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ASReml-S reference manual - VSN International

ASReml-S reference manual - VSN International

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8.4 Sources of variability in unbalanced data 87Dose 2 24.0 12.05 11.42 A 3.278549e-04Sex 1 301.7 58.27 58.27 A 0.000000e+00$stratumVariancesdf Variance Dam R!varianceDam 22.60301 1.2878697 11.47231 1R!variance 294.39699 0.1645245 0.00000 1>Note that the variance parameters are re-estimated, though there is little change fromthe previous analysis.The impact of (wrongly) dropping dam from this model is shown below:> rats3.asr wald(rats3.asr,denDF="default",ssType="conditional")$WaldDf denDF F_inc F_con Margin Pr(Intercept) 1 317 47080.00 3309.00 0.000000e+00littersize 1 317 68.48 146.50 A 0.000000e+00Dose 2 317 60.99 58.43 A 0.000000e+00Sex 1 317 24.52 24.52 A 2.328158e-06$stratumVariancesNULL>Even if a random term is not ’significant’, it should not be dropped from the model ifit represents a strata of the design as in this case. The impact of deleting Dam on thesignificance tests for the fixed effects is substantial and not surprising. This reinforcesthe importance of preserving the strata of the design when assessing the significance offixed effects.8.4 Sources of variability in unbalanced dataThis example illustrates an approach to the analysis of unbalanced data where the mainaim is to determine the sources of variation rather than assess the significance of imposedtreatments. The data are taken from Cox and Snell [1981] and involve an experiment toexamine the variability in the production of car voltage regulators. Standard productionof regulators involves two steps: 1) Regulators are taken from the production line andpassed to a setting station which adjusts the regulator to operate within a specifiedrange of voltages, and, 2) from the setting station the regulator is then passed to atesting station where it is tested and returned if outside the required range.A total of 64 regulators was tested at four testing stations (Teststat). The voltagefor individual regulators was set at a total of 10 setting stations (Setstat). A variablenumber of regulators (between 4 to 8) were set at each station, however each regulatorwas tested at every testing station. The asreml function call is:> voltage.asr summary(voltage.asr)$varcomp

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