Hi,

There is no assumption about normality on independent variable. You don't need to transform your variables.

You can found some explanations here: 

http://stats.stackexchange.com/questions/4831/logistic-regression-transforming-variables/4833#4833

http://stats.stackexchange.com/questions/4831/logistic-regression-transforming-variables/4833#4833

http://www.stata.com/statalist/archive/2008-03/msg00329.html

Hi,

There is no assumption about normality on independent variable. You don't need to transform your variables.

You can found some explanations here: 

http://stats.stackexchange.com/questions/4831/logistic-regression-transforming-variables/4833#4833

http://stats.stackexchange.com/questions/4831/logistic-regression-transforming-variables/4833#4833

http://www.stata.com/statalist/archive/2008-03/msg00329.html

In 'any' regression analysis, independent (explanatory/predictor) variables, need not be transformed no matter what distribution they follow. Sometimes they may be transformed, not for the sake of normality, but for making the relationship with the Y variable more clear, which may help improve the predictive ability of the the model.

I agree with the previous two answers, and add that when independent variables are very different scales, centering and scaling can help reduce multicolinearity problems.  I think that is probably what Subhash is saying about improving predictability.

Dear Tyron

I agree with the previous remarks. In LR, assumption of normality is not required, only issue, if you transform the variable, its interpretation varies. You have to be cations for the same.

Best of luck.

1. In line with the above: the search for transformations of independent variables ('X') in motivated by a better fit to the data. Standard transformations to consider indeed include the square root, but log, square, cubic, inverse are also quite standard. A rich set of combinations of transformations can be modeled with fractional polynomials, which combine 2 transformations of X; for example X^2 + X^-1. Another attractive approach is to use spline functions, specifically restricted cubic splines (rcs). These parsimonious functions have a lot of flexibility, and are stabilized at the tails of the X distribution, in contrast to other forms of splines, simple polynomials or fractional polynomials.

2. Re interpretation of coefficients: as always, a regression coefficient refers to a one unit change in the X value. If X is sqrt(X), the change is larger than on the original, linear scale (e.g. 4 -> 9 becomes 2 -> 3). Harrell has proposed to express effects for the 75 to the 25 percentile of the distribution of a continuous X variable to improve interpretability of effects. Natural units may also be chosen, e.g. an age effect per decade. For complex transformations, a graph may be best, with a 95% confidence interval. This is readily possible in R, using the rms library; not so easy in SPSS.

Both points are addressed in chapters 9 and 12 of my text Clinical Prediction Models

http://www.amazon.com/Clinical-Prediction-Models-Development-Validation/dp/1441926488

http://www.clinicalpredictionmodels.org/

Good contributions from all. I wonder why you transformed in the first place.

Pelumi: I suspect the reason why he transformed is because many non-statisticians have only a passing understanding of when "normality" is actually necessary.  I was visiting with one of my former professors recently, and he complained about this very thing.  Since most non-statisticians have only a vague knowledge of statistics, their understanding is basically limited to "Well, I'm supposed to have a normal distribution in my variables" so they rush to transform any variable that's not normally distributed - whether that's actually necessary or not.

Since it's not feasible for everyone to be a professional statistician, one might expect that these intricacies aren't obvious on the face of it, and that there should be more room allowed for those non-statisticians try to learn as much as they can along the way without making errors, hence the opening question being, "Should I transform non-normal independent variables in logistic regression?" Thankfully, Nicholas, Shubhash, John and Ewout have helped me avoid what now seems like an obvious error. With due respect, it is the sort of remark that leads good teachers and parents to have to tell their kids or students, "There is no such thing as a stupid question". 

Tyron, indeed, there is no such thing as a stupid question, and I am glad that you asked here, and received several excellent answers.  I was merely commenting to Pelumi that this is a common occurrence.  It was meant to be "in defense" of your right to ask the question, not as condescending as it sounded.  My apologies.

I generally think of transformations of independent/predictor variables as conditioning transformations.   The purpose of these conditioning transformations is not to make the predictor normally distributed necessarily.  Some of the motivations for conditioning transformations that I run into are:

1. Reduce the degree of skewness:  The observations in the heavy tails can have much more influence on the coefficient estimates resulting in improved fit for these observations, but distorted fit for the bulk of the data.  

2.  Eliminate extreme outliers:  This is similar in motivation to 1.  In the data I work with (Financial data) reducing the skewness is most commonly addressed with a log transform.  It is not uncommon that the extreme outliers results in the log transform not being effective enough.   Truncation of the extreme values is needed.

3. Bi modal or multi modal distributions.   In my field this generally implies the population needs to be segmented.  Portions of the model or the entire model is estimated separately in each segment.

4. Transform nonlinear relationships to linear ones:  This commonly goes hand in hand with 1. in my field.  Ideally the best transformation can be motivated by theory considerations.

This is only a small number of examples motivating transformations of predictors.  Any transformation will change the meaning of the coefficient.  My starting point in any regression modeling is understanding the distributions of the responses and predictors, the pairwise relationship between the response(s) and predictors and the relationships between the predictors.  This generally gives a firm foundation for understanding and motivating the conditioning transformations that are needed.

Thanks for your contribution, Ronald. Great insight!

Transforming variables so that your distribution is well behaved with extreme values tends to produce better fits in linear models like LDA, logistic regression etc. You can always check which i.e. transformed or non-transformed gives a better fit by checking the prediction error for your dependent error under k fold cross validation. 

I agree with Nicholas. If it's not an assumption to have normal distributions you don't need to transform. 

A logistic regression is very similar (though not identical) to a binomial logit model. This means the logarithm of the odds ratio can be interpreted as the deterministic utility difference Delta V between the two options (Y=1 and Y=0). Since in the standard logistic regression, this utility difference is formulated linearly in the exogenous variables,  Delta V=beta' x, the primary guidance for a possible transformation needs to be that the resulting independent variables contribute *linearly* to the utility difference. Thus, it depends on the specific problem. Formal criteria such as normality are more or less irrelevant. Notice that a nonlinear transformations influence both the x values *and* the estimated parameters beta. For example, when applying a sqrt transform to x components which are all above 1, the value of this component decreases but the estimate (absolute value of) the corresponding beta component increases. So, it is not a priori evident whether the odds ratio depending only on beta'x becomes more or less extreme. 

In a nutshell: Linearity in the utility difference is the only criterium for a possible transformation, and this depends on the problem at hand and not on formal criteria.

You can use CHAID data mining algorithm, a tree-based algorithm without getting any assumption. Thus, you will not need any transformation. 

try a new approach

Article TO DETERMINE SKEWNESS, MEAN AND DEVIATION WITH A NEW APPROAC...

Hi everyone.

I was wondering which publication I could consult/cite in order to support in my own research that "there is no assumption about normality on independent variable"? (I wish one could tag contributors on researchgate: Nicolas Martin, Andrew D Althouse, Martin Treiber)

Tyron Louw, what did you decide in the end?

Glad to find interesting answers like all yours.