Modified F ‐tests for assessing tree radial growth under linear‐circular regression models with correlated errors: A comprehensive toolbox rooted in G. E. P. Box's theorems

Annual tree growth is a complex biological process. Modelling radial growth in the trunk by linear‐circular regression with one mode and correlated errors has allowed the definition and assessment of a preferred direction for 1 and 2 years. Here, modified ‐tests are presented for 3 years, 1 mode/year; 1 year, 2 modes for possible main and secondary preferred directions; 2 years, 2 modes/year; and 1 year, multiple (4, 8) modes. The tests derive from the application of G. E. P. Box's theorems; model parameters are estimated by REML (restricted maximum likelihood), and the Kronecker product is used for variance‐covariance structures over 2 years and more. Test validity is studied by simulation, in relation to the number of angular observations and their correlation (sign, strength, autoregressive symmetric circulant structure), for relevant null and alternative hypotheses. Empirical power is also analyzed. This flexible and general framework is illustrated with ring‐width datasets obtained from computed tomography (CT) images for spruce trees with distinct annual growth patterns.