Omitted because of collinearity

[Dominik Tuider]

Dear forum members,

I am facing an issue and I'm hoping to get your assistance. In my current data analysis, I have a dummy variable that seems to always be omitted in my models.

I have tried various approaches to address this problem. I have made sure that my dummy variable is correctly coded and that there are no missing values. However, the dummy variable is not being included in the regression models and is consistently displayed as "omitted".

I'm not sure what could be the exact cause of this behavior. Could there be collinearity issues with other variables? Or are there other potential reasons for this omitted behavior?

I would greatly appreciate your help and advice. What steps can I take to identify the problem and properly include the dummy variable in my analyses?

Thank you in advance for your support!

Best regards,
Dominik Tuider


reg Sprd_Opt_log Stockvolume_ln StockReturn_log Pre_Ban_Period BAN_Period Post_Ban_Period VIX_Change_log Marketreturn_log
note: Pre_Ban_Period omitted because of collinearity.

Source | SS df MS Number of obs = 25,282
-------------+---------------------------------- F(6, 25275) = 323.43
Model | 1925.50184 6 320.916973 Prob > F = 0.0000
Residual | 25078.5259 25,275 .992226546 R-squared = 0.0713
-------------+---------------------------------- Adj R-squared = 0.0711
Total | 27004.0278 25,281 1.06815505 Root MSE = .99611

----------------------------------------------------------------------------------
Sprd_Opt_log | Coefficient Std. err. t P>|t| [95% conf. interval]
-----------------+----------------------------------------------------------------
Stockvolume_ln | .0824025 .0069687 11.82 0.000 .0687436 .0960615
StockReturn_log | -.0448981 .0061554 -7.29 0.000 -.056963 -.0328332
Pre_Ban_Period | 0 (omitted)
BAN_Period | .2539663 .0204097 12.44 0.000 .213962 .2939705
Post_Ban_Period | -.3762999 .0176403 -21.33 0.000 -.410876 -.3417238
VIX_Change_log | .1249523 .0077915 16.04 0.000 .1096806 .140224
Marketreturn_log | .1850272 .0075623 24.47 0.000 .1702046 .1998498
_cons | -2.316229 .1347388 -17.19 0.000 -2.580325 -2.052133
----------------------------------------------------------------------------------


. dataex Sprd_Opt_log Stockvolume_ln StockReturn_log Pre_Ban_Period BAN_Period Post_Ban_Period VIX_Change_log Marketreturn_log

----------------------- copy starting from the next line -----------------------

* Example generated by -dataex-. For more info, type help dataex
clear
input float(Sprd_Opt_log Stockvolume_ln StockReturn_log Pre_Ban_Period BAN_Period Post_Ban_Period VIX_Change_log Marketreturn_log)
 -2.442347 12.969944 -5.109517 1 0 0          . -3.72991
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 -2.516455 12.969944 -5.109517 1 0 0          . -3.72991
-1.4816043 12.994682 -6.591486 1 0 0 -1.7978293        .
 -2.533268 12.994682 -6.591486 1 0 0 -1.7978293        .
  -1.81529 12.994682 -6.591486 1 0 0 -1.7978293        .
-2.3690746 12.994682 -6.591486 1 0 0 -1.7978293        .
-2.7502825 12.994682 -6.591486 1 0 0 -1.7978293        .
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-2.0877397 12.994682 -6.591486 1 0 0 -1.7978293        .
 -3.324521 12.994682 -6.591486 1 0 0 -1.7978293        .
-2.7051475 12.994682 -6.591486 1 0 0 -1.7978293        .
 -3.189888 12.994682 -6.591486 1 0 0 -1.7978293        .
  -3.89284 12.994682 -6.591486 1 0 0 -1.7978293        .
end

------------------ copy up to and including the previous line ------------------

[Carlo Lazzaro]

Dominik:
welcome to this forum.
The reason is that your dummy values do not change:

. reg Sprd_Opt_log Stockvolume_ln Pre_Ban_Period
note: Pre_Ban_Period omitted because of collinearity.

      Source |       SS           df       MS      Number of obs   =       100
-------------+----------------------------------   F(1, 98)        =      1.33
       Model |  .987696543         1  .987696543   Prob > F        =    0.2516
    Residual |  72.7596727        98   .74244564   R-squared       =    0.0134
-------------+----------------------------------   Adj R-squared   =    0.0033
       Total |  73.7473692        99  .744922922   Root MSE        =    .86165

--------------------------------------------------------------------------------
  Sprd_Opt_log | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
Stockvolume_ln |   8.369518   7.256397     1.15   0.252    -6.030565     22.7696
Pre_Ban_Period |          0  (omitted)
         _cons |  -111.2961   94.17973    -1.18   0.240    -298.1927    75.60053
--------------------------------------------------------------------------------

.

[Ken Chui]

There are three ice-cream flavors: vanilla, chocolate, and coffee. If it's NOT vanilla and NOT coffee, then it has to be chocolate.

Just like in your case, if a time is NOT post ban and NOT during the ban, then it has to be pre ban. Because the existence of any two of these time dummies can perfectly do the job of the third, the third one is not needed.

There is also a better way to model categorical variables, check out help fvvarlist.

[Dominik Tuider]

Hello Ken,

thank you very much for your help. Then where do I find the result in the regression of the pre-ban period? To possibly clarify the background of my regression: I want to determine option data based on before, during and after the Corona crisis and in this respect I have added these 3 dummy variables to analyze the volume and the calculated spread. However, to analyze the 3 phases, I need the results of all 3 phases. I hope I could provide more understanding by this.

Carlo, they do. Unfortunately, there are 25 thousand observations and the dataex only took the ones where the one dummy variable occurred.

At fvvarlist I will have a look!

Thanks in advance!

[Carlo Lazzaro]

Dominik_
you may want to consider the following toy-example (domestic=0; foreign=1):

. sysuse auto.dta
(1978 automobile data)

. regress price i.foreign

      Source |       SS           df       MS      Number of obs   =        74
-------------+----------------------------------   F(1, 72)        =      0.17
       Model |  1507382.66         1  1507382.66   Prob > F        =    0.6802
    Residual |   633558013        72  8799416.85   R-squared       =    0.0024
-------------+----------------------------------   Adj R-squared   =   -0.0115
       Total |   635065396        73  8699525.97   Root MSE        =    2966.4

------------------------------------------------------------------------------
       price | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
     foreign |
    Foreign  |   312.2587   754.4488     0.41   0.680    -1191.708    1816.225
       _cons |   6072.423    411.363    14.76   0.000     5252.386     6892.46
------------------------------------------------------------------------------

. predict fitted, xb

. mat list e(b)

e(b)[1,3]
           0b.         1.           
      foreign    foreign      _cons
y1          0  312.25874  6072.4231


. bysort foreign: list price foreign fitted if _n==1

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

     +-----------------------------+
     | price    foreign     fitted |
     |-----------------------------|
  1. | 4,099   Domestic   6072.423 |
     +-----------------------------+

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

     +----------------------------+
     | price   foreign     fitted |
     |----------------------------|
  1. | 9,690   Foreign   6384.682 |
     +----------------------------+


. di 6072.4231 + (312.25874*0)
6072.4231

. di 6072.4231 + (312.25874*1)
6384.6818

.