Unsatisfactory residual plots

If a general lack of normality is indicated in the residuals, a transformation of the data can be considered. Alternatively, if a residual plot indicates outlying values, then checks should first be made to determine any possible reasons for them being extreme. Plots of standardised residuals (e.g. studentised or Pearson residuals) can help to assess whether the observation is a genuine outlier or is outlying by chance. These residuals take account of the fact that the observed residuals have differing variances given by the diagonals of (XV—1X)—1. When a value is clearly wrong (e.g. recording error, punching error, machine error) it should be corrected if possible, or else removed from the analysis. An outlier will not necessarily have as much effect on the parameter estimate so, if there is no clear reason for removing it, its influence should be assessed. This can by carried out by calculating influence statistics (e.g. Cook's D statistic). proc mixed (Version 9) contains options for producing influence statistics. By reanalysing the data with the outlier removed we can determine whether parameter estimates alter noticeably. If the estimates are similar, then the outliers can be retained. If they differ, then it would seem sensible to remove them provided there is a convincing external reason for doing so (e.g. measurement suspected to be inaccurate because a blood sample was clotted; centre did not follow protocol). If there is no apparent reason for the outlier, then two alternative analyses and sets of conclusions may need to be presented. We also note that another alternative would be to construct a robust method to reduce the influence of the outlier; however, we will not be considering these methods here. Huber (1981) gives an introduction to robust methods.

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