I will appreciate it very much if someone can help me with the following problem. I am testing whether the effect of my key independent variable (mother's weekly work hours in 3 categories - 0, 1 and 2) is different for each developmental stage of the child (3 categories - 1- early childhood, 2- middle childhood and 3- adolescence). This is a panel design (fixed-effects) but this should make no difference.
In stata I use the following command: xtreg dep_var devstage##moth_work, fe
Before that I set the reference category for mother's work hours to be the middle category (which is 1 in my case). In case I don't specify a reference category stata just picks the first one but it drops it in the main as well as in the interaction effects "because of multicolinearity".
You can see the results in the attached file. The interpretation of the main effects I think is clear but not the interaction effects. What is my reference category for the interaction effects in my case? Why there are so many combinations missing (there are only 4 coefficients while 3x3 =9? How can I interpret the coefficients of the interaction terms which are in the apposite direction compared to the main effect of the key explanatory variable? Or maybe I do something wrong?
Thank you for your help!
Hi Plamen,
I have attached two links to videos which will help you.
I am unsure what data is contained within ind_var or it's unit, so I will simply refer to your dependent variable as Y.
First, your constant will tell you the estimated value of Y when devstage==1 and moth_work==1; notice that STATA has dropped these two, therefore they are absorbed into the constant. This value may be significant or insignificant. Every estimated coefficient is positive or negative shifts to the constant as one of the categories change.
Always remember that the base is moth_work==1 and devstage==1. To calculate the estimated Y value, simply add the constant and the estimated coefficient in question.
The top four coefficients in your results estimate the main effect, in isolation.
Addressing devstage, held in isolation:
devstage==2, estimated Y significantly decreases by -7.187
devstage==3, estimated Y significant decreases by -19.319
Conclusion, as devstage increases, the estimated value of Y decreases.
Addressing moth_work, in isolation:
moth_work==0, estimated Y significantly increases by 4.386,
moth_work==2, estimated Y is not significantly different to the constant; i.e. Y does not change if moth_work==2.
Conclusion: estimated value of Y only increases if moth_work==0. There is no difference in estimated Y whether moth_work==1 (the base) or moth_work==2.
Addressing your interactions:
What would be the estimated value of Y if moth_work==2 AND devstage==0, simultaneously?
Your estimated Y would significantly decrease by -3.533. Notice that in your estimated coefficients devstage==1 significantly decreases the value of Y while moth_work==0 significant increases the value of Y; the net effect is a decrease in Y.
Also, if moth_work==2 and devstage==2 there is an insignificant effect; similarly, if moth_work==3 and devstage==2 the effect is also insignificant.
Clearly, whatever data is contained within moth_work==2 does not significantly affect Y compared to the base (moth_work==1). Therefore, there is little difference between moth_work==1 and moth_work==2.
My interpretation of your results is that moth_work==1 and moth_work==2 may actually be part of the same group (i.e. mothers working X or more hours per week). You should investigate this further, try some multicollinearity tests such as VIFs and correlation matrices.
Also, you do have all 9 estimated coefficients. Your constant denotes the base, 4 interactions, 2 for moth_work and 2 for devstage; 9 in total.
I have attached a photo to demonstrate.
Hope this helps.
VIDEOS:
Specifying interaction:
http://www.youtube.com/watch?v=f-tLLX8v11c
Interpreting interactions:
http://www.youtube.com/watch?v=ScKL40dp8M4
The problem may arise if one level in your categorical variable is coded as 0 which results in all interaction variables with those levels becoming 0. It would a good idea to recode the categories of your variables as 1,2,3 rather than 0,1,2. Can you confirm if this is already the case? Thanks.
I just tried as you suggested and I confirm that the results are exactly the same. Do you have any other ideas? Is there a problem there at all or I just can't figure out how to interpret the results?
At this point it more about how you read the results.
The levels in the interaction term with the base categories from the original variables will be dropped every time. I would recommend that you write out the the entire equation and see how the odds add up every time.
http://www.ats.ucla.edu/stat/stata/webbooks/reg/chapter6/statareg6.htm
Well, this exactly is the problem - that I can't figure out how to interpret the coefficients - and this text doesn't help much, first, because it uses some outdated command and second, because it doesn't explain how to make sense of the coefficients.
Is there anyone who can help with that or suggest a decent and easy to read literature on the topic?
Hi Plamen,
I have attached two links to videos which will help you.
I am unsure what data is contained within ind_var or it's unit, so I will simply refer to your dependent variable as Y.
First, your constant will tell you the estimated value of Y when devstage==1 and moth_work==1; notice that STATA has dropped these two, therefore they are absorbed into the constant. This value may be significant or insignificant. Every estimated coefficient is positive or negative shifts to the constant as one of the categories change.
Always remember that the base is moth_work==1 and devstage==1. To calculate the estimated Y value, simply add the constant and the estimated coefficient in question.
The top four coefficients in your results estimate the main effect, in isolation.
Addressing devstage, held in isolation:
devstage==2, estimated Y significantly decreases by -7.187
devstage==3, estimated Y significant decreases by -19.319
Conclusion, as devstage increases, the estimated value of Y decreases.
Addressing moth_work, in isolation:
moth_work==0, estimated Y significantly increases by 4.386,
moth_work==2, estimated Y is not significantly different to the constant; i.e. Y does not change if moth_work==2.
Conclusion: estimated value of Y only increases if moth_work==0. There is no difference in estimated Y whether moth_work==1 (the base) or moth_work==2.
Addressing your interactions:
What would be the estimated value of Y if moth_work==2 AND devstage==0, simultaneously?
Your estimated Y would significantly decrease by -3.533. Notice that in your estimated coefficients devstage==1 significantly decreases the value of Y while moth_work==0 significant increases the value of Y; the net effect is a decrease in Y.
Also, if moth_work==2 and devstage==2 there is an insignificant effect; similarly, if moth_work==3 and devstage==2 the effect is also insignificant.
Clearly, whatever data is contained within moth_work==2 does not significantly affect Y compared to the base (moth_work==1). Therefore, there is little difference between moth_work==1 and moth_work==2.
My interpretation of your results is that moth_work==1 and moth_work==2 may actually be part of the same group (i.e. mothers working X or more hours per week). You should investigate this further, try some multicollinearity tests such as VIFs and correlation matrices.
Also, you do have all 9 estimated coefficients. Your constant denotes the base, 4 interactions, 2 for moth_work and 2 for devstage; 9 in total.
I have attached a photo to demonstrate.
Hope this helps.
VIDEOS:
Specifying interaction:
http://www.youtube.com/watch?v=f-tLLX8v11c
Interpreting interactions:
http://www.youtube.com/watch?v=ScKL40dp8M4
The results look correct.
If you have two 3 category main effect variables (A,B) they are each parametrized in the design matrix as two columns.
Example Eye colour: Blue/Green/Other.
Now Using Green as the references subclass.
X1a X2a
Blue 1 0
Other 0 1
Green 0 0
And similarly for the variable b - whatever your categories are yielding X1b and X2b,
Now the main effects model contains regressors
Xo X1a X2a X1b X2b where Xo in the intercept term
and the interaction model contains
Xo X1a X2a X1b X2b + 4 interaction terms
found by multiplying the main effect columns in pairs eg .X1a* X1b is the first one.
So the structure given by Stat looks correct.
The detailed interpretation depends on the nature of Y ie are we dealing with a linear model, a logistic model of something else.
When you explain I can send the interpretation.
Two really great answers - thank you so much!
Dear Gilbert MacKenzie, my dependent variable is metric so yes, it is a linear model.
To follow up on the hugely terrific Daniel's explanation: one of the links he provided leads to Stata Corp video on factor variables. You can follow them up to https://www.youtube.com/watch?v=XAG4CbIbH0k&list=PLN5IskQdgXWl5MoRJi0aypXL4nXyl2hFW on margins and marginsplots: visualizing your results that way may be the easiest way to see what the interactions really are, term by term. See also the book devoted specifically to interpreting regression results that involve interactions: http://www.michaelnormanmitchell.com/stow/.
Thank you for your suggestion, Stanislav Kolenikov! Actually, I would be interested to see the results graphically somehow. The thing is that I have longitudinal data. I am not sure if that matters?
Plamen, -margins- work after -xtreg-, so I don't see any reason not to try.
"Addressing devstage, held in isolation:
devstage==2, estimated Y significantly decreases by -7.187
devstage==3, estimated Y significant decreases by -19.319
Conclusion, as devstage increases, the estimated value of Y decreases"
The main effect of devstage in this case is more complex, because is the value when moth_work==1.
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