As described in Chapter 2, ASReml uses the Average Information algorithm to obtain maximum likelihood estimates of the variance parameters from the data. This requires iteration beginning from some starting values, at each step obtaining maximum likelihood estimates for one parameter at a time dependent on current values of the other parameters. These steps are repeated until the parameter estimates change only very little from step to step. This is referred to as ‘convergence’ on the maximum likelihood solution. Specifically, ASReml stops iterating if the successive REML log-likelihood (LogL) values of two iterations do not change more than 0.002 and if the parameter estimates are stable.