When does the sign of a variable change in logistic regression?

When does the sign of a variable change in logistic regression?

In my logistic regression the sign of coefficients of a variable (location distance of an amenity) changes based on other variables (with time -ve, with travel distance +ve) in the model. When the location distance is the only variable in the model, it has +ve sign. This isn’t surprising.

How is a regression coefficient related to log of Y?

Since this is just an ordinary least squares regression, we can easily interpret a regression coefficient, say β 1, as the expected change in log of y with respect to a one-unit increase in x 1 holding all other variables at any fixed value, assuming that x 1 enters the model only as a main effect.

How is the rate of change of a regression coefficient interpreted?

Even when a regression coefficient is (correctly) interpreted as a rate of change of a conditional mean (rather than a rate of change of the response variable), it is important to take into account the uncertainty in the estimation of the regression coefficient.

How is OLS used in a regression model?

OLS regression of the original variable (y) is used to to estimate the expected arithmetic mean and OLS regression of the log transformed outcome variable is to estimated the expected geometric mean of the original variable. Now let’s move on to a model with a single binary predictor variable.

How to understand the coefficients of a logistic regression?

The logistic regression model is Where X is the vector of observed values for an observation (including a constant), β is the vector of coefficients, and σ is the sigmoid function above. This immediately tells us that we can interpret a coefficient as the amount of evidence provided per change in the associated predictor.

When does the sign of the regression coefficient flip?

When you also include IV2 to IV4 the sign of the standardised regression coefficient of IV1 flips to -.25 (i.e., it’s become negative). With regards to terminology, do you call this a “suppressor effect”?

How are estimated coefficients interpreted in OLS regression?

The estimated coefficients must be interpreted with care. Instead of the slope coefficients (B) being the rate of change in Y (the dependent variables) as X changes (as in the LP model or OLS regression), now the slope coefficient is interpreted as the rate of change in the “log odds” as X changes. This explanation is not very intuitive.

How to interpret the coefficients of logistic regression?

To interpret the coefficients we need to know the order of the two categories in the outcome variable. The most straightforward way to do this is to create a table of the outcome variable, which I have done below.

Why are regression coefficients that flip sign after including other predictors?

The differences essentially relate to the type of variable. It’s more useful to understand the underlying phenomenon rather than think in terms of a particular “paradox” or effect. For a causal perspective, the paper below does a good job of explaining why and I’ll quote at length their introduction and conclusion to whet your appetite.

What causes a wrong sign on a regression?

Multicollinearity is the usual suspect as JoFrhwld mentioned. Basically, if your variables are positively correlated, then the coefficients will be negatively correlated, which can lead to a wrong sign on one of the coefficients. One check would be to perform a principal components regression or ridge regression.