FAQ: Polynomial regression

Adjustment factors

The default form of regression equation in WOMBAT is chosen to account for rank deficiencies in the fixed effects part of the coefficient matrix in the MME when estimating variance components. If your aim is to obtain `adjustment factors' for other analyses, it is best to fit the appropriate model from the start.

  • Intercepts are readily fitted, but may cause additional dependencies among fixed effects, in particular for nested covariables. If so, you will need to identify suitable fixed effects levels to be `zero-ed out' to account for these dependencies, and specify them in the parameter file via the ZEROUT statement.
  • An alternative way to fit a higher order polynomial regression is to include appropriate powers of the covariable as additional columns in the data file and fit these as additional, linear covariables. This will directly yield the βi type regression coefficients.

When fitting a complicated fixed effects model, care is needed in the interpretation of results, paying particular attention to the estimability of individual effects!