# Thread: Multiple Regression - Is it possible to constrain the coefficients to be positive?

1. ## Multiple Regression - Is it possible to constrain the coefficients to be positive?

Another stumper ... I am running a multiple regression with two independent variables. The regression results look good, except that one coefficient is positive and the second is negative. I need both coefficients to be positive because I am working with a system where I cannot have negative units (it is acceptable for the intercept constant to be negative). Is it possible to force the coefficients to be positive? Or at least is there some way to examine all combinations of coefficients and select the best pair that is positive?

2. ## Re: Multiple Regression - Is it possible to constrain the coefficients to be positive

What do you mean by "system"? Do you mean the outcome cannot be negative? If so, that shouldn't be a problem, as your intercept and the other IV would, I assume, ensure that your outcome makes sense (as long as the predictor values you input are in the range of the predictors used to establish the model).

3. ## Re: Multiple Regression - Is it possible to constrain the coefficients to be positive

All the values of the data series are positive (greater than zero) for the dependent variable (DV) as well as the two independent variables(IV1, IV2). My problem is that the resulting regression equation has a positive coefficient for IV1 and a negative coefficient for IV2. The system being modeled requires me to combine physical units of IV1 and IV2 to make DV. So I need to combine some positive quantities of IV1 and IV2. I need the best fit equation that has positive coefficients for each IV. I can't work with a negative coefficient.

4. ## Re: Multiple Regression - Is it possible to constrain the coefficients to be positive

Just because the outcome and the predictors are always positive isn't a reason to force the coefficients to be positive.

5. ## Re: Multiple Regression - Is it possible to constrain the coefficients to be positive

Let me offer an example to illustrate my challenge: The DV (dependent variable or outcome) is the taste of food, with high values indicating very sweet and low values indicating very sour. The two IV's (independent variables or predictors) are sugar and vinegar. A high proportion of sugar and the taste is extremely sweet. Of course, a high proportion of vinegar and the taste is extremely sour. Some combination of sugar and vinegar result in a taste measurement between these extremes. The coefficients of the IV's represent the quantities of units of sugar and vinegar that make up the recipe. I have to work with positive quantities (coefficients) because I can only add measured amounts, I cannot subtract them. So I cannot deal with a negative coefficient.

6. ## Re: Multiple Regression - Is it possible to constrain the coefficients to be positive

There is no reason that vinegar cannot have a negative coefficient and any sensible model of sweetness will have a negative coefficient for vinegar.

The coefficients of the IVs in a regression do not represent the quantities of sugar and vinegar. They are what the quantities are multiplied by.

However, if the DV is measured on a Likert type scale, then you might want ordinal logistic regression. That will avoid having a negative predicted value for the flavor.

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CowboyBear (05-11-2015)

8. ## Re: Multiple Regression - Is it possible to constrain the coefficients to be positive

Statburner, why don't you try out the regression model by hand with the output you got?

Assuming that all 3 variables are a 5 point scale, give a "1" to sugar and "5" to vinegar so Y = intercept + 1*(coefficient for sugar) + 5*(coefficient for vinegar). You should get a value somewhere between 1 and 5, and I assume it would be close to 1.

Given that sweetness and sour are two opposing tastes, it's not a surprise you end up with a positive coefficient for one and negative for the other.

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