Margins interaction variables Beta regression

[Jesse Boskamp]

Dear Statalisters,

I am running a regression with proportions as dependent variable. In the beta regression I run interactions between independent variables. The interactions work perfectly in the regression but when trying to find the margins, Stata does not deliver the margin values.

Some background:
I am interested to see if the probability of a partner business deal (Dealprob) increase when the CEO has the same nationality as the partner (CEOhomebias). For further insights I use Multinationality as interacting continuous variable, which measures foreign sales/total sales.

I am using the following regression model:

betareg Dealprob CEOhomebias Multinationality CEOhomebias#c.Multinationality

Hereafter I use the following commands to find marginal effects:

 margins CEOhomebias#c.Multinationality
only factor variables and their interactions are allowed r(198);

 margins CEOhomebias#Multinationality Multinationality 
factor variables may not contain noninteger values r(452)

 margins, dydx(CEOhomebias#c.Multinationality)
invalid dydx() option; levels of interactions not allowed r(198);

 margins, dydx(i.CEOhomebias#c.Multinationality)
i:  operator invalid

 margins, dyex(CEOhomebias#c.Multinationality)
invalid dyex() option; levels of interactions not allowed

I hope you guys can help me out, thank you in advance!

[Ken Chui]

Hello,

Spend about 15-20 minutes to work through the examples featured under -help margins-. To break it down, the errors shown above fell into two types:

1. Lacking familiarity with the syntax structure of -margins-. In margins, only factor variable(s) are supplied after the margins command. If there are continuous variables, a set of user-specific values need to be supplied to confine the number of estimates returned to you, as there are practically infinite of them.
2. Try to visualize what this interaction does, it allows Dealprob and Multinationality to have different regression lines for each level in CEOhombias. So, when -dydx- is used without specifying which line, nothing returned.

Both of which can be readily clarified if you work through all those margins commands in the help manual.

[John Mullahy]

I would use the factor-variable notation in your –betareg– command itself and then continue with that same factor-variable notation into your –margins– command. For example, this code

sysuse auto
reg price i.foreign c.mpg
margins, dydx(i.foreign c.mpg)
reg price foreign mpg
margins, dydx(i.foreign c.mpg)

gives this result

. reg price i.foreign c.mpg

      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(2, 71)        =     14.07
       Model |   180261702         2  90130850.8   Prob > F        =    0.0000
    Residual |   454803695        71  6405685.84   R-squared       =    0.2838
-------------+----------------------------------   Adj R-squared   =    0.2637
       Total |   635065396        73  8699525.97   Root MSE        =    2530.9

------------------------------------------------------------------------------
       price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
     foreign |
    Foreign  |   1767.292    700.158     2.52   0.014     371.2169    3163.368
         mpg |  -294.1955   55.69172    -5.28   0.000    -405.2417   -183.1494
       _cons |   11905.42   1158.634    10.28   0.000     9595.164    14215.67
------------------------------------------------------------------------------

. margins, dydx(i.foreign c.mpg)

Average marginal effects                        Number of obs     =         74
Model VCE    : OLS

Expression   : Linear prediction, predict()
dy/dx w.r.t. : 1.foreign mpg

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
     foreign |
    Foreign  |   1767.292    700.158     2.52   0.014     371.2169    3163.368
         mpg |  -294.1955   55.69172    -5.28   0.000    -405.2417   -183.1494
------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.

. reg price foreign mpg

      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(2, 71)        =     14.07
       Model |   180261702         2  90130850.8   Prob > F        =    0.0000
    Residual |   454803695        71  6405685.84   R-squared       =    0.2838
-------------+----------------------------------   Adj R-squared   =    0.2637
       Total |   635065396        73  8699525.97   Root MSE        =    2530.9

------------------------------------------------------------------------------
       price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
     foreign |   1767.292    700.158     2.52   0.014     371.2169    3163.368
         mpg |  -294.1955   55.69172    -5.28   0.000    -405.2417   -183.1494
       _cons |   11905.42   1158.634    10.28   0.000     9595.164    14215.67
------------------------------------------------------------------------------

. margins, dydx(i.foreign c.mpg)
i:  operator invalid
r(198);

end of do-file

r(198);

[Jesse Boskamp]

Thank you very much guys! This helps a lot!