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Findings, implications and lessons
learned
- This case study has shown methods for evaluating the
contributions of different explanatory variables to a statistical model.
Different representations of one of the explanatory variables, namely the age of
the dam, are investigated to determine the most suitable way to express the
relationship. The appropriate formulations of the terms for inclusion in the
model are determined by first exploring the patterns of the associations of
weaning weight with these factors and covariates.
- There were major variations in mean weaning weights
among years. Because of the imbalance across years in the distribution of lambs
belonging to the different genotypes, it would have been clearly wrong to ignore
year of birth when making comparisons across genotypes. It is thus important to
make sure that all potentially important factors and covariates are accommodated
in the model.
- The example also shows how to calculate the sums of
squares remaining when fewer degrees of freedom are used to represent an
alternative parameterisation for a variable in the model. It was shown, for
example, that age of dam was best fitted using a quadratic relationship term and
that this accounted for most of the variation among the individual age
categories.
- Sometimes reparameterisation results in the remainder
mean square falling to a value below that of the residual mean square. Had it
happened here (it did not) then it is possible that the curve might have been
over fitting the data and that the quadratic term was probably not necessary. To
find out whether this might have been the case the DL term could have been tried
on its own.
- A common mistake (when individual values are known, as
here) is to fit a regression model to mean values and then to calculate standard
errors and draw conclusions based on the residual variation among the means
alone. By doing so the precision with which the mean values have themselves been
calculated is ignored. The correct approach is the one described
here.
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