Using a variable in logit units in a regression (interpretation)

Question

Suppose a dependent variable amath measures student's ability in math. The range of this variable is -5 to 5 and it is measured in logit units (it classifies the ability of students that took a standardised test using a Rasch model).

If I used amath as a dependent variable in a regression with one independent dummy variable for sex, let's say man.

And the coefficient I get as a result is -0.229.

My question is ¿How should this coefficient be interpreted? ¿Does the number has an interpretation or only the sign?

I got confused because I do not know how the units of my dependent variable should be treated.

Answer 1

That would mean that, regarding the student's ability in math amath in the scale -5 to 5, men had on average, a score 0.229 points lower than women.

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Note that to use a regression is OK if you have other variables besides sex. However, if you are studying the relation between only these two variables, you may use the t-Student's test to compare the score between sexes.

Answer 2

Logit is essential the logarithm of odds, so taking the anti-logarithm of the coefficient of the dummy variable would give $e^{-0.229} \approx 0.7953$

This is an odds-ratio figure, and is not easy to interpret. For example, near the centre and extremes of the distribution of $\pm5$ logit scores:

• If a woman with particular characteristics was expected to get a maths mark of $50\%$ (corresponding to odds of $1$ and a logit score of $0$) then a man with similar characteristics would be expected to get a mark of around $44.3\%$ (corresponding to odds of $0.7953$ and a logit score of $-0.229$)

• If a woman with particular characteristics was expected to get a maths mark of $99\%$ (corresponding to odds of $99$ and a logit score of $4.595$) then a man with similar characteristics would be expected to get a mark of around $98.75\%$ (corresponding to odds of $78.7375$ and a logit score of $4.366$)

• If a woman with particular characteristics was expected to get a maths mark of $1\%$ (corresponding to odds of $0.0101$ and a logit score of $-4.595$) then a man with similar characteristics would be expected to get a mark of around $0.8\%$ (corresponding to odds of $0.0803$ and a logit score of $-4.824$)