I am running a logistic regression by using dichotomous dependent variable and five independent variable. I found one of the independent variable is getting -ve regression coefficient.
1) What does mean by the positive and negative regression coefficient in logistic regression? How can I interpret this ?
The coefficients in a logistic regression are log odds ratios. Negative values mean that the odds ratio is smaller than 1, that is, the odds of the test group are lower than the odds of the reference group.
Jochen is correct, but marginal effects are also a very useful tool when interpreting estimates from logistic regression. In this case, you would have a negative marginal effect. Marginal effects are an absolute change in the probability of an outcome while holding all other variables constant. If it is negative, it would be a decrease in probability. Most statistical software will readily calculate marginal effects as part of model estimation.
I agree with the previous answers. Further, the negative log odds ratios, can be interpreted to mean that the factor under study is actually a protective factor.
Caution should be taken when considering the estimated probabilities from a logistic regression model in a case-control study. The coefficients of the independent variables are valid (and thus the odds ratios) but the probability estimation may not, depending on the intercept value.
Perhaps, you're unfamiliar with interpreting a negative regression coefficient from a logistic regression because you're used to see it in its exponentiated form (i.e. as an OR, rather than a log-OR) - it is straightforward that an OR
It is quite simple: if you are running a logit regression, a negative coefficient simply implies that the probability that the event identified by the DV happens decreases as the value of the IV increases. If you run logistic regression, there are no negative values (logistic has always positive ones) but in this case a value below 1 implies a reduction in the probability that the event happens. To sum up:
a) logit positive value = logistic > 1 = increase in the probability of the event when you have a positive change in the IV
b) logit negative value = logistic < 1 = decrease in the probability of the event when you have a positive change in the IV
Hope this helps.
Best regards
Andrea
Thanks to all for the response. I know -Ve coefficient means the value DV decreases as the value of the IV increases. But still I have confusion about logistics regression. Why one of the variable have high -ve coefficient value than other variables ?
It is very simple: the probability that the event associated to the value 1 is reduced when the value associated to the IV increases. In other words, when the value of the IV increases the probability decreases.
Marginal effect shows the impact of independent variable on the dependent variable in logistic regression. It enables the researcher to determine the rate of the variability of x that accounts to the variability of y in a logistic regression.
Absolutely. When you compute the marginal effect you would be able to determine the actual influence of the negative coefficient on the dichotomous dependent variable.
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