Jim, I agree that the term ‘bias’ without any clarification can be confusing. Your classic 2003 was clear to state bias ‘in what’ up-front (bias in estimating the mean shape) as well as provide clear definitions in terms of how you were using the word. That was then connected to the statistical use of the term regarding parameter estimation.
Bias in how something is digitized is somewhat different and discussions do need to make that clear. Several posts in the thread did make it clear to what they were referring by explicitly stating ‘bias in digitizing’ or ‘bias in ME’. But simply using the term bias without any clarification can be confusing and is not precise. Off the top of my head I’m not sure of a single word that describes what we the thread was discussing. However, with proper definition/description, I think that any of these phrases could be appropriate: ‘digitizing bias’, ‘bias in digitizing error’, ‘systematically-biased measurement error’, ‘systematic measurement error’. Dean Dr. Dean C. Adams (he/him) Distinguished Professor of Evolutionary Biology Department of Ecology, Evolution, and Organismal Biology Iowa State University https://faculty.sites.iastate.edu/dcadams/ phone: 515-294-3834 From: 'F. James Rohlf' via Morphmet <[email protected]> Sent: Friday, November 18, 2022 5:07 PM To: Mike Collyer <[email protected]>; andrea cardini <[email protected]> Cc: [email protected] Subject: Re: [MORPHMET2] Measurement error in geometric morphometrics I wonder whether it would help to be more strict about the use of the word "bias". There is the statistical meaning where there is a problem with the statistical estimate estimate being used. Must have to treat and correct for that differently than if the problem is that the investigator is making the measurements themselves incorrectly. With a statistic one can investigate properties assuming various statistical distributions. Not sure how to investigate theoretically the effect of an investigator who systematically measures something a little differently than intended or at least differently from other investigators working on the same or similar material. They are effectively measuring a different variable. Suggestions for a different word? __________________ F. James Rohlf, Distinguished Prof. Emeritus Dept. Anthropology and Ecology & Evolution Stonybrook University -------- Original message -------- From: Mike Collyer <[email protected]<mailto:[email protected]>> Date: 11/8/22 1:16 PM (GMT-05:00) To: andrea cardini <[email protected]<mailto:[email protected]>> Cc: [email protected]<mailto:[email protected]> Subject: Re: [MORPHMET2] Measurement error in geometric morphometrics Dear Andrea, I have to argue against one of your points. Nevertheless, I could miss a bias, but if ME has an Rsq of, say, less than 1/30 of individual variation within species, when I test species the bias will be negligible. This is, if I am correct, what you implied when wrote that "one can argue that if measurement error is very small, then randomness and homogeneity across groups are less of an issue”. If we come full-circle to Philipp’s first point — that choice of individuals can mislead one’s interpretation — I believe it is dangerous to use a value of Rsq to conclude systematic ME (bias) is negligible. I hope I can demonstrate this with an example (in R). To set this up, I create 10 shapes based on a template that is a square. I then add a digitizing bias by shifting two of the four landmarks (plus some random error). > # Create 10 specimens > > coords1 <- lapply(1:10, function(.) mat + rnorm(8, sd = 1)) > > # Add digitizing bias for each, shifting two landmarks a little right > # plus add a little random error > > coords2 <- lapply(coords1, function(x) + x + matrix(c(0, 0, 1.5, 0, 0, 0, 1.5, 0), 4, 2, byrow = T) + rnorm(8, sd = 0.1)) > > # string together and test for ME > > lmks <- simplify2array(c(coords1, coords2)) > GPA <- gpagen(lmks, print.progress = FALSE) > ind <- factor(c(rep(1:10, 2))) > summary(procD.lm(coords ~ ind, data = GPA)) Analysis of Variance, using Residual Randomization Permutation procedure: Randomization of null model residuals Number of permutations: 1000 Estimation method: Ordinary Least Squares Sums of Squares and Cross-products: Type I Effect sizes (Z) based on F distributions Df SS MS Rsq F Z Pr(>F) ind 9 1.54733 0.171926 0.94906 20.7 5.5944 0.001 ** Residuals 10 0.08306 0.008306 0.05094 Total 19 1.63039 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Call: procD.lm(f1 = coords ~ ind, data = GPA) If we plot PC scores, the systematic bias is obvious: > # plot PC scores, with lines showing systematic ME > > PCA <- gm.prcomp(GPA$coords) > plot(PCA, pch = 19, asp = 1, col = rep(1:2, each = 10)) > > for(i in 1:10) { + points(rbind(PCA$x[i,], PCA$x[10 + i,]), + type = "l", + lty = 3) + } [PastedGraphic-1.tiff] So one might see the bias in the plot and the 5% ME — if we want to call it that based on Rsq in the ANOVA — might be too high for one’s comfort. But now let's repeat the process on 10 specimens using instead of a square template, a long rectangle. > # Now add some more individuals to the mix, perhaps from > # a much differently shaped species (long rectangle, not square) > # using the same strategy > > mat3 <- matrix(c(0, 0, 50, 0, 0, 5, 50, 5), 4, 2, byrow = T) > coords3 <- lapply(1:10, function(.) mat3 + rnorm(8, sd = 1)) > coords4 <- lapply(coords3, function(x) + x + matrix(c(0, 0, 1.5, 0, 0, 0, 1.5, 0), 4, 2, byrow = T) + rnorm(8, sd = 0.1)) > > > lmks <- simplify2array(c(coords1, coords2, coords3, coords4)) > GPA <- gpagen(lmks, print.progress = FALSE) > ind <- factor(c(rep(1:10, 2), rep(11:20, 2))) > summary(procD.lm(coords ~ ind, data = GPA)) Analysis of Variance, using Residual Randomization Permutation procedure: Randomization of null model residuals Number of permutations: 1000 Estimation method: Ordinary Least Squares Sums of Squares and Cross-products: Type I Effect sizes (Z) based on F distributions Df SS MS Rsq F Z Pr(>F) ind 19 4.9087 0.258351 0.98567 72.39 8.8918 0.001 ** Residuals 20 0.0714 0.003569 0.01433 Total 39 4.9801 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Call: procD.lm(f1 = coords ~ ind, data = GPA) > > > PCA <- gm.prcomp(GPA$coords) > P <- plot(PCA, pch = c(rep(19, 20), rep(20, 20)), asp = 1, col = rep(rep(1:2, > each = 10), 2)) > > for(i in 1:10) { + points(rbind(PCA$x[i,], PCA$x[10 + i,]), + type = "l", + lty = 3) + } [PastedGraphic-2.tiff] Note that the corresponding 10 vectors are shown in this PC plot as in the first, but 20 more values have been added (the cluster of points to the right). The mean is no longer the mean of 20 square-like shapes, but is the mean of 40 rectangles, with the square-like shapes now having negative PC scores in the plot. Square shapes and long rectangle shapes are clearly separated in this plot. Here is a transformation grid (scaled 1x) for the approximate middle of the points on the left: [PastedGraphic-3.png] and the same for the cluster of points on the right: [PastedGraphic-4.png] But let’s pay attention to the same 20 configurations in both plots. Now the systematic ME is clearly associated with the first PC, which is also representing more of the overall shape variation, and the signal remains even though the ANOVA results suggest this is no big deal (1.4 % of variation). Worse, the bias now appears to be associated with, e.g., species differences. The bias in this example did not become negligible in spite of changing the sample, and in spite of a conclusion to the contrary that might be made with ANOVA results. Again, evaluating the relative portion of variance explained (especially if based on dispersion of points, alone) is dangerous, and a comforting statistic should not be sufficient evidence to not worry about a systematic measurement error. Best, Mike -- 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 [email protected]<mailto:[email protected]>. To view this discussion on the web visit https://groups.google.com/d/msgid/morphmet2/C30FAD86-E64E-4AEB-8B8C-041768B131D8%40gmail.com<https://groups.google.com/d/msgid/morphmet2/C30FAD86-E64E-4AEB-8B8C-041768B131D8%40gmail.com?utm_medium=email&utm_source=footer>. -- 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 [email protected]<mailto:[email protected]>. 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