Hi Statalist,
I noticed the following issue using a simple fixed effect regression and am wondering what the rationale is for this decision by STATA.
I have a set of 30 observations of y across 7 values of categorical x. Within each value of x, the means of y are given here:
I do the simple fe regression and the coefficients give the deviations of means of y for x= 2-7 from mean of y when x=1, and the mean of y for x=1 in the constant:
It would be neater for my purposes if the means of each bin was the coefficient, so I want to suppress the constant:
I now have the means of y for bins of x=2-7, but the fixed effect for x=1 is still suppressed. My question: Why is STATA suppressing this fixed effect when the constant term has been dropped? The final fixed effect would no longer cause collinearity issues without the constant term, so I don't see why it should be dropped. For comparison, I can do the regression manually like this, including all the fixed effects, and it works fine.
If it is of interest, the reason I want the coefficients organized this way is in order to take residuals that are equal to deviations from within-x means as follows:
Thanks,
Julian
I noticed the following issue using a simple fixed effect regression and am wondering what the rationale is for this decision by STATA.
I have a set of 30 observations of y across 7 values of categorical x. Within each value of x, the means of y are given here:
Code:
tabstat y, by(x) stat(mean)
Summary for variables: y
by categories of: x
x | mean
---------+----------
1 | 1521.594
2 | 2434.029
3 | 1824.588
4 | 2239.116
5 | 2109.643
6 | 2234.62
7 | 1997.953
---------+----------
Total | 2083.711
--------------------
Code:
. reg y i.x
Source | SS df MS Number of obs = 30
-------------+---------------------------------- F(6, 23) = 0.49
Model | 2801202.94 6 466867.157 Prob > F = 0.8083
Residual | 21868456.1 23 950802.44 R-squared = 0.1135
-------------+---------------------------------- Adj R-squared = -0.1177
Total | 24669659.1 29 850677.898 Root MSE = 975.09
------------------------------------------------------------------------------
y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
x |
2 | 912.4347 590.4469 1.55 0.136 -308.9978 2133.867
3 | 302.9935 712.1058 0.43 0.674 -1170.11 1776.097
4 | 717.5212 570.9548 1.26 0.221 -463.5888 1898.631
5 | 588.0482 815.8197 0.72 0.478 -1099.603 2275.7
6 | 713.0255 654.1109 1.09 0.287 -640.1061 2066.157
7 | 476.3585 712.1058 0.67 0.510 -996.7445 1949.462
|
_cons | 1521.594 436.0739 3.49 0.002 619.5066 2423.682
------------------------------------------------------------------------------
Code:
. reg y i.x, noconstant
Source | SS df MS Number of obs = 30
-------------+---------------------------------- F(6, 24) = 14.53
Model | 121480550 6 20246758.3 Prob > F = 0.0000
Residual | 33444702.7 24 1393529.28 R-squared = 0.7841
-------------+---------------------------------- Adj R-squared = 0.7302
Total | 154925252 30 5164175.08 Root MSE = 1180.5
------------------------------------------------------------------------------
y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
x |
2 | 2434.029 481.9283 5.05 0.000 1439.378 3428.68
3 | 1824.588 681.5495 2.68 0.013 417.9387 3231.237
4 | 2239.116 446.1789 5.02 0.000 1318.248 3159.984
5 | 2109.643 834.7243 2.53 0.018 386.8563 3832.429
6 | 2234.62 590.2392 3.79 0.001 1016.426 3452.814
7 | 1997.953 681.5495 2.93 0.007 591.3037 3404.602
------------------------------------------------------------------------------
Code:
. tab x, gen(x)
x | Freq. Percent Cum.
------------+-----------------------------------
1 | 5 14.29 14.29
2 | 6 17.14 31.43
3 | 3 8.57 40.00
4 | 9 25.71 65.71
5 | 2 5.71 71.43
6 | 6 17.14 88.57
7 | 4 11.43 100.00
------------+-----------------------------------
Total | 35 100.00
. reg y x?, noconstant
Source | SS df MS Number of obs = 30
-------------+---------------------------------- F(7, 23) = 19.99
Model | 133056796 7 19008113.8 Prob > F = 0.0000
Residual | 21868456.1 23 950802.44 R-squared = 0.8588
-------------+---------------------------------- Adj R-squared = 0.8159
Total | 154925252 30 5164175.08 Root MSE = 975.09
------------------------------------------------------------------------------
y | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
x1 | 1521.594 436.0739 3.49 0.002 619.5066 2423.682
x2 | 2434.029 398.0792 6.11 0.000 1610.539 3257.519
x3 | 1824.588 562.969 3.24 0.004 659.9976 2989.178
x4 | 2239.116 368.5498 6.08 0.000 1476.712 3001.519
x5 | 2109.643 689.4935 3.06 0.006 683.3166 3535.968
x6 | 2234.62 487.5455 4.58 0.000 1226.055 3243.185
x7 | 1997.953 562.969 3.55 0.002 833.3626 3162.543
------------------------------------------------------------------------------
Code:
predict yres, residuals
Julian
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