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I am struggling interpreting the coefficient of a variable which is expressed as a proportion in a probit model. As it currently stands , I am interpreting the average partial effects of this variable (0.14) as a one unit increase in share of debt raises the probability of innovation by 14 percentage points.

However, if I multiply this variable by 100 and turn it into a percentage, the average average partial effect is (.0014556 ), does it mean that a 1 percentage point change in the percentage of debt increases the probability of innovation by 0.0014556.

Questions : a) are my interpretations correct

b) Instead of saying a one percentage change increases can I write in terms of a 10 percentage point increase and if so what should I do .

Regards, naveed

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if 0.14 is your coefficient, then you should exponentiate it [exp(0.14) = 1.15], which says that one unit increase of whatever your original variable, you will get 0.15 (1.15-1=0.15) or 15% increase in your response.

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  • $\begingroup$ This makes sense in a logit model for multiplicative effects on the odd ratio (which is not the same as the probability of success), but is not meaningful for a probit model. Sometimes people will multiply the probit coefficient by 1.6 or 1.8 to get approximate logit coefficients, and then exponentiate, but this is may not work well in the tails (near 0 or 1). $\endgroup$ – Dimitriy V. Masterov Dec 4 '19 at 18:27

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