ftest
Author: Maarten L. Buis
ftest compares two nested models estimated using regress and performs an F-test for the null hypothesis that the constraint implicit in the restricted model holds. For example if a variable is left out of the restricted model, the implicit constraint is that the coefficient for that variable equals zero. ftest is a convenience command; anything that can be done with ftest can be done with test, and it will produce exactly the same results. The difference is that with test the constraint needs to be explicitly specified, while with ftest the constraint is implicit. ftest can be convenient when all the models you want to compare are already estimated and stored for use by for example Ben Jann's estout.
This package can be installed by typing into Stata: ssc install ftest
.Supporting materials
Examples
These are the different ways in which you can refer to the different models that you want to compare.
. sysuse auto, clear (1978 Automobile Data)
. reg price mpg foreign
Source | SS df MS Number of obs = 74 -------------+------------------------------ F( 2, 71) = 14.07 Model | 180261702 2 90130850.8 Prob > F = 0.0000 Residual | 454803695 71 6405685.84 R-squared = 0.2838 -------------+------------------------------ Adj R-squared = 0.2637 Total | 635065396 73 8699525.97 Root MSE = 2530.9
------------------------------------------------------------------------------ price | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- mpg | -294.1955 55.69172 -5.28 0.000 -405.2417 -183.1494 foreign | 1767.292 700.158 2.52 0.014 371.2169 3163.368 _cons | 11905.42 1158.634 10.28 0.000 9595.164 14215.67 ------------------------------------------------------------------------------
. est store a
. reg price mpg
Source | SS df MS Number of obs = 74 -------------+------------------------------ F( 1, 72) = 20.26 Model | 139449474 1 139449474 Prob > F = 0.0000 Residual | 495615923 72 6883554.48 R-squared = 0.2196 -------------+------------------------------ Adj R-squared = 0.2087 Total | 635065396 73 8699525.97 Root MSE = 2623.7
------------------------------------------------------------------------------ price | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- mpg | -238.8943 53.07669 -4.50 0.000 -344.7008 -133.0879 _cons | 11253.06 1170.813 9.61 0.000 8919.088 13587.03 ------------------------------------------------------------------------------
. est store b
. ftest a b Assumption: b nested in a
F( 1, 71) = 6.37 prob > F = 0.0138
. ftest a . Assumption: . nested in a
F( 1, 71) = 6.37 prob > F = 0.0138
. ftest a Assumption: . nested in a
F( 1, 71) = 6.37 prob > F = 0.0138
.
ftest is just a convenience command; these results could also be obtained by using the official Stata command test
. sysuse auto, clear (1978 Automobile Data)
. reg price mpg foreign
Source | SS df MS Number of obs = 74 -------------+------------------------------ F( 2, 71) = 14.07 Model | 180261702 2 90130850.8 Prob > F = 0.0000 Residual | 454803695 71 6405685.84 R-squared = 0.2838 -------------+------------------------------ Adj R-squared = 0.2637 Total | 635065396 73 8699525.97 Root MSE = 2530.9
------------------------------------------------------------------------------ price | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- mpg | -294.1955 55.69172 -5.28 0.000 -405.2417 -183.1494 foreign | 1767.292 700.158 2.52 0.014 371.2169 3163.368 _cons | 11905.42 1158.634 10.28 0.000 9595.164 14215.67 ------------------------------------------------------------------------------
. test foreign
( 1) foreign = 0
F( 1, 71) = 6.37 Prob > F = 0.0138
.
It is necessary that both models are estimated on the same sample. This requirement can easily be violated if some variables have missing values, like rep78 in the example below
. sysuse auto, clear (1978 Automobile Data)
. reg price mpg rep78
Source | SS df MS Number of obs = 69 -------------+------------------------------ F( 2, 66) = 11.06 Model | 144754063 2 72377031.7 Prob > F = 0.0001 Residual | 432042896 66 6546104.48 R-squared = 0.2510 -------------+------------------------------ Adj R-squared = 0.2283 Total | 576796959 68 8482308.22 Root MSE = 2558.5
------------------------------------------------------------------------------ price | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- mpg | -271.6425 57.77115 -4.70 0.000 -386.9864 -156.2987 rep78 | 666.9568 342.3559 1.95 0.056 -16.5789 1350.492 _cons | 9657.754 1346.54 7.17 0.000 6969.3 12346.21 ------------------------------------------------------------------------------
. est store a
. reg price mpg
Source | SS df MS Number of obs = 74 -------------+------------------------------ F( 1, 72) = 20.26 Model | 139449474 1 139449474 Prob > F = 0.0000 Residual | 495615923 72 6883554.48 R-squared = 0.2196 -------------+------------------------------ Adj R-squared = 0.2087 Total | 635065396 73 8699525.97 Root MSE = 2623.7
------------------------------------------------------------------------------ price | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- mpg | -238.8943 53.07669 -4.50 0.000 -344.7008 -133.0879 _cons | 11253.06 1170.813 9.61 0.000 8919.088 13587.03 ------------------------------------------------------------------------------
. est store b
. ftest a b models are estimated on different samples r(198);
.
This can be fixed by making sure that all models are estimated on the same sample using the if qualifier while estimating the models, like in the examples below.
. sysuse auto, clear (1978 Automobile Data)
. reg price mpg rep78
Source | SS df MS Number of obs = 69 -------------+------------------------------ F( 2, 66) = 11.06 Model | 144754063 2 72377031.7 Prob > F = 0.0001 Residual | 432042896 66 6546104.48 R-squared = 0.2510 -------------+------------------------------ Adj R-squared = 0.2283 Total | 576796959 68 8482308.22 Root MSE = 2558.5
------------------------------------------------------------------------------ price | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- mpg | -271.6425 57.77115 -4.70 0.000 -386.9864 -156.2987 rep78 | 666.9568 342.3559 1.95 0.056 -16.5789 1350.492 _cons | 9657.754 1346.54 7.17 0.000 6969.3 12346.21 ------------------------------------------------------------------------------
. est store a
. reg price mpg if e(sample)
Source | SS df MS Number of obs = 69 -------------+------------------------------ F( 1, 67) = 17.58 Model | 119910002 1 119910002 Prob > F = 0.0001 Residual | 456886957 67 6819208.31 R-squared = 0.2079 -------------+------------------------------ Adj R-squared = 0.1961 Total | 576796959 68 8482308.22 Root MSE = 2611.4
------------------------------------------------------------------------------ price | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- mpg | -226.3607 53.98091 -4.19 0.000 -334.107 -118.6143 _cons | 10965.23 1191.468 9.20 0.000 8587.05 13343.41 ------------------------------------------------------------------------------
. est store b
. reg price mpg if rep78 < .
Source | SS df MS Number of obs = 69 -------------+------------------------------ F( 1, 67) = 17.58 Model | 119910002 1 119910002 Prob > F = 0.0001 Residual | 456886957 67 6819208.31 R-squared = 0.2079 -------------+------------------------------ Adj R-squared = 0.1961 Total | 576796959 68 8482308.22 Root MSE = 2611.4
------------------------------------------------------------------------------ price | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- mpg | -226.3607 53.98091 -4.19 0.000 -334.107 -118.6143 _cons | 10965.23 1191.468 9.20 0.000 8587.05 13343.41 ------------------------------------------------------------------------------
. est store c
. ftest a b Assumption: b nested in a
F( 1, 66) = 3.80 prob > F = 0.0557
. ftest a c Assumption: c nested in a
F( 1, 66) = 3.80 prob > F = 0.0557