Making logits behave

Making logits behave For the multivariate analysis of binary (or n-ary) dependent variables, common statistical analysis systems offer models with non-homogeneous error variance (LSN-models), and optionally transformations (“response functions”) of the relative frequencies, above all the logit function. Using the simplest possible example—two groups with a relative frequency in each—it is shown that significance tests based on transformed and non-transformed variables can yield substantially diverging results, and even an example of flagrantly inadequate behavior of logit as a response function in significance tests is presented. Dispensing with LSN models can remedy the latter problem; this recommendation is in line with other known objections against using LSN with binary dependents. Furthermore, an improved approximation for the variance of (any) response function makes tests based on transformed and non-transformed variables equivalent, so that problems of discrepant results depending on the response function used are completely removed. In the Appendix a sketch is given of a method to extend the approach to more general situations. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quality & Quantity Springer Journals

Making logits behave

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Publisher
Springer Journals
Copyright
Copyright © 2010 by Springer Science+Business Media B.V.
Subject
Social Sciences; Methodology of the Social Sciences; Social Sciences, general
ISSN
0033-5177
eISSN
1573-7845
D.O.I.
10.1007/s11135-010-9311-2
Publisher site
See Article on Publisher Site

Abstract

For the multivariate analysis of binary (or n-ary) dependent variables, common statistical analysis systems offer models with non-homogeneous error variance (LSN-models), and optionally transformations (“response functions”) of the relative frequencies, above all the logit function. Using the simplest possible example—two groups with a relative frequency in each—it is shown that significance tests based on transformed and non-transformed variables can yield substantially diverging results, and even an example of flagrantly inadequate behavior of logit as a response function in significance tests is presented. Dispensing with LSN models can remedy the latter problem; this recommendation is in line with other known objections against using LSN with binary dependents. Furthermore, an improved approximation for the variance of (any) response function makes tests based on transformed and non-transformed variables equivalent, so that problems of discrepant results depending on the response function used are completely removed. In the Appendix a sketch is given of a method to extend the approach to more general situations.

Journal

Quality & QuantitySpringer Journals

Published: Apr 30, 2010

References

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