How to graph and interpret the interaction between 2 continuous variables in poisson model with a countinous dependent variable?

[David Lu]

Hi all,

I am running a poisson model using poisson looking at the effect of 2 continuous variables and the interaction between these on a continuous outcome variable (such as income,sales).
My code is as follows:

poisson depvar c_var1 c_var1(square term) c_var2 c_var2(square term) c_var1_c_var2, vce(robust)

The interaction effect is significant (β=-.000041, SE=.0000214, p=0.055) so in order to understand what direction the effect is in I want to picture the interaction.

which code should I use in this case? Also, what does the scale on the y-axis refer to?

Before posting, I've read the previous posts below, but they are a bit far from the case i am facing
http://www.statalist.org/forums/foru...ts-panel-model
http://www.ats.ucla.edu/stat/stata/dae/poissonreg.htm
http://www.stata.com/statalist/archi.../msg01198.html

Many thanks for any help,
David

[Carlo Lazzaro]

David:
-please post what you typed and what Stata gave you back via CODE delimiters (as per FAQ). It 's easy to do (and makes threads easy to read and to reply to): read FAQ #12 on this topic. Thanks.
. more in general: for interactions and squared terms, it's better to rely on -fvvarlist- capabilities, especially for the valuable relationships that -fvvarlist- has with some important Stata postestimation commands (e.g.: -margins-; -marginsplot-).

[David Lu]

David:
-please post what you typed and what Stata gave you back via CODE delimiters (as per FAQ). It 's easy to do (and makes threads easy to read and to reply to): read FAQ #12 on this topic. Thanks.
. more in general: for interactions and squared terms, it's better to rely on -fvvarlist- capabilities, especially for the valuable relationships that -fvvarlist- has with some important Stata postestimation commands (e.g.: -margins-; -marginsplot-).

Hi Carlo,

Thanks for your advice. I've read FAQ#12.

poisson depvar c_var1 c_var1square c_var2 c_var2square c_var1_c_var2, vce(robust)

Stata gave me the results, no error encounting. What I want to know is how to graph and interpret the interaction between 2 continuous variables in poisson model with a countinous dependent variable? Since they're not catergorial variables, and also the dependent variable is not a count variable typical for poisson regression. So, i am not sure if it is still ok to graph it and interpret it in the same way as that for catergorial variable. Any relevant example on graphing and interpretation of these cases would be helpful.

Thx in advance,
David

[Carlo Lazzaro]

David:
thanks for the effort, but the same issue apply to what Stata gave you back; otherwise, there's too little to comment upon.
You can copy the output of your poisson regression and paste it in between CODE delimiters, just like you did for Stata code. Thanks.

[David Lu]

David:
thanks for the effort, but the same issue apply to what Stata gave you back; otherwise, there's too little to comment upon.
You can copy the output of your poisson regression and paste it in between CODE delimiters, just like you did for Stata code. Thanks.

Hi Carlo,

I copy the output of my poisson regression and paste it in between CODE delimiters

 
poisson yus crco cr co sqco lna lnemp
lnenv ca i.indcode i.areacode ,vce(robust)

Iteration 0: log pseudolikelihood =
-1.288e+11

Iteration 1: log pseudolikelihood =
-9.349e+10 (backed up)

Iteration 2: log pseudolikelihood =
-3.457e+10 (backed up)

Iteration 3: log pseudolikelihood =
-2.309e+10

Iteration 4: log pseudolikelihood =
-9.985e+09

Iteration 5: log pseudolikelihood =
-7.780e+09

Iteration 6: log pseudolikelihood =
-7.577e+09

Iteration 7: log pseudolikelihood =
-7.564e+09

Iteration 8: log pseudolikelihood =
-7.564e+09

Iteration 9: log pseudolikelihood =
-7.564e+09

Poisson regression
Number of obs = 267

Wald chi2(33) = .

Prob > chi2 = .

Log pseudolikelihood = -7.564e+09
Pseudo R2 = 0.8102



Robust

yus Coef. Std. Err.
z P>z [95% Conf. Interval]



crco -.000018 .0000101
-1.79 0.074 -.0000378 1.76e-06

cr .000033 6.96e-06
4.74 0.000 .0000193 .0000466

co -2.934839 1.341334
-2.19 0.029 -5.563805 -.3058731

sqco 2.875029 1.719234
1.67 0.094 -.4946069 6.244665

lna .6264417 .244957
2.56 0.011 .1463348 1.106549

lnemp 1.450958 .1173224
12.37 0.000 1.22101 1.680905

lnenv 4.069176 4.939343
0.82 0.410 -5.611758 13.75011

ca .8251975 .556747
1.48 0.138 -.2660066 1.916402



indcode

14 -.0793765 .5011181
-0.16 0.874 -1.06155 .9027969

15 -.4016717 .6432274
-0.62 0.532 -1.662374 .8590309

17 -3.492987 .5866811
-5.95 0.000 -4.642861 -2.343114

18 -3.177437 .6597376
-4.82 0.000 -4.470499 -1.884375

19 -2.439427 .5643795
-4.32 0.000 -3.54559 -1.333263

20 -3.239832 .5690849
-5.69 0.000 -4.355218 -2.124446

21 -1.262463 .5230638
-2.41 0.016 -2.287649 -.2372772

22 -2.314654 .5099875
-4.54 0.000 -3.314211 -1.315097

23 -4.660993 .5027886
-9.27 0.000 -5.646441 -3.675546

24 -1.454168 .5667438
-2.57 0.010 -2.564965 -.3433706

25 -1.322538 1.153481
-1.15 0.252 -3.583319 .9382435

26 -.1996439 .5176629
-0.39 0.700 -1.214245 .8149567

27 -2.114506 .8622672
-2.45 0.014 -3.804518 -.4244931

28 -2.323168 .6243446
-3.72 0.000 -3.546861 -1.099475

29 -1.748035 .6420591
-2.72 0.006 -3.006447 -.4896219

30 -1.747706 .6440939
-2.71 0.007 -3.010107 -.4853056

32 -2.474927 .7158799
-3.46 0.001 -3.878026 -1.071829

33 -1.738281 .708673
-2.45 0.014 -3.127255 -.3493075

34 -.5889574 .6293833
-0.94 0.349 -1.822526 .6446112

35 .796434 .5091535
1.56 0.118 -.2014885 1.794356

36 -2.070739 .6046242
-3.42 0.001 -3.25578 -.8856969

37 -4.219452 .5485687
-7.69 0.000 -5.294627 -3.144278

38 -.7643772 .5256057
-1.45 0.146 -1.794546 .2657911

39 -2.695696 .6022238
-4.48 0.000 -3.876033 -1.515359

40 -.7558563 .6634599
-1.14 0.255 -2.056214 .5445012

41 -2.917633 .5558032
-5.25 0.000 -4.006987 -1.828279



areacode

2 .7348222 .3819149
1.92 0.054 -.0137172 1.483362

3 -.1834387 .7052367
-0.26 0.795 -1.565677 1.1988

4 .7522449 .7714681
0.98 0.330 -.7598047 2.264295

5 .4795861 .4573231
1.05 0.294 -.4167507 1.375923

6 1.194868 .5141567
2.32 0.020 .1871399 2.202597

7 1.792535 .5958973
3.01 0.003 .6245981 2.960473



_cons .3935997 5.78161
0.07 0.946 -10.93815 11.72535



.

Thx,
David

[Carlo Lazzaro]

David:
which are the interacted variables in your code?

[David Lu]

David:
which are the interacted variables in your code?

Hi Carlo,

It's crco, the interacted variables.

David

[Carlo Lazzaro]

David:
the way you create interactions betweem -cr- and -co- leads you astray.
Please consider re-creating each interaction via -fvvarlist-.

[David Lu]

David:
the way you create interactions betweem -cr- and -co- leads you astray.
Please consider re-creating each interaction via -fvvarlist-.

Hi Carlo,
I read the manual of stata about -fvvarlist-, and it's for factor variable, is it still proper to generate interaction between two continuous variables via -fvvarlist- ? Also, could you explain more why it improper to create interactions between -cr and -co- ?

David

[Carlo Lazzaro]

David:
-please see

c. unary operator to treat as continuous

in -help fvvarlist-;
- -fvvarlist- will give you the conditional main effect of the predictors included in the interactions and, even more important, has a preference link with very useful post-restimation commnands, such as -margins- and -marginsplot-.

[wbuchanan]

If you have access to the data sets used for Michael N Mitchell's book Interpretting and Visualizing Regression models using Stata you'll be able to replicate the example below:

use gss_ivrm
poisson children c.educ##(c.educ c.realrinc) c.realrinc#c.realrinc, vce(robust)
margins, at(educ=(0(5)20) realrinc=(259(100000)480144.5))
marginsplot

So in addition to Carlo Lazzaro's initial suggestion, you can see that it also makes your code more concise and will use less memory (since you won't be creating additional copies of the data already in memory to generate new variables for the interactions).

[David Lu]

If you have access to the data sets used for Michael N Mitchell's book Interpretting and Visualizing Regression models using Stata you'll be able to replicate the example below:

use gss_ivrm
poisson children c.educ##(c.educ c.realrinc) c.realrinc#c.realrinc, vce(robust)
margins, at(educ=(0(5)20) realrinc=(259(100000)480144.5))
marginsplot

So in addition to Carlo Lazzaro's initial suggestion, you can see that it also makes your code more concise and will use less memory (since you won't be creating additional copies of the data already in memory to generate new variables for the interactions).

Hi wbuchanan,

Thx for the great example and clarification. I applied this code to my data and got the graph now. But as can be seen from the graph, it's almost flat for most of the data. Also,since my dependent variable is a continuos variable like income (not the number of events), how to interpret this graph especially, what is the exact meaning of Y axis here? Is there any method I can apply to make the curve here not so plain?

Thx in advance,
David

poisson income iv1 iv2 c.iv1#c.iv2 c.iv2#c.iv2 cv1 cv2 cv3 cv4 i.indcode i.areacode, vce(robust)
margins, at(iv1=(0(20000)180000) iv2=(0(0.2)1))
marginsplot

[David Lu]

David:
-please see in -help fvvarlist-;
- -fvvarlist- will give you the conditional main effect of the predictors included in the interactions and, even more important, has a preference link with very useful post-restimation commnands, such as -margins- and -marginsplot-.

Hi Carlo,

Thx for your further explanation.

David