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added STATA equation and results based on Noah's comment.
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I ran this equation on Stata:

Y = b0i.EMPLOYED + b1i.FEMALE + b3c.EDU_YEARS + 
   probit ownland b4(i.EMPLOYED##iemployed##i.FEMALE##cfemale##c.EDU_YEARS)eduyrs

where EMPLOYED =ownland is =1 if the respondent owns agricultural land; employed= 1 if the respondent is currently working, FEMALE =female= 1 if the respondent is a woman, and EDU_YEARS captures years of education.

b0 would be the effect of being employed on Y for uneducated men b1 would be the effect of being a female on Y for unemployed and uneducated women, compared to men. b3 would be the effect of years of education for unemployed menThe results I receive is

Own landCoef.Std. Err.zP>z[95% Conf. Interval]
Employed.2022467.14317651.410.158-.078374 .4828674
Female.2049693.19943311.030.304-.1859123 .5958509
Employed#Female-.0853641.267807-0.320.750-.6102563 .439528
eduyrs-.0240563.0113061-2.130.033-.046216 -.0018967
Employed#c.eduyrs-.0061285.0191439-0.320.749-.0436497 .0313928
Female#c.eduyrs-.0248372.0321575-0.770.440-.0878647 .0381902
Employed#Female#c.eduyrs.0368203.04285350.860.390-.047171 .1208115

How would you interpret b4? Would it beI am pretty clear on the effectinterpretation of being employed women"employed", "female", and "eduyrs" on Y for a unit change in years of education?the outcome:

  • Employed variable would be the effect of being employed on Y (ownland) for uneducated men
  • Female variable would be the effect of being a female on Y for unemployed and uneducated women, compared to men.
  • eduyrs variable would be the effect of years of education for unemployed men

How canBut I obtainam confused about the net effect of an increase in yearinterpretation of education for employed female versus unemployed female? Would that be (b0+b2+b3+b4)-(b1+b3) = b0+b2?other variables.

  1. How would you interpret the estimated coefficient for Employed#Female#c.eduyrs? Would it be the effect of being employed women on Y for a unit change in years of education?
  2. How can I obtain the net effect of an increase in year of education for employed female versus unemployed male? Would that be nlcom (employed+ female+ i.employed#i.female+eduyrs + Employed#Female#c.eduyrs)-(eduyrs)?
  3. How can I obtain the net effect of an increase in year of education for employed female versus unemployed female? Would that be
    (employed+ female+ i.employed#i.female+eduyrs + Employed#Female#c.eduyrs)-(female + eduyrs + female#eduyrs)?

If someone could enlighten me on this, that would be very helpful. Thank you so much!

Y = b0i.EMPLOYED + b1i.FEMALE + b3c.EDU_YEARS + 
     b4(i.EMPLOYED##i.FEMALE##c.EDU_YEARS)

where EMPLOYED = 1 if the respondent is currently working, FEMALE = 1 if the respondent is a woman, and EDU_YEARS captures years of education.

b0 would be the effect of being employed on Y for uneducated men b1 would be the effect of being a female on Y for unemployed and uneducated women, compared to men. b3 would be the effect of years of education for unemployed men

How would you interpret b4? Would it be the effect of being employed women on Y for a unit change in years of education?

How can I obtain the net effect of an increase in year of education for employed female versus unemployed female? Would that be (b0+b2+b3+b4)-(b1+b3) = b0+b2?

If someone could enlighten me on this, that would be very helpful.

I ran this equation on Stata:

probit ownland i.employed##i.female##c.eduyrs

where ownland is =1 if the respondent owns agricultural land; employed= 1 if the respondent is currently working, female= 1 if the respondent is a woman, and EDU_YEARS captures years of education.

The results I receive is

Own landCoef.Std. Err.zP>z[95% Conf. Interval]
Employed.2022467.14317651.410.158-.078374 .4828674
Female.2049693.19943311.030.304-.1859123 .5958509
Employed#Female-.0853641.267807-0.320.750-.6102563 .439528
eduyrs-.0240563.0113061-2.130.033-.046216 -.0018967
Employed#c.eduyrs-.0061285.0191439-0.320.749-.0436497 .0313928
Female#c.eduyrs-.0248372.0321575-0.770.440-.0878647 .0381902
Employed#Female#c.eduyrs.0368203.04285350.860.390-.047171 .1208115

I am pretty clear on the interpretation of "employed", "female", and "eduyrs" on the outcome:

  • Employed variable would be the effect of being employed on Y (ownland) for uneducated men
  • Female variable would be the effect of being a female on Y for unemployed and uneducated women, compared to men.
  • eduyrs variable would be the effect of years of education for unemployed men

But I am confused about the interpretation of other variables.

  1. How would you interpret the estimated coefficient for Employed#Female#c.eduyrs? Would it be the effect of being employed women on Y for a unit change in years of education?
  2. How can I obtain the net effect of an increase in year of education for employed female versus unemployed male? Would that be nlcom (employed+ female+ i.employed#i.female+eduyrs + Employed#Female#c.eduyrs)-(eduyrs)?
  3. How can I obtain the net effect of an increase in year of education for employed female versus unemployed female? Would that be
    (employed+ female+ i.employed#i.female+eduyrs + Employed#Female#c.eduyrs)-(female + eduyrs + female#eduyrs)?

If someone could enlighten me on this, that would be very helpful. Thank you so much!

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kjetil b halvorsen
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Hi StackExchange community,

I am currently looking at the following equation using Stata and unsure of how to interpret the interaction terms when there are three variables interacted together (2 binary variables and one continuous variable).

Y = b0i.EMPLOYED + b1i.FEMALE + b3c.EDU_YEARS + b4(i.EMPLOYED##i.FEMALE##c.EDU_YEARS)

Y = b0i.EMPLOYED + b1i.FEMALE + b3c.EDU_YEARS + 
     b4(i.EMPLOYED##i.FEMALE##c.EDU_YEARS)

where EMPLOYED = 1 if the respondent is currently working, FEMALE = 1 if the respondent is a woman, and EDU_YEARS captures years of education.

b0 would be the effect of being employed on Y for uneducated men b1 would be the effect of being a female on Y for unemployed and uneducated women, compared to men. b3 would be the effect of years of education for unemployed men

How would you interpret b4? Would it be the effect of being employed women on Y for a unit change in years of education?

How can I obtain the net effect of an increase in year of education for employed female versus unemployed female? Would that be (b0+b2+b3+b4)-(b1+b3) = b0+b2?

If someone could enlighten me on this, that would be very helpful.

Thank you.

Hi StackExchange community,

I am currently looking at the following equation using Stata and unsure of how to interpret the interaction terms when there are three variables interacted together (2 binary variables and one continuous variable).

Y = b0i.EMPLOYED + b1i.FEMALE + b3c.EDU_YEARS + b4(i.EMPLOYED##i.FEMALE##c.EDU_YEARS)

where EMPLOYED = 1 if the respondent is currently working, FEMALE = 1 if the respondent is a woman, and EDU_YEARS captures years of education.

b0 would be the effect of being employed on Y for uneducated men b1 would be the effect of being a female on Y for unemployed and uneducated women, compared to men. b3 would be the effect of years of education for unemployed men

How would you interpret b4? Would it be the effect of being employed women on Y for a unit change in years of education?

How can I obtain the net effect of an increase in year of education for employed female versus unemployed female? Would that be (b0+b2+b3+b4)-(b1+b3) = b0+b2?

If someone could enlighten me on this, that would be very helpful.

Thank you.

I am currently looking at the following equation using Stata and unsure of how to interpret the interaction terms when there are three variables interacted together (2 binary variables and one continuous variable).

Y = b0i.EMPLOYED + b1i.FEMALE + b3c.EDU_YEARS + 
     b4(i.EMPLOYED##i.FEMALE##c.EDU_YEARS)

where EMPLOYED = 1 if the respondent is currently working, FEMALE = 1 if the respondent is a woman, and EDU_YEARS captures years of education.

b0 would be the effect of being employed on Y for uneducated men b1 would be the effect of being a female on Y for unemployed and uneducated women, compared to men. b3 would be the effect of years of education for unemployed men

How would you interpret b4? Would it be the effect of being employed women on Y for a unit change in years of education?

How can I obtain the net effect of an increase in year of education for employed female versus unemployed female? Would that be (b0+b2+b3+b4)-(b1+b3) = b0+b2?

If someone could enlighten me on this, that would be very helpful.

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Alisa
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Interpretation of two dummies interacted with one continuous variable

Hi StackExchange community,

I am currently looking at the following equation using Stata and unsure of how to interpret the interaction terms when there are three variables interacted together (2 binary variables and one continuous variable).

Y = b0i.EMPLOYED + b1i.FEMALE + b3c.EDU_YEARS + b4(i.EMPLOYED##i.FEMALE##c.EDU_YEARS)

where EMPLOYED = 1 if the respondent is currently working, FEMALE = 1 if the respondent is a woman, and EDU_YEARS captures years of education.

b0 would be the effect of being employed on Y for uneducated men b1 would be the effect of being a female on Y for unemployed and uneducated women, compared to men. b3 would be the effect of years of education for unemployed men

How would you interpret b4? Would it be the effect of being employed women on Y for a unit change in years of education?

How can I obtain the net effect of an increase in year of education for employed female versus unemployed female? Would that be (b0+b2+b3+b4)-(b1+b3) = b0+b2?

If someone could enlighten me on this, that would be very helpful.

Thank you.