ASReml-S reference manual - VSN International

8.4 Sources of variability in unbalanced data 88gamma component std.error z.ratio constraintSetstat 2.334163e-01 1.193692e-02 8.814339e-03 1.354262 PositiveSetstat:Regulatr 6.018174e-01 3.077697e-02 8.453330e-03 3.640810 PositiveTeststat 6.427520e-02 3.287037e-03 3.337300e-03 0.984939 PositiveSetstat:Teststat 1.011929e-07 5.175009e-09 5.323475e-10 9.721111 BoundaryR!variance 1.000000e+00 5.114004e-02 5.260720e-03 9.721111 PositiveThe convergence criterion was satisfied, however, the variance component estimate forthe Setstat:Teststat term has been fixed at the boundary. The default constraintfor variance components is to ensure that the REML estimate remains positive. If anupdate for any variance component results in a negative value then asreml sets thatvariance component to a small positive value. If this occurs in subsequent iterationsthe parameter is fixed at the boundary. The default parameter constraints (Positivefor variance components) can be altered (to Unconstrained, for example) by changingthe constraint code in the initial value list object(s) for random parameters, that is,the R.param and G.param arguments to asreml. These lists are returned in the asremlobject and are best accessed via the function asreml.gammas.ed(). In this example, thefollowing sequence would achieve this:> temp voltage.asr plot(voltage.asr, option = ”f”)gives a residual plot which indicates two unusual data values (Figure 8.2). These valuesare successive observations, 210 and 211, respectively, being testing stations 2 and 3 forsetting station J, regulator 2. These observations will be retained for consistency withother analyses conducted by Cox and Snell [1981].The model omitting the Setstat:Teststat term:> voltage2.asr summary(voltage2.asr)$varcompgamma component std.error z.ratio constraintSetstat 0.23341667 0.011936975 0.008813969 1.3543246 PositiveSetstat:Regulatr 0.60181723 0.030777054 0.008453248 3.6408553 PositiveTeststat 0.06427521 0.003287047 0.003337314 0.9849378 PositiveR!variance 1.00000000 0.051140201 0.005260744 9.7210963 PositiveThe column labelled z.ratio is calculated to give a guide as to the significance of thevariance components. The statistic is simply the REML estimate of the variance componentdivided by the square root of the diagonal element (for each component) of theinverse of the average information matrix. The diagonal elements of the expected informationmatrix are the asymptotic variances of the REML estimates of the varianceparameters. These statistics cannot be used to test the null hypothesis that the variancecomponent is zero. The conclusions using this crude measure are inconsistent with theconclusions obtained from the REML log-likelihood ratio (Table 8.3).