing out-of-sample predictive ability -- say via cross-validation (of MSE or RMSE perhaps). That will reduce, but not completely eliminate the effect of having seen the data, and avoid the issue of different numbers of parameters.