& Context Tree height prediction is an important issue in forest management since tree heights are usually measured only in a sample of trees. Although numerous model approaches have been used for this purpose, no agreement on which one is more appropriate has been achieved. & Aims To analyse the random effects of basic and generalised height–diameter (h–d) models fitted to multi-species uneven-aged forest stands, and to establish their ability to explain differences between ecoregions, plots and species. & Methods Height and diameter measurements for 29,084 trees from 187 sample plots located in the state of Durango (Mexico) were used. Basic and generalised h–d models were fitted in a mixed-models framework. The variability between ecoregions, plots and species was con-sidered in the random effects definition. Model calibration for different height sampling designs and sampling sizes was also analysed. & Results Random components performed well in explaining the differences in the h –d relationship between the different plots and species; however, no significant var-iance for the random effects was found for the different ecoregions. A calibrated basic h –d model produced similar results to a fixed-effects generalised h –d model when a sufficiently large number of trees was used in the calibration process. & Conclusion From a practical point of view, if no calibration is carried out, different models should be used for the different species, so that at least the variation among species is captured.