The effects of transformations and preliminary tests for non‐linearity in regression

The effects of transformations and preliminary tests for non‐linearity in regression Non‐linear relationships between two variables are often detected as a result of a preliminary statistical test for linearity. Common approaches to dealing with non‐linearity are to (a) make a linearizing transformation in the independent variable or (b) fit a relationship that is non‐linear in the independent variable, such as including a quadratic term. With either approach, the resulting test for association between the two variables can have an inflated type I error. We consider testing the significance of the quadratic term in a quadratic model as a preliminary test for non‐linearity. Using simulation experiments and asymptotic arguments, we quantify the type I error inflation and suggest simple modifications of standard practice to protect the size of the type I error. In the case of quadratic regression, the type I error will be increased by roughly 50 per cent. The simple strategy of appropriately correcting the α‐level is shown to have minimal loss of power if the relationship is truly linear. In the case of a linearizing transformation, the impact on the type I error will depend on the values of the independent variable and on the set of potential linearizing transformations considered. Simulation results suggest that a procedure which adjusts the test statistic according to the results of the preliminary test may offer adequate protection. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Statistics in Medicine Wiley

The effects of transformations and preliminary tests for non‐linearity in regression

Loading next page...
 
/lp/wiley/the-effects-of-transformations-and-preliminary-tests-for-non-linearity-8va0d1ZyJ1
Publisher
Wiley
Copyright
Copyright © 1991 John Wiley & Sons, Ltd.
ISSN
0277-6715
eISSN
1097-0258
D.O.I.
10.1002/sim.4780100504
Publisher site
See Article on Publisher Site

Abstract

Non‐linear relationships between two variables are often detected as a result of a preliminary statistical test for linearity. Common approaches to dealing with non‐linearity are to (a) make a linearizing transformation in the independent variable or (b) fit a relationship that is non‐linear in the independent variable, such as including a quadratic term. With either approach, the resulting test for association between the two variables can have an inflated type I error. We consider testing the significance of the quadratic term in a quadratic model as a preliminary test for non‐linearity. Using simulation experiments and asymptotic arguments, we quantify the type I error inflation and suggest simple modifications of standard practice to protect the size of the type I error. In the case of quadratic regression, the type I error will be increased by roughly 50 per cent. The simple strategy of appropriately correcting the α‐level is shown to have minimal loss of power if the relationship is truly linear. In the case of a linearizing transformation, the impact on the type I error will depend on the values of the independent variable and on the set of potential linearizing transformations considered. Simulation results suggest that a procedure which adjusts the test statistic according to the results of the preliminary test may offer adequate protection.

Journal

Statistics in MedicineWiley

Published: May 1, 1991

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create folders to
organize your research

Export folders, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off