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I have a hard time interpreting these coefficients in collum 2. So my dependent variable is if you have a supervisory job yes=1 and my independent variables are female=1 and traditional values=1. Now how can i compare the likelihood of a supervisory job for traditional men vs traditional woman, should i then add trad*fem+ female?

Thank you in advance!

  • $\begingroup$ Welcome! Was this estimated using least squares? $\endgroup$ – Thomas Bilach Apr 19 '20 at 23:19
  • $\begingroup$ Thank you for your response, yes this is a OLS regression $\endgroup$ – Sabine Apr 20 '20 at 9:19

Unless you're partial to linear probability models, I would also suggest fitting a maximum likelihood logit model.

Now how can I compare the likelihood of a supervisory job for traditional men vs traditional woman, should I then add trad*fem + female?

You're on the right track. First, to get a precise estimate, you should also report your intercept.

\begin{align*} \widehat{\text{Supervisor}} &= \hat{\alpha} + 0.086\text{Traditional} - 0.214\text{Female} - 0.169(\underbrace{\text{Traditional}\times\text{Female}}_{\text{Interaction}}) \\ \end{align*}

The interaction shows how the effect of traditional values on obtaining a supervisory position is modified by gender. All you have to do is keep track of which dummies are turned 'on/off' as you interpret your model.

First, the probability of a non-traditional male securing a supervisory position is the base condition (i.e., the intercept). The probability of a male with traditional values obtaining a supervisory position is the base condition plus 0.086 (i.e., $\text{Traditional} = 1$). The interpretation of the coefficient on $\text{Traditional}$ is the effect of exhibiting traditional values on the probability of obtaining a supervisory position with all other predictors equal to 0. To put this in the context of your equation, the estimate for the effect of traditional men in your sample is as follows:

\begin{align*} \widehat{\text{Supervisor}} &= \hat{\alpha} + 0.086(1) - 0.214(0) - 0.169(1 \times 0) \\ \widehat{\text{Supervisor}} &= \hat{\alpha} + 0.086 \end{align*}

This is your estimate of the probability of a traditional male landing a supervisory job. Now, you correctly note that a female with traditional values is the effect when $\text{Traditional = 1}$ and $\text{Female = 1}$, so you should assess the combined effect of these two coefficients.

The main effect of being a non-traditional female is negative (i.e., -0.214). You can think of this as offsetting the male intercept. In non-technical terms, females start with a lower probability. The interaction of the traditionalist variable with gender, though, further offsets the effect of being female. Here is the final derivation:

\begin{align*} \widehat{\text{Supervisor}} &= \hat{\alpha} + 0.086(1) - 0.214(1) - 0.169(1 \times 1) \\ \widehat{\text{Supervisor}} &= \hat{\alpha} + 0.086 - 0.214 - 0.169 \\ \widehat{\text{Supervisor}} &= \hat{\alpha} - 0.297 \end{align*}

In sum, these estimates allow you to compare traditionalist men with traditionalist women. Your model suggests non-traditional women have a lower probability of securing a management position, and their chances are further reduced if they espouse traditional values.

  • $\begingroup$ This is very helpful, thank you very much! $\endgroup$ – Sabine Apr 21 '20 at 10:15
  • $\begingroup$ @Sabine If this helped, please select this as the answer using the check mark on the left. $\endgroup$ – Dimitriy V. Masterov Apr 28 '20 at 18:31

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