A Bayesian approach to retransformation bias in transformed regression.
Ecological data analysis often involves fitting linear or nonlinear equations to data after transforming either the response variable, the right side of the equation, or both, so that the standard suite of regression assumptions are more closely met. However, inference is usually done in the natural metric and it is well known that retransforming back to the original metric provides a biased estimator for the mean of the response variable. For the normal linear model, fit under a log-transformation, correction factors are available to reduce this bias, but these factors may not be generally applicable to all model forms or other transformations. We demonstrate that this problem is handled in a straightforward manner using a Bayesian approach, which is general for linear and nonlinear models and other transformations and model error structures. The Bayesian framework provides a predictive distribution for the response variable so that inference can be made at the mean, or over the entire distribution to incorporate the predictive uncertainty.
Duke Scholars
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Related Subject Headings
- Regression Analysis
- Models, Biological
- Linear Models
- Ecosystem
- Ecology
- Bayes Theorem
- 4102 Ecological applications
- 3109 Zoology
- 3103 Ecology
- 0603 Evolutionary Biology
Citation
Published In
DOI
EISSN
ISSN
Publication Date
Volume
Issue
Start / End Page
Related Subject Headings
- Regression Analysis
- Models, Biological
- Linear Models
- Ecosystem
- Ecology
- Bayes Theorem
- 4102 Ecological applications
- 3109 Zoology
- 3103 Ecology
- 0603 Evolutionary Biology