Measurement error

Authors
Affiliation

Samuel Bédécarrats

CNRS, Univ. Bordeaux, MCC – UMR 5199 PACEA

Floriane Rémy

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, along with several references to go further.

1 General considerations about measurement error

  • Intra-observer error should usually be lower than inter-observer error (Shearer et al. 2017).
  • There is a learning curve in landmark acquisition: experienced users (for a given set of landmarks) will usually get a lower error (Shearer et al. 2017; Valeri et al. 1998).
  • The measurement error is not necessarily expected to be constant across groups of individuals, or across landmark types. For instance, Barbeito-Andrés et al. (2012) note that measurement error is usually higher for “type III landmarks”, and may also be higher for younger specimens when their anatomical structures are less clear.
  • Thus, it might be difficult to determine ex-ante what would be an acceptable amount of measurement error, but some reference guidelines can help you (Corner, Lele, and Richtsmeier 1992).
  • Intraobserver error can be reduced by training sessions, and by acquiring landmarks in as few sessions as possible. Errors should be systematically measured and discussed (Engelkes et al. 2019).

2 Statistical assessment measurement error

  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.
Barbeito-Andrés, Jimena, Marisol Anzelmo, Fernando Ventrice, and Marina L. Sardi. 2012. “Measurement Error of 3D Cranial Landmarks of an Ontogenetic Sample Using Computed Tomography.” Journal of Oral Biology and Craniofacial Research 2 (2): 77–82. https://doi.org/10.1016/j.jobcr.2012.05.005.
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, December. 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, February. https://doi.org/10.1007/s11692-024-09627-6.
Corner, Brian D., Subhash Lele, and Joan T. Richtsmeier. 1992. “Measuring Precision of Three-Dimensional Landmark Data.” Journal of Quantitative Anthropology 3: 347–259.
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.
Engelkes, Karolin, Jennice Helfsgott, Jörg U. Hammel, Sebastian Büsse, Thomas Kleinteich, André Beerlink, Stanislav N. Gorb, and Alexander Haas. 2019. “Measurement Error in \(\mu\)CT-based Three-Dimensional Geometric Morphometrics Introduced by Surface Generation and Landmark Data Acquisition.” Journal of Anatomy 235 (2): 357–78. https://doi.org/10.1111/joa.12999.
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.
Shearer, Brian M., Siobhán B. Cooke, Lauren B. Halenar, Samantha L. Reber, Jeannette E. Plummer, Eric Delson, and Melissa Tallman. 2017. “Evaluating Causes of Error in Landmark-Based Data Collection Using Scanners.” PLOS ONE 12 (11): e0187452. https://doi.org/10.1371/journal.pone.0187452.
Valeri, Christopher J., Theodore M. Cole III, Subhash Lele, and Joan T. Richtsmeier. 1998. “Capturing Data from Three-Dimensional Surfaces Using Fuzzy Landmarks.” American Journal of Physical Anthropology 107 (1): 113–24. https://doi.org/10.1002/(SICI)1096-8644(199809)107:1<113::AID-AJPA9>3.0.CO;2-O.