The problem is: how do we restore the necessary independence of residuals?Īt the basic level, the main way to account for the ‘plot’ effect is by including a random term in the model in this way, we recognise that there is a plot-to-plot variability, following a gaussian distribution, with mean equal to 0 and standard deviation equal to \(\sigma^2_B\) (‘plot’ error). Thus, there will be a ‘plot’ effect, which will induce a within-plot correlation. Indeed, all measurements taken on one specific plot will be affected by the peculiar characteristics of that plot and they will be more alike than measurements taken in different plots. With LTEs, observations are repeatedly taken on the same plot and, therefore, the residuals cannot be independent. We know that, with linear models, once the effects of experimental factors have been accounted for, the residuals must be independent. The main problem with LTEs: lack of independence
