# Negative value in logistic regression

Being my dependent variable (0 = firm innovates incremental, 1 = company innovates radical), positive values of beta means greater effect on the propensity of firm innovates radically.

My question: what does negative coefficient estimates values mean? Increasing the propensity of the company to innovate incrementally?

In other words, can I interpret the results in the same way in both directions, negative and positive?

For example, my predictors are binary variables (0 = no, 1 = yes) that indicate whether the company cooperated with suppliers, customers, and universities. Since my dependent variable is 0 = innovated incremental, 1 = innovated radical, how to interpret these results: • there should not be negative values when using logit – Aksakal Oct 25 '17 at 19:41
• What are you referring to: negative coefficient estimates, negative predicted log odds, or negative predicted probabilities? – gung - Reinstate Monica Oct 25 '17 at 19:55
• The interpretation is no different than it would be for positive coefficients. If you are concerned about seeing a negative number, then change how you code suppliers: switch 1 to 0 and 0 to 1 in the dataset. Now the estimate will be +0.107. – whuber Oct 25 '17 at 21:14

## 2 Answers

I assume that by you mean: what does negative [betas -- i.e. coefficient] values mean? Increasing the propensity of the company to innovate incrementally?.

It means that the log odds that a "firm that innovates radical" is lower if a firm has higher value of covariate with a negative coefficient compared to another firm -- all other covariates being equal. You can flip this around and say that the firm has a higher log odds of being a "firm that innovates incremental".

When doing logistic regression, the output is reported in terms of the log-odds ratio, which is just an unexponentiated odds ratio.

Typically, when we interpret the results of a logistic regression, we aren't usually interested in those numbers (i.e., the numbers below Coef(b) in your output). I could tell you that a negative coefficient implies that the odds in the case when the corresponding binary variable = 1 are lesser than the odds in the case when that variable = 0, but that's beside the point, as the number itself has no real interpretation.

You can more easily infer the "direction" of the odds ratio after exponentiating the coefficients, as in e^{Coef}, or e^(-0.107) = 0.899. This number has a tangible interpretation; in your case, it is the ratio of the odds of innovating radically given that the company cooperated with its suppliers, compared to the odds of innovating radically for a company that did not cooperate with its suppliers, customers, or universities.

In other words, a company that cooperates with its suppliers has a 10% reduced odds of innovating radically compared to a company that does not cooperate with its suppliers, customers, or universities.

It is always important to remember that the odds ratio is a ratio: it has a numerator and a denominator. When interpreting it, you have to call attention to the numerator--the case "described" by a particular combination of variables-- as well as the denominator--the "reference case" (usually when all covariates are set =0, but this is an assumption on my part).