As of late, I've been increasingly worried with the fact that many works dealing with multivariate allometry analysis do not log-transform their data.
As far as I'm concerned, if data is not log-transformed (and are treated with regular linear statistics), then we implicitly assume that their relationship is isometric (e.g. they scale with the same rate), something that is obviously not true for most of the data. As far as we are dealing with predicting values of one variable from another or to investigate their relationship, maybe that's fine, but I feel that all implications to allometric growth/change are lost in the process.
Am I missing something here?
Not necessarily. One can also detect size-correlated shape changes in raw data space (see Mosimann on size and shape). However, logs are required for Jolicouer's multivariate generalization of allometry via the first eigenvector of a logged dispersion matrix (or Leamy's multivariate version of the reduced major axis).
I think that multivariate normality is rarely met if linear measurements are not log transformed. This could be probably one of the most important reason to do the log transformation in traditional morphometrics. Based on some theoretical arguments, log transformation is a way to take already allometry into account (the inverse of log is exponential by a factor X so log transformation is a way to take different allometric differences into account using a common base -that could be 10 or e in the case of natural log). In geometric morphometrics there are more complex reason to natural log transform centroid size (see Dryden & Mardia book for more detalis) for multivariate allometry.
My experience with linear measurements support log transformation strongly for all kind of multivariate analyses (see this paper for an example on discriminant function: http://www.bioone.org/doi/abs/10.1666/12001).
It all depends also on your kind of data: are you comparing babies with adults or lions with small cats??? In that case log transformation is necessary to minimize the already large size differences between your specimens.
Hope this might help
Carlo
I find it curious that you are seeing an increase in papers that do not log transform. I thought this was nearly always done with linear measures (i.e., traditional morphometrics) especially as you almost always see heteroscedasticity (increasing variation with size). Contrary to what many of my reviewers have suggested, this really has nothing to do with isometry, allometry, or anisometry. I was not aware that people thought you should log transform centroid size in geometric morphometrics as mentioned by Carlo. I will have to read up on this. I guess I agree with you, if people are doing traditional morphometric analyses without transforming, and don't provide a justification for this, then I would be highly suspicious of their results, especially if they are reporting statistical results or conducting a PCA on the covariance matrix.
When I did my work on allometric heterochrony of planktic foraminifereal Globoconella lineage, I used covariance matrix of 12 log-transformed linear measurements on 110 specimens belonging to three morhphotypes. The covariance data matrix was subjected to a sheared PCA (Humpheries et al 1981). The results were interpreted following Jolicouer, 1963. Although Humpheries et al 1981 was questioned by Rholf and Bookstein 1987, but my experience with the Globoconella case was quite good and illuminating. Intrested please see the attached Wei 1994 in Paleobiology 20(1): 66-84.
Log transformation is not a statistical panacea nor a necessary strategy for all analyses of size and shape. The Packard-Kerkhoff debate about this is illuminating.
My own PCA ordinations of Mosimann shape variables and their log-shape counterparts are often almost indistinguishable. Researchers should explore their data a bit in raw space before migrating into log space. I think that Bryant's observations in 1986 ( http://sysbio.oxfordjournals.org/content/35/4/552.short) also remain relevant.
Hi All,
We are very lucky to have Bill Jungers adding to this conversation. He is clearly the leading authority on morphological scaling in the fields of anthropology and primate morphology.
Bill, could you provide a couple more links (or fuller citations) to good references on this?
Hi All,
I have a relevant query that I am hoping you can help me with… When looking at a single morphometric variable over time (e.g. mean size/ mass of individuals within a population) is it appropriate/recommended to log transform the timeseries data if they show heteroscedasticity and/or log normal distribution? Thanks.