Why you cannot transform your way out of trouble for small counts

Biometrics
David I Warton

Abstract

While data transformation is a common strategy to satisfy linear modeling assumptions, a theoretical result is used to show that transformation cannot reasonably be expected to stabilize variances for small counts. Under broad assumptions, as counts get smaller, it is shown that the variance becomes proportional to the mean under monotonic transformations g(·) that satisfy g(0)=0, excepting a few pathological cases. A suggested rule-of-thumb is that if many predicted counts are less than one then data transformation cannot reasonably be expected to stabilize variances, even for a well-chosen transformation. This result has clear implications for the analysis of counts as often implemented in the applied sciences, but particularly for multivariate analysis in ecology. Multivariate discrete data are often collected in ecology, typically with a large proportion of zeros, and it is currently widespread to use methods of analysis that do not account for differences in variance across observations nor across responses. Simulations demonstrate that failure to account for the mean-variance relationship can have particularly severe consequences in this context, and also in the univariate context if the sampling design is unbalanced.

References

Aug 14, 2009·Biometrics·Philip T ReissMichael P Milham
Sep 26, 2012·Biometrics·Irène Gijbels, Marek Omelka
May 9, 2015·Environmental Science and Pollution Research International·Eduard Szöcs, Ralf B Schäfer
Nov 1, 2015·Trends in Ecology & Evolution·David I WartonFrancis K C Hui

❮ Previous
Next ❯

Related Concepts

Trending Feeds

COVID-19

Coronaviruses encompass a large family of viruses that cause the common cold as well as more serious diseases, such as the ongoing outbreak of coronavirus disease 2019 (COVID-19; formally known as 2019-nCoV). Coronaviruses can spread from animals to humans; symptoms include fever, cough, shortness of breath, and breathing difficulties; in more severe cases, infection can lead to death. This feed covers recent research on COVID-19.

Blastomycosis

Blastomycosis fungal infections spread through inhaling Blastomyces dermatitidis spores. Discover the latest research on blastomycosis fungal infections here.

Nuclear Pore Complex in ALS/FTD

Alterations in nucleocytoplasmic transport, controlled by the nuclear pore complex, may be involved in the pathomechanism underlying multiple neurodegenerative diseases including Amyotrophic Lateral Sclerosis and Frontotemporal Dementia. Here is the latest research on the nuclear pore complex in ALS and FTD.

Applications of Molecular Barcoding

The concept of molecular barcoding is that each original DNA or RNA molecule is attached to a unique sequence barcode. Sequence reads having different barcodes represent different original molecules, while sequence reads having the same barcode are results of PCR duplication from one original molecule. Discover the latest research on molecular barcoding here.

Chronic Fatigue Syndrome

Chronic fatigue syndrome is a disease characterized by unexplained disabling fatigue; the pathology of which is incompletely understood. Discover the latest research on chronic fatigue syndrome here.

Evolution of Pluripotency

Pluripotency refers to the ability of a cell to develop into three primary germ cell layers of the embryo. This feed focuses on the mechanisms that underlie the evolution of pluripotency. Here is the latest research.

Position Effect Variegation

Position Effect Variagation occurs when a gene is inactivated due to its positioning near heterochromatic regions within a chromosome. Discover the latest research on Position Effect Variagation here.

STING Receptor Agonists

Stimulator of IFN genes (STING) are a group of transmembrane proteins that are involved in the induction of type I interferon that is important in the innate immune response. The stimulation of STING has been an active area of research in the treatment of cancer and infectious diseases. Here is the latest research on STING receptor agonists.

Microbicide

Microbicides are products that can be applied to vaginal or rectal mucosal surfaces with the goal of preventing, or at least significantly reducing, the transmission of sexually transmitted infections. Here is the latest research on microbicides.