Dummy variables and their interactions with Continuous variables

[Michael Bond]

Dear All,

Although, I created a thread before but I have urgent and focus question to ask.

I have a question concerning the dummy and dummy interactions. Performance is a continuous variable (variable of interest) and while Plan 1, Plan 2 and Plan 3 are dummy plans (reference category, zero plans). While, interaction terms are Plan 1*Performance, Plan 2*Performance, and Plan 3*Performance

  
Log of expense (Dependent Vairabe)
Model 1
Model 2
Model 3

PERFORMANCE
0.1231***
0.123
0.105**

Plan 1 (Dummy)
0.923**
0.837**
0.637**

Plan 2 (Dummy)
1.388***
1.032**
0.932**

Plan 3 (Dummy)
2.622**
2.905***
2.123***

Plan 1*Performance

0.11**
0.11**

PLan 2*Performance

0.228*
0.198*

Plan 3* Performance

0.232**
0.201**

Control Variables
2
2
6

For Model 1

Stata Code:
regress c Performance plan1 plan2 plan3 Performance firmsize

For Model 2
Stata Code:
 regress c Performance plan1 plan2 plan3 i.plan1#c.Performance i.plan2#c.Performance i.plan3#c.Performance Performance firmsize

For Model 3
Stata Code:
regress c Performance plan1 plan2 plan3 i.plan1#c.Performance i.plan2#c.Performance i.plan3#c.Performance Performance firmsize

I am very interested in analyzing the effect of performance on expense. How do we interpret the coefficient of plan 1, plan 2 in model 2.As no of plan increases, the expense also increases, can we claim that and how do interpret the coefficients in Model 2. In Model 2, can we say that firm which grant Plan 1 gives 83.7% increase in expense


Aso for interaction term, for a 10% increase (or percentage point increase ) in performance leads to 1.1% increase in expense in plan 1. Please help me with interpretation!


Michael

[Carlo Lazzaro]

Michael:
the recommendations addressed to the former -Andy Macrobarty- still hold: https://www.statalist.org/forums/forum/general-stata-discussion/general/1411603-interpreting-dummy-and-dummy-interactions.
That is:
- please post what Stata gave you back, too;
- please note that you could write your code more efficiently (let's take Model 2: I assume that -c- is the logged dependent variable):

regress c  i.plan1##c.Performance i.plan2##c.Performance i.plan3##c.Performance  firmsize

As far as your questions are concerned:

- in Model 2, can we say that firm which grant Plan 1 gives 83.7% increase in expense if it has -Performance=0- (it' up to you to consider whether this value is reasonable);
- interactions: I'm not clear with the way -plan1- is expressed. Hence, I cannot be more helpful in this respect.

[Nick Cox]

Michael/Andy/Adrian (*):

You are evidently focusing on the dissertation that you told us was due in yesterday. (On 28 September you posted that it was due in "tomorrow".)

But while you are posting to Statalist we ask that you follow posted guidance on using the list, which has been brought to your attention in previous posts.

https://www.statalist.org/forums/help

https://www.statalist.org/forums/help#adviceextras

1. It is evident that you are also posting as andy macrobarty. So, at least one of these names is not your real name. Statalist FAQ asks that you use your full real name. Using a fake name so obviously and indeed using two identities is a betrayal of trust.

2. Your question was posted on CV at https://stats.stackexchange.com/ques...r-interactions Our policy on cross-posting is explicit: we ask that you tell us about it.

3. You have now more than once emphasised the urgency of your project. This I imagine we do not doubt, modulo an error bar on when your dissertation is really due, but there is explicit guidance that stress on urgency should be avoided. There is no queue to be jumped because you are nearing your deadline, which in my experience is almost always the poster's own responsibility (and that applies to us all, regardless of status or age).

4. Perhaps most of all, it seems that you are repeating questions again and again. You are in something a mess and that deserves concern, but the same questions can only elicit the same answers.

(*) Michael Bond's first post here was signed "Adrian".

[Michael Bond]

Unlike others, Carlo, you are a real star But do we need to take an exponential of coefficient or 10% percentage increase will lead to expense also works. It's just that I am not finding any book which talks about dummy variables and continuous variable with a log dependent variable. So I can follow, and I have extended my deadline for few days.

[Michael Bond]

If I do not understand something, I need to ask this question somewhere else. Is it mater of concern?

[Nick Cox]

The links given in #3 already explain. It's a matter of concern if you don't tell us -- insofar as people here could waste time if there's a better answer already posted somewhere else.

As you've been asking the same question repeatedly, and it has been answered repeatedly here, I doubt that you will get better answers on Cross Validated. I take no pleasure in that doubt. Sorry, but I don't have anything to add to what others have already explained very competently and lucidly.

[Michael Bond]

I just posted this yesterday, how come this becomes a concern. But, every person has its own way of interpreting things. I want to understand things simple as that. Journal papers tells me something but i got different answer here

[Michael Bond]

Simple 2 questions, In Model 1, when log is the dependent variable. can we say 10% increase in TSR lead to 1.2% increase in expense. However, in model 2, for plan, can we say 10 increase in TSR leads to (.837+.11) increase in expense. that's it. or do we necessarily have to take exponential values?

[Carlo Lazzaro]

Michael:
I'm not clear whether you're actually using Stata or a spreadsheet, as you're seemingly shying away from posting what Stata gave you back.
I'm symphatetic with pressure related to incoming deadline, but I fail to get why you're mixing up your previous posts in umpteen new ones: for instance, where did you mention -TSR- in this thread?
That said, you've received diferent helpful threads both on this forum and outside.
I suspect that you problems stem from a confusion between the effect of predictor on the (logged) dependent variable and the linear predictor in log-linear regression model.s
I will try to address this issue via a toy-example:

use "C:\Program Files (x86)\Stata14\ado\base\a\auto.dta", clear
g ln_price=ln(price)
. reg ln_price i.foreign##c.turn, allbasel

      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(3, 70)        =      8.57
       Model |  3.01535964         3  1.00511988   Prob > F        =    0.0001
    Residual |  8.20817344        70  .117259621   R-squared       =    0.2687
-------------+----------------------------------   Adj R-squared   =    0.2373
       Total |  11.2235331        73  .153747029   Root MSE        =    .34243

--------------------------------------------------------------------------------
      ln_price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
---------------+----------------------------------------------------------------
       foreign |
     Domestic  |          0  (base)
      Foreign  |  -3.257694   1.834529    -1.78   0.080    -6.916548    .4011588
               |
          turn |   .0481288   .0120855     3.98   0.000     .0240251    .0722325
               |
foreign#c.turn |
     Domestic  |          0  (base)
      Foreign  |   .1022963   .0512266     2.00   0.050      .000128    .2044646
               |
         _cons |   6.624018   .5030956    13.17   0.000     5.620626    7.627411
--------------------------------------------------------------------------------

*If foreign=1 and turn=0, when adjusted for the remaining predictors being foreign=1 reduce the car price of about 96.15%:*
. di exp(-3.257694)-1
-.96152298

*However, as Clyde stated in one of his previous reply to your queries, you should go through algebra and contrast your results with those obtained via -predict-:*
. predict predict, xb

. bysort foreign: list ln_price foreign turn predict if _n==1

-------------------------------------------------------------------------------------------------------------------------
-> foreign = Domestic

     +--------------------------------------+
     | ln_price    foreign   turn   predict |
     |--------------------------------------|
  1. | 8.318499   Domestic     40   8.54917 |
     +--------------------------------------+

-------------------------------------------------------------------------------------------------------------------------
-> foreign = Foreign

     +--------------------------------------+
     | ln_price   foreign   turn    predict |
     |--------------------------------------|
  1. |  9.17885   Foreign     37   8.932052 |
     +--------------------------------------+
 
*For the domestic car, the predicted value of -ln_price- is:*
. di 6.624018 + (0)+(.0481288* 40)
8.54917

*For the foreing car, the predicted value of -ln_price- is:*
. di 6.624018 + (1* -3.257694)+((.0481288+.1022963)* 37)
8.9320527

[Michael Bond]

Thanks a lot Carlo. You have been very nice and I think I won't ask for more.

[Michael Bond]

My worry is that I have two-three dummy plans and two three interaction. I meant TSR by saying performance

[Carlo Lazzaro]

Michael:
the same logic applies.