5  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; Fruciano 2016; Menéndez 2017; Cramon-Taubadel, Frazier, and Lahr 2007). Here are some quick tips, along with several references to go further.

5.1 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).

5.2 Statistical assessment of 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 yet efficient method may consist in using principal component analysis: see Lockwood, Lynch, and Kimbel (2002) or Cucchi et al. (2011) for two nice examples.
  3. Finally, the R functions geomorph::gm.measurement.error() and/or geomorph::procD.lm() may be useful (or not, depending on the study design). For more information, see this blog post. Furthermore, recent developments by Collyer and Adams (2024) allow for a more precise decomposition of the measurement error into systematic and fluctuating components, and allow for richer interpretations.