Google:

"Confounding and collinearity in logistic regression"

"Collinearity diagnostics of binary logistic regression model"

I suggest to check it. To be sure of the variables which will explain independent variable. I will let you know which method is the convenient one.

The problem of collinearity is one of the most desperate problems with which one can find in a regression analysis. As we saw when speaking of estimation coefficients, if in a model of RLM an independent variable is linear combination of others, the model is unresolvable, because, in this case, the matrix X'X is singular, i.e. its determinant is zero and inver cannot be TIR. It is called this phenomenon collinearity. That a variable X 1 is a linear combination of other X 2, means that both are related by the expression X 1 = b1 + b2X2, being constants b1 and b2, therefore the coefficient of correlation between the two variables will be 1. In the same way that a variable X 1 is a linear combination of other X 2,..., Xi with i > 2, means that these variables are related by the expression X 1 = b1 > + b2 X 2 +... + bi Xi, being b1,..., bi constants and therefore the coefficient of multiple correlation RX1 | 2 X... XI will also be 1.

Hello Sarita,

You check this texts:

• Article Collinearity diagnostics of binary logistic regression model

• http://www-01.ibm.com/support/docview.wss?uid=swg21476696

In practice, exact collinearity rarely occurs, but if arises often called near-collinearity, or by extension, simply collinearity that some variable is "almost" linear combination of another or others, or put another way, some single or multiple correlation between independent variables coefficients are close to 1, even if they do not reach this value.

In this case the matrix X'X is almost-singular, i.e. its determinant is not zero, but is very small. As to reverse an array you must divide by its determinant, in this situation arise problems of accuracy in the estimation of the coefficients, matrix inversion algorithms will lose accuracy by having to divide by a very small number, being also unstable.

In addition, as the matrix of variances of the estimators is proportional to X'X, is that in the presence of collinearity, the standard errors of coefficients are large (there are inaccuracies also statistical sense).

Therefore, when implementing models of RLM should be previously studying the existence of almost-collinearity (exact collinearity is not necessary to study it previously, already that all algorithms detect it, in fact they can not finish the estimate). As a measure of it there are several statisticians proposed, the simplest are the coefficients of determination of each independent variable with all other, i.e.📷

and related to them, the factor of inflation of the variance (IVF) and tolerance (T), defined as 📷

A rule of thumb, cited by Kleinbaum, consists in considering that there are problems of collinearity if some IVF is greater than 10, which corresponds to some 0.9 R2i and Ti < 0,1.

Although it can exist with low IVF collinearity, there also may be colinealidades that do not involve all the independent variables and, therefore, are not well detected by FIV.

Otherwise, more complete, detect collinearity is an analysis of the main components of the independent variables. This technique is mathematically complex and here only a summary of the same necessary to understand the diagnosis of collinearity is made. Find formulas and ecuations becouse I could not insert them.

Thanks Jochen, Margarita and Mohammed for your valuable suggestions. It will definitely help.

As far i understood, VIF may be used to detect multicolinearity in logistic regression.

@Sarita Gupta: Sure, yes you use VIF.

You may be interested in this recent paper

Article Confounding and collinearity in regression analysis: a cauti...