Hi Andrea, It is generally preferable to perform the more complex analysis with size included as a covariate. Using a sequential approach that first obtains the shape residuals and then examines patterns using these as data is not guaranteed to get to the same, or even the correct, place. And this approach can leave potentially important biology out.
Consider the simplest case with shape, size, and groups (i.e., mancova). Here the full model is: shape~size+group+size:group. Say for instance, that one finds a significant interaction term. This means that the groups have different shape~size relationships (ie different allometric slopes). In this case, using residuals from a shape~size regression in a subsequent manova is not correct, as these are residuals from a common-slope model, whereas the mancova has found evidence that the groups have different slopes. Thus the residuals are not capturing what one intends. (As a side note there was a nice paper in the mid-1990s on the univariate equivalent of this, describing why anova of regression residuals is not the same as ancova). But additionally, using the sequential-analysis approach eliminates the possibility of identifying interesting interactions between effects that one had not considered. Again take this simple example. Here, performing a manova on the regression residuals is intended to evaluate differences in the mean shapes among groups. But this explicitly ignores the possibility that the groups may differ in their allometries themselves, rather than their size-adjusted least squares means. Such allometric differences represent potentially important biological information that is left unexplored using the piecewise analysis procedure. For these reasons the analysis including size as a covariate is preferred. And while it is more complicated to consider models that include interactions, and various post-hoc comparisons are required (of group means, of slopes, etc.), one ought to do so when possible, so as to properly identify where patterns of shape variation occur, and what potential factors associate with it. Dean Dr. Dean C. Adams Professor Department of Ecology, Evolution, and Organismal Biology Department of Statistics Iowa State University www.public.iastate.edu/~dcadams/ phone: 515-294-3834 -----Original Message----- From: andrea cardini [mailto:alcard...@gmail.com] Sent: Thursday, March 24, 2016 12:01 PM To: morphmet@morphometrics.org Subject: [MORPHMET] using regression residuals for other analyses Dear All, this is something that, I believe, has already come up in the past. However, I'd like to check it again. What are the issues with, say, regressing shape on size, saving residuals and using those in further analyses (e.g., other regressions or testing group differences etc.)? I suspect that all the factors (size, other predictors, groups etc.) should be incorporated in a single model and may have a partial intuition about some of the problems with rerunning, instead, analyses on residuals but I'd be very grateful to know how those with a better understanding of the methods see it. Thanks in advance. Cheers Andrea -- Dr. Andrea Cardini Researcher, Dipartimento di Scienze Chimiche e Geologiche, Università di Modena e Reggio Emilia, Via Campi, 103 - 41125 Modena - Italy tel. 0039 059 2058472 Adjunct Associate Professor, Centre for Forensic Science , The University of Western Australia, 35 Stirling Highway, Crawley WA 6009, Australia E-mail address: alcard...@gmail.com, andrea.card...@unimore.it WEBPAGE: https://sites.google.com/site/alcardini/home/main FREE Yellow BOOK on Geometric Morphometrics: http://www.italian-journal-of-mammalogy.it/public/journals/3/issue_241_complete_100.pdf -- MORPHMET may be accessed via its webpage at http://www.morphometrics.org --- You received this message because you are subscribed to the Google Groups "MORPHMET" group. To unsubscribe from this group and stop receiving emails from it, send an email to morphmet+unsubscr...@morphometrics.org. -- MORPHMET may be accessed via its webpage at http://www.morphometrics.org --- You received this message because you are subscribed to the Google Groups "MORPHMET" group. To unsubscribe from this group and stop receiving emails from it, send an email to morphmet+unsubscr...@morphometrics.org.
