I am using a GAM model to study the effects of time (in weeks) and quality parameters (qp1, qp2, qp3 and qp4) on a response variable. Since the effect of time is modelled best by a spline, I am using a gam. The effects of quality parameters are modeled linearly. The model looks like below -
model.gam <- gam(RV ~ s(week) + qp1 + qp2 + qp3 + qp4, data)
I am using the mgcv package to carry out analysis. My model is highly significant (p < 0.0001) but with very low R-square (0.08). I have two related questions:
First, is it statistically sound to infer association of significant quality parameters to response variable, despite the low R-square. I am not using the model for prediction but only for proving association.
Secondly, my plan is to use the standardized beta coefficents (magnitude as well as sign) to explain the relationship between RV and qp's. Is this correct, and how can I calculate standardized beta coefficents for a GAM? Is there a R function available, and if not, can I divide the unstandardized beta coefficients with the ratio of standard deviation of independent variable with the dependent variable to obtain standardized coefficents, like in a linear model? I want to calculate standardized beta coefficents for only the parametric terms (qp1, qp2, qp3 and qp4) not the smooth terms (weeks in this case).