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Keywords:

  • Beta distribution;
  • Latent variable;
  • Ordered categorical data;
  • Plant abundance;
  • Proportional odds model;
  • Sample size;
  • Trend detection

Abstract

Question: We provide a method to calculate the power of ordinal regression models for detecting temporal trends in plant abundance measured as ordinal cover classes. Does power depend on the shape of the unobserved (latent) distribution of percentage cover? How do cover class schemes that differ in the number of categories affect power?

Methods: We simulated cover class data by “cutting-up” a continuous logit-beta distributed variable using 7-point and 15-point cover classification schemes. We used Monte Carlo simulation to estimate power for detecting trends with two ordinal models, proportional odds logistic regression (POM) and logistic regression with cover classes re-binned into two categories, a model we term an assessment point model (APM). We include a model fit to the logit-transformed percentage cover data for comparison, which is a latent model.

Results: The POM had equal or higher power compared to the APM and latent model, but power varied in complex ways as a function of the assumed latent beta distribution. We discovered that if the latent distribution is skewed, a cover class scheme with more categories might yield higher power to detect trend.

Conclusions: Our power analysis method maintains the connection between the observed ordinal cover classes and the unmeasured (latent) percentage cover variable, allowing for a biologically meaningful trend to be defined on the percentage cover scale. Both the shape of the latent beta distribution and the alternative hypothesis should be considered carefully when determining sample size requirements for long-term vegetation monitoring using cover class measurements.