Interpreting continuous interaction term

[Liam Jansen]

Hi all,

I have a question regarding the interpretation of an interaction term in the following model:

  Y=β0+β1X+β2Z+β3XZ

X and Z are continuous and X is negatively related to Y, whereas Z is positively related to Y.
Is it true that a negative coefficient in front of the interaction term suggest that the relationship between X and Y becomes less negative as the value of Z increases? And a positive interaction suggests that the relationship between X and Y becomes more negative as the value of Z increases?
Thank you very much

[Ariel Karlinsky]

For any given value of Z, a 1 unit increase in X increases/decreases Y by beta_1 + beta_3 * Z .

[Ariel Karlinsky]

margins & marginsplot give you great tools to see how changes in covariates affect the dependent variable at various combinations. This can probably help:
http://www.stata.com/meeting/uk12/ab...k12_rising.pdf

[Liam Jansen]

Thank you very much Ariel.

Yeah I'm aware of using the margins command, however I can't make use of it.
As I'm running Fama-Macbeth regressions (which is a user written program) and this doesn't allow me to include an interaction term...

[Marcos Almeida]

I don't have any experience with Fama-Macbeth regressions but, considering it doesn't provide - margins -commands, maybe a visual presentation could be helpful to the interpretation of continuous variable by continous variable interaction.

You may have Yar as the predicted ("fitted") values. For the x-axis you may choose either Z or X, depending on what you wish to underline. If you have discrete values, that's already set, If not, you may change them into discrete (or group intervals)

Then, you may have a view of the phenomenon. When the interaction term is positive, we are bound to see lines whose slopes "open" on a par with the increase in the x-axis' values. When we have a negative interaction term, these slopes are bound to "close" on a par with the increase in the x-axis's values.

Hopefully it helps!

Best,

Marcos

[Carlo Lazzaro]

Liam:
have you considered using the old-fashioned -xi- prefix as a way to include interaction among predictors of Fama-Macbeth regression?

[Liam Jansen]

@ Marco, thank you. I'll try to visualize it.

@ Carlo, thank you for your reply and yes I've tried the following command

  xi: xtfmb Weight Age c.Weight##c.Age

however it says interactions not allowed, so I multiplied weight*age and included it in the regression but than I can't visualize/interpret it easily.

[Rich Goldstein]

I am not familiar with Fama-Macbeth, but I have used "twoway function" to graph regression results not amenable to "margins" in the past - have you tried looking into that?

[Liam Jansen]

Thank you Rich,

However it says Weigh is not a twoway plot type

[Dick Campbell]

You need to show the code you ran when you got a message that told you that Weigh is not a twoway plot type.

[Rich Goldstein]

showing your code, as Dick points out, is necessary for a complete diagnosis of what you did wrong; however, my guess is that you used one of your variable names in the command and you should not be doing that - please read the help file (h twoway function)

[Phil Bromiley]

Liam probably should to read a bit about interactions along with the programming issues. I have found Robert Friedrich, In Defense of Multiplicative Terms in Multiple Regression Equations, American Journal of Political Science, 1982 sometimes helpful.

Phil