Multivariate estimation fitting a common structure to estimates of genetic and environmental covariance matrices is examined in a simple simulation study. It is shown that such parsimonious estimation can considerably reduce sampling variation. However, if the assumption of similarity in structure does not hold at least approximately, bias in estimates of the genetic covariance matrix can be substantial. For small samples and more than a few traits, structured estimation is likely to reduce mean square error even if bias is quite large. Hence such models should be used cautiously.

There are many sources of variation in microarray studies that need to be accounted for so that gene expression estimates are accurate. One such source of variation is spatial trends that can accumulate on the microarray slides. This spatial variation may arise from printing blocks, pin effects and uneven washing of the solution over the slide. These trends can significantly change the biological conclusions of an experiment depending on how they are modeled. Hence, it is important to test various methods of removing spatial trends in microarray slides so that a method can be recommended for a particular slide depending on its properties. Complexities in the procedures and high costs of microarrays mean that performing real microarray experiments to test methods of removing bias is not always viable. Simulation is a practical way to test potential strategies in processing microarray experiments. Previous simulation studies consider sources of variation such as background noise, expression signals, spot location, spot shape and irregularities on the slide (Wierling et al. 2002; Y. Balagurunathan and Trent 2004). Simulation of spatial trends in the single channel background adjusted signal will be considered here. In this paper, results from a previous murine study (Woolaston et al. 2005) are used to generate data to assess the effectiveness of three methods of modeling spatial noise in microarray slides. Spatial effects of varying roughness or fractal dimension are also simulated.