Measurement error

Authors
Affiliation

Floriane Remy

CNRS, Univ. Bordeaux, MCC – UMR 5199 PACEA

Frédéric Santos

CNRS, Univ. Bordeaux, MCC – UMR 5199 PACEA

Measurement error in morphometrics (for landmark data) is a wide topic that we will not fully cover here. However, exhaustive references do exist (Arnqvist and Martensson 1998; Bertsatos et al. 2019; Collyer and Adams 2024; Fruciano 2016; Menéndez 2017). Here are some quick tips:

  1. Simple (but not very efficient) methods may consist in using intraclass correlation coefficients (Koo and Li 2016) or concordance correlation coefficients (Lin 1989) directly on each coordinate \((x,y,z)\) of each landmark.
  2. A simpler and more efficient method may consist in using principal component analysis: see Cucchi et al. (2011) for a nice example.
  3. Finally, the R functions geomorph::gm.measurement.error() and/or geomorph::procD.lm() may be useful (or not, depending on the study design). See also this blog post.
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References

Arnqvist, G., and T. Martensson. 1998. “Measurement Error in Geometric Morphometrics: Empirical Strategies to Assess and Reduce Its Impact on Measures of Shape.” Acta Zoologica Academiae Scientiarum Hungaricae 44 (1): 73–96.
Bertsatos, Andreas, Elissavet Gkaniatsou, Christina Papageorgopoulou, and Maria-Eleni Chovalopoulou. 2019. “‘What and How Should We Share?’ An Inter-Method Inter-Observer Comparison of Measurement Error with Landmark-Based Craniometric Datasets.” Anthropologischer Anzeiger. https://doi.org/10.1127/anthranz/2019/1047.
Collyer, Michael L., and Dean C. Adams. 2024. “Interrogating Random and Systematic Measurement Error in Morphometric Data.” Evolutionary Biology. https://doi.org/10.1007/s11692-024-09627-6.
Cucchi, T., A. Hulme-Beaman, J. Yuan, and K. Dobney. 2011. “Early Neolithic Pig Domestication at Jiahu, Henan Province, China: Clues from Molar Shape Analyses Using Geometric Morphometric Approaches.” Journal of Archaeological Science 38 (1): 11–22. https://doi.org/10.1016/j.jas.2010.07.024.
Fruciano, Carmelo. 2016. “Measurement Error in Geometric Morphometrics.” Development Genes and Evolution 226 (3): 139–58. https://doi.org/10.1007/s00427-016-0537-4.
Koo, Terry K., and Mae Y. Li. 2016. “A Guideline of Selecting and Reporting Intraclass Correlation Coefficients for Reliability Research.” Journal of Chiropractic Medicine 15 (2): 155–63. https://doi.org/10.1016/j.jcm.2016.02.012.
Lin, Lawrence. 1989. “A Concordance Correlation Coefficient to Evaluate Reproducibility.” Biometrics 45 (1): 255. https://doi.org/10.2307/2532051.
Menéndez, Lumila Paula. 2017. “Comparing Methods to Assess Intraobserver Measurement Error of 3D Craniofacial Landmarks Using Geometric Morphometrics Through a Digitizer Arm.” Journal of Forensic Sciences 62 (3): 741–46. https://doi.org/10.1111/1556-4029.13301.