I need to compare two different estimation methods and see if there are statistically same or not. However one of my estimation methods is SUR (Seemingly Unrelated Regression). And, I estimated the my 11 different models using
sureg (Y1 trend X1 .... X106) (Y2 trend X1..... X181) ..... (Y11 trend X1 .... X 130)
Then I estimated single OLS model as shown in following
glm(Y1 trend X1 ...... X106)
Now I need to test if parameter estimates of X1 to X106 comming from sureg is equal to glm estimates of same variables or not? I need to use Haussman specification test. I couldn't figure how can I store parameters estimates for specific equation in an SUR system estimation.
I couldn't find object should I add to estimates store XXX to subset a part of SUR estimates.
It's not easy to give a working example using my own crowded data, but let me present same problem using stata's auto data.
. sysuse auto (1978 automobile data)
. sureg (price mpg headroom) (trunk weight length) (gear_ratio turn headroom)
Seemingly unrelated regression
------------------------------------------------------------------------------ Equation Obs Params RMSE "R-squared" chi2 P>chi2
------------------------------------------------------------------------------ price 74 2 2576.37 0.2266 21.24
0.0000 trunk 74 2 2.912933 0.5299 82.93 0.0000 gear_ratio 74 2 .3307276 0.4674 65.12 0.0000
------------------------------------------------------------------------------
------------------------------------------------------------------------------
| Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+---------------------------------------------------------------- price |
mpg | -258.2886 57.06953 -4.53 0.000 -370.1428 -146.4344
headroom | -419.4592 390.4048 -1.07 0.283 -1184.639 345.7201
_cons | 12921.65 2025.737 6.38 0.000 8951.277 16892.02
-------------+---------------------------------------------------------------- trunk |
weight | -.0010525 .0013499 -0.78 0.436 -.0036983 .0015933
length | .1735274 .0471176 3.68 0.000 .0811785 .2658762
_cons | -15.6766 5.182878 -3.02 0.002 -25.83485 -5.518345
-------------+---------------------------------------------------------------- gear_ratio |
turn | -.0652416 .0097031 -6.72 0.000 -.0842594 -.0462238
headroom | -.0601831 .0505198 -1.19 0.234 -.1592001 .0388339
_cons | 5.781748 .3507486 16.48 0.000 5.094293 6.469202
------------------------------------------------------------------------------
. glm (price mpg headroom)
Iteration 0: log likelihood = -686.17715
Generalized linear models Number of obs = 74 Optimization : ML Residual df = 71
Scale parameter = 6912463 Deviance = 490784895.4 (1/df) Deviance = 6912463 Pearson = 490784895.4 (1/df) Pearson = 6912463
Variance function: V(u) = 1 [Gaussian] Link function : g(u) = u [Identity]
AIC = 18.62641 Log likelihood = -686.1771533 BIC = 4.91e+08
------------------------------------------------------------------------------
| OIM
price | Coefficient std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
mpg | -259.1057 58.42485 -4.43 0.000 -373.6163 -144.5951
headroom | -334.0215 399.5499 -0.84 0.403 -1117.125 449.082
_cons | 12683.31 2074.497 6.11 0.000 8617.375 16749.25
------------------------------------------------------------------------------
as you see for the price model (glm) parameter estimate of mpg coef is -259.10 and parameter for same variable estimated in SUR system is -258.288
Now I wanted to test if parameter estimates of GLM and SUR methods are statistically equal or not.
Related
I have a dataset in Stata that looks something like this
Variable | Obs Mean Std. dev. Min Max
-------------+---------------------------------------------------------
dv2 | 1,904 .5395645 .427109 -1.034977 1.071396
xvar | 1,904 3.074055 1.387308 1 5
with xvar being a categorical independent variable and dv2 a dependent variable of interest.
I am estimating a simple model with the categorical variable as a dummy:
reg dv2 ib4.xvar
eststo myest
Source | SS df MS Number of obs = 1,904
-------------+---------------------------------- F(4, 1899) = 13.51
Model | 9.60846364 4 2.40211591 Prob > F = 0.0000
Residual | 337.540713 1,899 .177746558 R-squared = 0.0277
-------------+---------------------------------- Adj R-squared = 0.0256
Total | 347.149177 1,903 .182422058 Root MSE = .4216
------------------------------------------------------------------------------
dv2 | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
xvar |
A | .015635 .0307356 0.51 0.611 -.044644 .075914
B | .1435987 .029325 4.90 0.000 .0860861 .2011113
C | .1711176 .0299331 5.72 0.000 .1124124 .2298228
E | .1337754 .0295877 4.52 0.000 .0757477 .1918032
|
_cons | .447794 .020191 22.18 0.000 .4081952 .4873928
------------------------------------------------------------------------------
These are the results. As you can see B, C and E have larger effect than D which is the excluded category.
However, coefplot does not account for the in categorical variable the coefficient is composite true_A=D+A.
coefplot myest, scheme(s1color) vert
As you can see the plot shows the constant to be the largest coefficient, while the other to be smaller.
Is there a systematic way I can adjust for this problem and plot the true coefficients and SEs of each category?
Thanks a lot for your help
In response to your second comment, here is an example of how you can use marginsplot to plot estimated effects from a linear regression.
sysuse auto, clear
replace price = price/100
reg price i.rep78, cformat(%9.2f)
------------------------------------------------------------------------------
price | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
rep78 |
2 | 14.03 23.56 0.60 0.554 -33.04 61.10
3 | 18.65 21.76 0.86 0.395 -24.83 62.13
4 | 15.07 22.21 0.68 0.500 -29.31 59.45
5 | 13.48 22.91 0.59 0.558 -32.28 59.25
|
_cons | 45.65 21.07 2.17 0.034 3.55 87.74
------------------------------------------------------------------------------
margins i.rep78, cformat(%9.2f)
------------------------------------------------------------------------------
| Delta-method
| Margin std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
rep78 |
1 | 45.65 21.07 2.17 0.034 3.55 87.74
2 | 59.68 10.54 5.66 0.000 38.63 80.73
3 | 64.29 5.44 11.82 0.000 53.42 75.16
4 | 60.72 7.02 8.64 0.000 46.68 74.75
5 | 59.13 8.99 6.58 0.000 41.18 77.08
------------------------------------------------------------------------------
marginsplot
Note that these values are the constant plus the appropriate coefficient.
And then using the marginsplot command we can produce the following plot, which includes the marginal estimates and confidence intervals:
I am running a regression on categorical variables in Stata:
regress y i.age i.birth
Part of the regression results output is below:
coef
age
28 .1
29 -.2
birth
1958 .2
1959 .5
I want the above results to be shown in the reverse order, so that I can export them to Excel using the putexcel command:
coef
age
29 -.2
28 .1
birth
1959 .5
1958 .2
I tried sorting the birth and age variables before regression, but this does not work.
Can someone help?
You cannot directly reverse the factor levels of a variable in the regression output.
However, if your end goal is to create a table in Microsoft Excel one way to do this is the following:
sysuse auto.dta, clear
estimates clear
keep if !missing(rep78)
tabulate rep78, generate(rep)
regress price mpg weight rep2-rep5
estimates store r1
regress price mpg weight rep5 rep4 rep3 rep2
estimates store r2
Normal results:
esttab r1 using results.csv, label refcat(rep2 "Repair record", nolabel)
------------------------------------
(1)
Price
------------------------------------
Mileage (mpg) -63.10
(-0.72)
Weight (lbs.) 2.093**
(3.29)
Repair record
rep78== 2.0000 753.7
(0.39)
rep78== 3.0000 1349.4
(0.76)
rep78== 4.0000 2030.5
(1.12)
rep78== 5.0000 3376.9
(1.78)
Constant -599.0
(-0.15)
------------------------------------
Observations 69
------------------------------------
t statistics in parentheses
* p<0.05, ** p<0.01, *** p<0.001
Reversed results:
esttab r2 using results.csv, label refcat(rep5 "Repair record", nolabel)
------------------------------------
(1)
Price
------------------------------------
Mileage (mpg) -63.10
(-0.72)
Weight (lbs.) 2.093**
(3.29)
Repair record
rep78== 5.0000 3376.9
(1.78)
rep78== 4.0000 2030.5
(1.12)
rep78== 3.0000 1349.4
(0.76)
rep78== 2.0000 753.7
(0.39)
Constant -599.0
(-0.15)
------------------------------------
Observations 69
------------------------------------
t statistics in parentheses
* p<0.05, ** p<0.01, *** p<0.001
Note that here I am using the commmunity-contributed command esttab to export the results.
You can make further tweaks if you fiddle with its options.
EDIT:
This solution manually creates dummies for esttab but instead you can also create a new variable with the reverse coding and use the opposite base level as #NickCox demonstrates in his solution.
You can reverse the coding and apply value labels to insist on what you will see:
sysuse auto, clear
generate rep78_2 = 6 - rep78
label define new 1 "5" 2 "4" 3 "3" 4 "2" 5 "1"
label values rep78_2 new
regress mpg i.rep78_2
Source | SS df MS Number of obs = 69
-------------+---------------------------------- F(4, 64) = 4.91
Model | 549.415777 4 137.353944 Prob > F = 0.0016
Residual | 1790.78712 64 27.9810488 R-squared = 0.2348
-------------+---------------------------------- Adj R-squared = 0.1869
Total | 2340.2029 68 34.4147485 Root MSE = 5.2897
------------------------------------------------------------------------------
mpg | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
rep78_2 |
4 | -5.69697 2.02441 -2.81 0.006 -9.741193 -1.652747
3 | -7.930303 1.86452 -4.25 0.000 -11.65511 -4.205497
2 | -8.238636 2.457918 -3.35 0.001 -13.14889 -3.32838
1 | -6.363636 4.066234 -1.56 0.123 -14.48687 1.759599
|
_cons | 27.36364 1.594908 17.16 0.000 24.17744 30.54983
------------------------------------------------------------------------------
regress mpg ib5.rep78_2
Source | SS df MS Number of obs = 69
-------------+---------------------------------- F(4, 64) = 4.91
Model | 549.415777 4 137.353944 Prob > F = 0.0016
Residual | 1790.78712 64 27.9810488 R-squared = 0.2348
-------------+---------------------------------- Adj R-squared = 0.1869
Total | 2340.2029 68 34.4147485 Root MSE = 5.2897
------------------------------------------------------------------------------
mpg | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
rep78_2 |
5 | 6.363636 4.066234 1.56 0.123 -1.759599 14.48687
4 | .6666667 3.942718 0.17 0.866 -7.209818 8.543152
3 | -1.566667 3.863059 -0.41 0.686 -9.284014 6.150681
2 | -1.875 4.181884 -0.45 0.655 -10.22927 6.479274
|
_cons | 21 3.740391 5.61 0.000 13.52771 28.47229
------------------------------------------------------------------------------
If you wanted to see the same variable name as before, you could also do the following:
drop rep78
rename rep78_2
I am running several simple regressions and I wish to save the value of the significance (P > |t|) of a regression for a given coefficient in a local macro.
For example, I know that:
local consCoeff = _b[_cons]
will save the coefficient for the constant, and that with _se[_cons] I can get the standard error. However, there doesn't seem to be any documentation on how to get the significance.
It would be best if the underscore format worked (like _pt etc.), but anything will do.
There is no need to calculate anything yourself because Stata already does that for you.
For example:
. sysuse auto, clear
(1978 Automobile Data)
. regress price weight mpg
Source | SS df MS Number of obs = 74
-------------+---------------------------------- F(2, 71) = 14.74
Model | 186321280 2 93160639.9 Prob > F = 0.0000
Residual | 448744116 71 6320339.67 R-squared = 0.2934
-------------+---------------------------------- Adj R-squared = 0.2735
Total | 635065396 73 8699525.97 Root MSE = 2514
------------------------------------------------------------------------------
price | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
weight | 1.746559 .6413538 2.72 0.008 .467736 3.025382
mpg | -49.51222 86.15604 -0.57 0.567 -221.3025 122.278
_cons | 1946.069 3597.05 0.54 0.590 -5226.245 9118.382
------------------------------------------------------------------------------
The results are also returned in matrix r(table):
. matrix list r(table)
r(table)[9,3]
weight mpg _cons
b 1.7465592 -49.512221 1946.0687
se .64135379 86.156039 3597.0496
t 2.7232382 -.57468079 .54101802
pvalue .00812981 .56732373 .59018863
ll .46773602 -221.30248 -5226.2445
ul 3.0253823 122.27804 9118.3819
df 71 71 71
crit 1.9939434 1.9939434 1.9939434
eform 0 0 0
So for the p-value of, say weight, you type:
. matrix A = r(table)
. local pval = A[4,1]
. display `pval'
.00812981
The t-stat for the coefficient is the coefficient divided by the standard error. The p-value can then be calculated using the ttail function with the appropriate degrees of freedom. Since you are looking for the two-tailed p-value, the result gets multiplied by two.
In your case, the following should do it:
local consPvalue = (2 * ttail(e(df_r), abs(_b[cons]/_se[cons])))
I want to do something very easy, but it doesnt work!
I need to see the predictions (and errors) of a GARCH model. The Main Variable es "dowclose", and my idea is look if the GARCH model has a good fitting on this variable.
Im using this easy code, but the prediction are just 0's
webuse dow1.dta
arch dowclose, noconstant arch(1) garch(1)
predict dow_hat, y
ARCH Results:
ARCH family regression
Sample: 1 - 9341 Number of obs = 9341
Distribution: Gaussian Wald chi2(.) = .
Log likelihood = -76191.43 Prob > chi2 = .
------------------------------------------------------------------------------
| OPG
dowclose | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
arch |
L1. | 1.00144 6.418855 0.16 0.876 -11.57929 13.58217
|
garch |
L1. | -.001033 6.264372 -0.00 1.000 -12.27898 12.27691
|
_cons | 56.60589 620784.7 0.00 1.000 -1216659 1216772
------------------------------------------------------------------------------
This is to be expected: you have no covariates and no intercept, so there's nothing to predict.
Here's a simple OLS regression that makes the problem apparent:
. sysuse auto
(1978 Automobile Data)
. reg price, nocons
Source | SS df MS Number of obs = 74
-------------+------------------------------ F( 0, 74) = 0.00
Model | 0 0 . Prob > F = .
Residual | 3.4478e+09 74 46592355.7 R-squared = 0.0000
-------------+------------------------------ Adj R-squared = 0.0000
Total | 3.4478e+09 74 46592355.7 Root MSE = 6825.9
------------------------------------------------------------------------------
price | Coef. Std. Err. t P>|t| [95% Conf. Interval]
------------------------------------------------------------------------------
. predict phat
(option xb assumed; fitted values)
. sum phat
Variable | Obs Mean Std. Dev. Min Max
-------------+--------------------------------------------------------
phat | 74 0 0 0 0
In Stata the command nlcom employs the delta method to test nonlinear hypotheses about estimated coefficients. The command displays the standard errors in the results window, though unfortunately does not save them anywhere.
What is available after estimation is just the matrix r(V), but I cannot figure out how to use it to compute the standard errors.
You need to use the post option, like this:
. sysuse auto
(1978 Automobile Data)
. reg price mpg weight
Source | SS df MS Number of obs = 74
-------------+------------------------------ F( 2, 71) = 14.74
Model | 186321280 2 93160639.9 Prob > F = 0.0000
Residual | 448744116 71 6320339.67 R-squared = 0.2934
-------------+------------------------------ Adj R-squared = 0.2735
Total | 635065396 73 8699525.97 Root MSE = 2514
------------------------------------------------------------------------------
price | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
mpg | -49.51222 86.15604 -0.57 0.567 -221.3025 122.278
weight | 1.746559 .6413538 2.72 0.008 .467736 3.025382
_cons | 1946.069 3597.05 0.54 0.590 -5226.245 9118.382
------------------------------------------------------------------------------
. nlcom ratio: _b[mpg]/_b[weight], post
ratio: _b[mpg]/_b[weight]
------------------------------------------------------------------------------
price | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ratio | -28.34844 58.05769 -0.49 0.625 -142.1394 85.44254
------------------------------------------------------------------------------
. di _se[ratio]
58.057686
This standard error is the square root of the entry from the variance matrix r(V):
. matrix list r(V)
symmetric r(V)[1,1]
ratio
ratio 3370.6949
. di sqrt(3370.6949)
58.057686
Obviously you need to take square roots of the diagonal elements of r(V). Here's an approach that returns the standard errors as variables in a one-observation data set.
sysuse auto, clear
reg mpg weight turn
nlcom (v1: 1/_b[weight]) (v2: _b[weight]/_b[turn])
mata: se = sqrt(diagonal(st_matrix("r(V)")))'
clear
getmata (se1 se2 ) = se /* supply names as needed */
list