Stem taper data are usually hierarchical (several measurements per tree, and several trees
per plot), making application of a multilevel mixed-effects modelling approach essential.
However, correlation between trees in the same plot/stand has often been ignored in
previous studies. Fitting and calibration of a variable-exponent stem taper function were
conducted using data from 420 trees felled in even-aged maritime pine (Pinus pinaster Ait.)
stands in NW Spain. In the fitting step, the tree level explained much more variability than the …

3.847 10− 5 σ2 1.555 6.117 10− 3 δ 1.481 σ2 i, a1, σ2 i, b3and σ2 i, a1, b3, variances and
covariance of random effects in parameters a1 and b3 at plot level; σ2 ij, a1, σ2 ij, b3 and σ2
ij, a1, b3, variances and covariance of random effects in parameters a1 and b3 at tree level;
σ2, residual variance; δ parameter of power function. Note that the σ2 of the mixed-effects
model must be multiplied by g= d δ when applied (variance obtained from ordinary residuals
is 0.6866). doi: 10.1371/journal. pone. 0151297. t001