Certain effects of uncertain models

Brian Knaeble

doi:10.14419/ijasp.v2i2.3698

Article Details

Certain effects of uncertain models

Authors:

Brian Knaeble

Publisher:

Science Publishing Corporation

Journal:

International Journal of Advanced Statistics and Probability Vol.2 Issue 2, pp.124-134

Document Type:

Article

Publication Date:

5/2014

Document Language:

English

Document ID (Org No.):

2001386983

pISSN:

2307-9045

DOI:

10.14419/ijasp.v2i2.3698

Abstract:

 Statistical summaries of multiple regression analyses often state conclusions as if model uncertainty is of little concern. The error due to a mis-specified model, however, can be more significant in practice than the sampling error associated with commonly reported statistics. The true effect of an explanatory variable may be opposite that indicated by a fitted coefficient of a linear model, even if the model is well fit and the coefficient is deemed statistically significant. Here we study the sensitivity of the sign of a fitted coefficient to changes in the model structure. As a consequence of the principle of least squares, we show generally, that a set of covariates with a relatively weak coefficient of determination can not reverse the sign of a relatively strong fitted coefficient of a linear model that has been fit with a regression matrix having orthogonal columns. A consequence of the theory is a necessary condition for Simpson's paradox. Keywords: confounding, least squares, model uncertainty, regression, sensitivity analysis.

Article Details

Certain effects of uncertain models

Authors: Brian Knaeble

Publisher: Science Publishing Corporation

Journal: International Journal of Advanced Statistics and Probability Vol.2 Issue 2, pp.124-134

Document Type: Article

Publication Date: 5/2014

Document Language: English

Document ID (Org No.): 2001386983

pISSN: 2307-9045

DOI: 10.14419/ijasp.v2i2.3698

Issues

Authors:

Brian Knaeble

Publisher:

Science Publishing Corporation

Journal:

International Journal of Advanced Statistics and Probability Vol.2 Issue 2, pp.124-134

Document Type:

Article

Publication Date:

5/2014

Document Language:

English

Document ID (Org No.):

2001386983

pISSN:

2307-9045

DOI:

10.14419/ijasp.v2i2.3698