manually created interaction term versus ## command

[Katharina]

I would like to include an interaction term with two continuous variables in an OLS model, I originally computed the interactiont term by hand, i.e. gen new_ variable = variable_A * variable_B and included both variables and the interaction term in the model. Next, I created the same model but using c.variable_A##c.variable_B. I expected the coefficients to be the same but they differ dramatically. I use Stata 13. Why are the coefficients not identical?

[daniel klein]

Are you including the lower order terms (i.e. 'variable_A' and 'variable_B') in addition to 'new_ variable' in your first ('by hand') model? This is what factor variable operator ## does, and what you should do.


If this is not the reason for the differences, show us the exact commands you typed.

Best
Daniel

[Carlo Lazzaro]

Katharina should follow Daniel's advice, as proved by:

sysuse auto.dta
g Int= trunk* weight
reg price trunk weight Int
reg price trunk weight c.trunk#c.weight

I hope this helps.

Kind regards,
Carlo

[Sugandha Huria]

Hi,
Sorry to ask thus question, but could you please clarify the difference between the last two stata commands that you wrote?
reg price trunk weight Int reg price trunk weight c.trunk#c.weight Thank You

[Carlo Lazzaro]

Sugandha:
actually, there's no substantive difference, as you can see from the following toy-example (I also add a third code to express the same regression model):

. sysuse auto.dta
(1978 Automobile Data)

. g Int= trunk* weight

.
. reg price trunk weight Int

      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(3, 70)        =     10.01
       Model |   190636755         3  63545585.1   Prob > F        =    0.0000
    Residual |   444428641        70  6348980.58   R-squared       =    0.3002
-------------+----------------------------------   Adj R-squared   =    0.2702
       Total |   635065396        73  8699525.97   Root MSE        =    2519.7

------------------------------------------------------------------------------
       price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       trunk |  -287.6778   309.9737    -0.93   0.357    -905.9009    330.5452
      weight |   1.172154   1.510518     0.78   0.440    -1.840479    4.184786
         Int |   .0754153   .0979483     0.77   0.444    -.1199365     .270767
       _cons |   3284.654   4248.161     0.77   0.442    -5188.037    11757.34
------------------------------------------------------------------------------

.
. reg price trunk weight c.trunk#c.weight

      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(3, 70)        =     10.01
       Model |   190636755         3  63545585.1   Prob > F        =    0.0000
    Residual |   444428641        70  6348980.58   R-squared       =    0.3002
-------------+----------------------------------   Adj R-squared   =    0.2702
       Total |   635065396        73  8699525.97   Root MSE        =    2519.7

----------------------------------------------------------------------------------
           price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-----------------+----------------------------------------------------------------
           trunk |  -287.6778   309.9737    -0.93   0.357    -905.9009    330.5452
          weight |   1.172154   1.510518     0.78   0.440    -1.840479    4.184786
                 |
c.trunk#c.weight |   .0754153   .0979483     0.77   0.444    -.1199365     .270767
                 |
           _cons |   3284.654   4248.161     0.77   0.442    -5188.037    11757.34
----------------------------------------------------------------------------------

. reg price  c.trunk##c.weight

      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(3, 70)        =     10.01
       Model |   190636755         3  63545585.1   Prob > F        =    0.0000
    Residual |   444428641        70  6348980.58   R-squared       =    0.3002
-------------+----------------------------------   Adj R-squared   =    0.2702
       Total |   635065396        73  8699525.97   Root MSE        =    2519.7

----------------------------------------------------------------------------------
           price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-----------------+----------------------------------------------------------------
           trunk |  -287.6778   309.9737    -0.93   0.357    -905.9009    330.5452
          weight |   1.172154   1.510518     0.78   0.440    -1.840479    4.184786
                 |
c.trunk#c.weight |   .0754153   .0979483     0.77   0.444    -.1199365     .270767
                 |
           _cons |   3284.654   4248.161     0.77   0.442    -5188.037    11757.34
----------------------------------------------------------------------------------

.

However these coded behaves differently in terms of efficiency: the second one allows a relationship with -margins- and -marginsplot- (whereas the first one does not). The third code does the same job of the second one, but with a morer parsimonious code.

[Sugandha Huria]

Ok, thank you so much for your reply. I shall keep the differences in mind.
Thanks a lot.

[Farrukh Shahzad]

Dear Sir Carlo Lazzaro, while doing this command on my data its showing this error
. g int=intro* CFO_sd
too few variables specified
Would you please guide me why its not working?

[Nick Cox]

int is a reserved word indicating a storage type for variables. Choose a different name. See [U] 11.3 on your set-up or at https://www.stata.com/manuals/u11.pdf

[Carlo Lazzaro]

...or impose un upper-case starting i (that is -Int- vs -int-).

[Nick Cox]

Int would be a different name, so that's not a different suggestion. My advice, however, is to avoid reserved words or words close to them completely. All of us are in situations where we need to understand our own code later and many of us are in situations where other people need to understand our code. Minor tricks, dodges or fudges don't help either goal. Whatever your code, I would write in a comment like

* Note that -int- is a reserved word: See {U] 11.3

as a reminder to whoever reads the code, including yourself.

[Carlo Lazzaro]

Nick is obviously correct.
My previous reply was not intended as a different suggestion.
I should have been more detailed in adding that -Int- was the name of the variable I created in the toy-example reported in #5: that's why I mentioned it.
Admittedly, I've forgotten that -int- is a reserved word that Stata uses for storage type and I've just refreshed my memory by taking a look at -help data_types-: thanks to Nick for his precious reminder.