# What to do with ordered logistic regression when I have correlated predictors

I am currently trying to analyze a research project and I have very little experience dealing with this type of data and I am looking for a bit of help/suggestions.

The project revolves around frog mating behavior, specifically investigating the influence of length, weight, condition, and age on a female frogs willingness to travel certain distances (simulated by altering the volume of a males mate attraction call in a sound chamber playback experiment) to mate with an attractive male vs an unattractive (but nearby) male.

The response variable is the distance a given female is willing to travel to choose an attractive mate. This response variable is categorical and has 4 levels corresponding to 4 different volume settings (essentially simulating distance going from short distance to long distance).

The predictor variables I am interested in are length, weight, condition (which is calculated using the residuals of a length/weight regression), and age. Length, weight and condition are all continuous, while age is a factor (age is measured in years and all individuals are either 2 or 3 year olds).

From what I have read ordered logistic regression sounds like it might be a way to analyze this data since my response variable is categorical and has a natural ordering to the responses.

My problem is that from what I have read ordered logistic regression requires that the predictor variables are not correlated.

I know that my predictor variables are definitely correlated. For example if I were to run an anova or t-test with age and length (or age and weight) I find that the older females are significantly longer/heavier. Additionally length and weight are certainly strongly correlated (as you would expect).

Unfortunately I have not been able to find any good suggestions for what to do in this scenario where I have correlated predictors. Is there any way for me to tease apart these correlated predictors? Can I still use ordered logistic regression or would some other test be more appropriate?

Thanks!

• Welcome to crossvalidated. – Jeremy Miles Oct 16 '15 at 3:24
• This is not a problem. It's kind of the point of regression. The only way to get uncorrelated predictors is (usually) to assign individuals to conditions yourself. Random numbers will give you correlated variables. – Jeremy Miles Oct 16 '15 at 3:25

## 1 Answer

The main problem with your approach is the way you measured condition as the residuals from a regression explaining length with weight. Look at the regression equation

$length = \beta_0 + \beta_1 weight + \underbrace{\varepsilon}_{condition}$

If in a subsequent regression you include weight and condition, then you can exactly reconstruct the length from those two variables. So the variable length adds exactly no information whatsoever after you included weight and condition. So how can a regression model compute a separate effect for a variable that adds no information? It cannot.

As a solution I can only suggest that you find another way to measure the condition of your frogs or leave condition out of your model.