I would like to perform regression on an environmental dataset. The covariates are in the following form enter image description here I realize that the 4 repeated measures for each region are dependent because they come from the same region. For this reason, a model with mixed effects should be used. I also suspect that the data is spatially and temporally correlated.

I am not sure what models I should try on my dataset first. I am open to anything from very advanced state-of-the-art models (preferred) to the more simple models that are taught in textbooks. I would appreciate suggestions from those that are familiar with spatio-temporal data.


2 Answers 2


One possible approach here is to use a mixed effects model with random intercepts for Region to handle the within-region correlations.

In R, the glmmTMB package can handle several different correlation structures:

  • Heterogeneous unstructured
  • Heterogeneous Toeplitz
  • Heterogeneous compound symmetry
  • Heterogeneous diagonal
  • AR(1)
  • Ornstein-Uhlenbeck
  • Spatial exponential
  • Spatial Gaussian
  • Spatial Matern
  • Reduced rank


  • $\begingroup$ Hello Robert, how would I determine the kind of correlation structure in my spatio-temporal dataset? $\endgroup$
    – PiccolMan
    Commented Aug 8, 2021 at 8:49
  • $\begingroup$ Probably the best thing to do is to read the documentation together with a reference on spatio-temporal analysis $\endgroup$ Commented Aug 8, 2021 at 9:28

This is a longitudinal/panel data set. Standard textbook methods are fixed, random, or mixed effects. R has a package called plm to handle these.

Alternatively, one can use least squares dummy variable (LSDV) estimation, where one includes dummies for region (LSDV1), year (LSDV2), or both (LSDV3). This method is equivalent to fixed effects, as Cameron and Trivedi (2005) explain.


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