Test for harmful collinearity among predictor variables used in modeling global temperature

ABSTRACT: Lower tropospheric temperature anomalies from the global satellite MSU that have been available since 1979 are unique and play a significant role in the continuing climate debate. A number of investigators have analyzed the MSU data using regression analysis to remove the geophysical effects of volcanoes, El Niño/Southern Oscillation, and solar irradiance in an effort to determine any underlying trend line. In a recent paper Santer et al. (2001; J Geophys Res 106:28033- 28059) questioned the validity of such studies, noting that large El Niño events have occurred at the same time as 2 major volcanoes. They calculated a correlation between these 2 variables and claimed that this indicates collinearity, which can adversely affect any regression analyses. We examine the issue of collinearity between the volcano and El Niño/Southern Oscillation signals in the analysis of the MSU data. We do this by using the general tests for collinearity of Belsley. There are 2 tests. The first is for degrading collinearity on the data matrix of the predictor variables. If the first test fails, a second test for harmful collinearity is performed on the coefficients from any regression analysis. Employing these 2 tests, we find that there is no degrading or harmful collinearity used in the modeling of the MSU temperature anomalies.