In a discrete choice model setting, lets say my model function is $U(x)= \beta_0+\beta_1X_1+\beta_2X_2+\beta_3X_3+\beta_4X4+\epsilon$

with independent variable $X_1$ has a value ranges from -2.5 to 2.5 $X_2$ is always positive $X_3$ is always negative and $X_4$ is binary dummy

In this case How can I interpret sign of variable


The sign of the variable tells you the impact on the choice proba P(Y=1) when you increase the independent variable by +1 unit. So basically if you find a positive effect for (X2) it means that increasing the level of X2 makes the option/product more likely to be selected. If you want to obtain similar effect but for a decrease in the variable, simply take its negative. If you variable is categorical (e.g., X2 = {Male; Female}) then the sign will tell you the effect of moving from the reference level (say Male) to the target one (Female).

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