How to calculate Point Estimates in a regression

[Shashank Shukla]

Dear All;

Need your kind help. I have a file tea_data.csv (attached for reference). I generated the variable teaDum, which takes value 1 if any amount of tea is sown and 0 otherwise. I further generated the variable post, which takes a value of 1 if the cohort is born on or after 1979. I then generated the interaction term using #, however I am required to provide the point estimate which I am unable to figure.

Kindly help.

Regards

[Carlo Lazzaro]

Shashank:

if your questions refer to an assignement, please see https://www.statalist.org/forums/help#adviceextras #4.
As per your description, the ppoint estimates of your coefficients are those that Stata gives you back in the column named -Coefficient-.
As an aside, please use -dataex- to share examples/excerpts of your dataset. Thanks.

[Shashank Shukla]

Hi Carlo;
Thanks for your comments. The question is part of an assignment where I am unable to figure the difference between coefficient and point estimate. I also assumed the coefficients are the point estimates but apparently they are not as my answers were marked wrong.
Now I am seeking to learn from my mistakes for the future hence asking on this forum as to what is the difference between the two. I came across a command called lincom but could not figure the syntax!
Hope this explains and removes any moral dilemmas
Regards

[Maarten Buis]

The regression coefficient is a point estimate, but there are many other point estimates. So apparently the person teaching your course was looking for a different point estimate. We cannot read her/his mind, so you'll just have to ask her/him.

[Carlo Lazzaro]

Shashank:
I would not talk about moral dilemmas, but rules of the forum (as per FAQ).
I do share Maarten's point that interested listers need more details from your end to see what's the matter with your data.
Eventually, -lincom- is a post rstimation command that supports the linear combination of the regression coefficients.

[Joseph Coveney]

I'm guessing (and for reasons that Maarten and Carlo pointed out above it's just a guess) that you fitted your regression model with the interaction specified as

regress <outcome> i.teaDum##i.post

and provided your instructor with these regression coefficients as the point estimates, while your instructor wanted the point estimates that you'd get from, say,

regress <outcome> 0bn.teaDum#0bn.post 1.teaDum#0.post 0.teaDum#1.post 1.teaDum#1.post, noconstant

which are the same as what you'd get from

version 16.1: table teaDum post, contents(mean <outcome>)

and for that reason a regression model specified like that is also called a cell-means model, and is often fitted with something along the following lines.

egen byte cmm = group(teaDum post), label
regress <outcome> ibn.cmm, noconstant

Either that or you neglected to use double octothorpes to specify the interaction

I then generated the interaction term using #

or used a single octothorpe and neglected to separately include the main effects terms, and so ended up with a completely misspecified model and just the wrong answer.

[Shashank Shukla]

Dear Carlo, Marteen and Joseph;

I would like to extend my gratitude for taking out the time to guide me. I figured that the point estimate meant here was the coefficient itself. The mistake I made was using a single "#" instead of "##".

However, I would like to pose one more question for the sake of my learning. What is the difference between # and ## when it comes to interaction between variables?

Regards

[Carlo Lazzaro]

Shashank:
the difference is that, unlike -##- (which is the way to go most of the times), -#- does not include the conditional main effect of the predictors included in the interaction:

. use "C:\Program Files\Stata17\ado\base\a\auto.dta"
(1978 automobile data)

. regress price i.foreign##i.rep78
note: 1.foreign#1b.rep78 identifies no observations in the sample.
note: 1.foreign#2.rep78 identifies no observations in the sample.
note: 1.foreign#5.rep78 omitted because of collinearity.

      Source |       SS           df       MS      Number of obs   =        69
-------------+----------------------------------   F(7, 61)        =      0.39
       Model |    24684607         7  3526372.43   Prob > F        =    0.9049
    Residual |   552112352        61  9051022.16   R-squared       =    0.0428
-------------+----------------------------------   Adj R-squared   =   -0.0670
       Total |   576796959        68  8482308.22   Root MSE        =    3008.5

-------------------------------------------------------------------------------
        price | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
--------------+----------------------------------------------------------------
      foreign |
     Foreign  |   2088.167   2351.846     0.89   0.378     -2614.64    6790.974
              |
        rep78 |
           2  |   1403.125   2378.422     0.59   0.557    -3352.823    6159.073
           3  |   2042.574   2204.707     0.93   0.358    -2366.011    6451.159
           4  |   1317.056   2351.846     0.56   0.578    -3385.751    6019.863
           5  |       -360   3008.492    -0.12   0.905    -6375.851    5655.851
              |
foreign#rep78 |
   Foreign#1  |          0  (empty)
   Foreign#2  |          0  (empty)
   Foreign#3  |  -3866.574   2980.505    -1.30   0.199    -9826.462    2093.314
   Foreign#4  |  -1708.278   2746.365    -0.62   0.536    -7199.973    3783.418
   Foreign#5  |          0  (omitted)
              |
        _cons |     4564.5   2127.325     2.15   0.036      310.651    8818.349
-------------------------------------------------------------------------------

. regress price i.foreign#i.rep78
note: 1.foreign#1b.rep78 identifies no observations in the sample.
note: 1.foreign#2.rep78 identifies no observations in the sample.

      Source |       SS           df       MS      Number of obs   =        69
-------------+----------------------------------   F(7, 61)        =      0.39
       Model |    24684607         7  3526372.43   Prob > F        =    0.9049
    Residual |   552112352        61  9051022.16   R-squared       =    0.0428
-------------+----------------------------------   Adj R-squared   =   -0.0670
       Total |   576796959        68  8482308.22   Root MSE        =    3008.5

-------------------------------------------------------------------------------
        price | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
--------------+----------------------------------------------------------------
foreign#rep78 |
  Domestic#2  |   1403.125   2378.422     0.59   0.557    -3352.823    6159.073
  Domestic#3  |   2042.574   2204.707     0.93   0.358    -2366.011    6451.159
  Domestic#4  |   1317.056   2351.846     0.56   0.578    -3385.751    6019.863
  Domestic#5  |       -360   3008.492    -0.12   0.905    -6375.851    5655.851
   Foreign#1  |          0  (empty)
   Foreign#2  |          0  (empty)
   Foreign#3  |   264.1667   2746.365     0.10   0.924    -5227.529    5755.862
   Foreign#4  |   1696.944   2351.846     0.72   0.473    -3005.863    6399.751
   Foreign#5  |   1728.167   2351.846     0.73   0.465     -2974.64    6430.974
              |
        _cons |     4564.5   2127.325     2.15   0.036      310.651    8818.349
-------------------------------------------------------------------------------

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