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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).

Thank you!

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