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Log ratio for removing collinearity among variables

 

Log Ratio (LG) is a measure of the independent effect of a variable on a dependent variable. It is calculated as:

 

LG = n * log (SSr/SSf)

 

where n is the number of observations (entries), SSr is the residual sum of squares from the reduced model, i.e., the multiple regression model with a given variable, SSf is the residual sum of squares of full model, i.e., the model containing all independent variables.

 

Obviously, the more important the variable, the greater the LG, and the more the number of observations in the regression, the greater the LG. LG is related to the well-known F-test, and a LG of 2.5 is roughly a probability of 0.05.

 

NOTE BUT:

 

The LG can be 0 for two markers that are extremely closely located!!!!! In such a case, the QTL represented by these very closely linked markers will not be detected. This is a very serious preblem of this method. IF prevent this from happening, closely linked markers should be removed first so remaining markers are evenly distributed across the genome or chromesomes. The LG method can then be applied. One advantage of suing biplot is that it allows visualization of the marker linkages so that some markers can be removed visually before numerical analysis.