Examining the efficiency of models using tangent coordinates or principal component scores in allometry studies

Most of the studies in medical and biological sciences are related with the examination of geometrical properties of an organ or organism. Growth and allometry studies are important in the way of investigating the effects of diseases and the environmental factors effects on the structure of the organ or organism. Thus statistical shape analysis has recently become more important in the medical and biological sciences. Shape is all geometrical information that remains when location, scale and rotational effects are removed from an object. Allometry, which is a relationship between size and shape, plays an important role in the development of statistical shape analysis. The aim of the present study was to compare two different models for allometry which includes tangent coordinates and principal component scores of tangent coordinates as dependent variables in multivariate regression analysis. The results of the simulation study showed that, the model constructed by taking tangent coordinates as dependent variables is more appropriate than the model constructed by taking principal component scores of tangent coordinates as dependent variables, for all sample sizes.