I have a large dataset (101952 data points) where the response variable is sound pressure level (SPL) and the explanatory variables are mean number of boats (continuous) and frequency (Fc; categorical). Within the data there is heterogeneity of variances and regression slopes. I therefore modelled the data using a weighted least squares regression:

vf7 <- varConstPower(form =~ mean_BoatCount | Fc) 

mod_7<-gls(SPL ~ Fc * mean_BoatCount, 
                weights = vf7, data = TOL_data)

Denom. DF: 101936 
                  numDF  F-value p-value
(Intercept)           1 76114137  <.0001
Fc                    7    27573  <.0001
mean_BoatCount        1     7676  <.0001
Fc:mean_BoatCount     7      448  <.0001

enter image description here

I'm wondering if there is some way of quantifying/describing the heteroscedasticity of variance? For example, at low mean number of boats, it's clear that the variance is broader at low frequencies (63 Hz) and narrower at high frequencies (5011 Hz).

  • 1
    $\begingroup$ Side note -- You would expect there to be less variance at higher frequencies because the recorded sounds were located closer (as there is a great deal of sound absorption with higher frequency sounds) $\endgroup$
    – Chloe
    May 9, 2022 at 9:39
  • $\begingroup$ Yes :-) The data is also influenced by the fact that there are more instances of fewer boats, which you would expect based on how/where the data was collected. $\endgroup$ May 9, 2022 at 21:32


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