Based on the results of a regression analysis, I would like to perform a power analysis that accounts for robust standard errors.
To my knowledge, robust standard errors are usually greater than "non-robust" standard errors. This is why I would expect lower "power".
Here is an example:
"Non-robust" standard errors
Code:
sysuse auto
regress mpg price headroom weight displacement gear_ratio, beta
Source | SS df MS Number of obs = 74
-------------+---------------------------------- F(5, 68) = 26.18
Model | 1608.01499 5 321.602998 Prob > F = 0.0000
Residual | 835.444469 68 12.2859481 R-squared = 0.6581
-------------+---------------------------------- Adj R-squared = 0.6329
Total | 2443.45946 73 33.4720474 Root MSE = 3.5051
------------------------------------------------------------------------------
mpg | Coef. Std. Err. t P>|t| Beta
-------------+----------------------------------------------------------------
price | -.0001408 .0001736 -0.81 0.420 -.0717795
headroom | -.3553828 .5714143 -0.62 0.536 -.0519664
weight | -.0061447 .0012576 -4.89 0.000 -.825451
displacement | .0099741 .0119302 0.84 0.406 .1583254
gear_ratio | .9957116 1.659936 0.60 0.551 .0785291
_cons | 36.81308 6.773891 5.43 0.000 .
------------------------------------------------------------------------------By using the option "beta" I also get the standardized coefficients, so I can easily calculate the power. As example I use "headroom".
Code:
power onemean 0 -.0519664, n(74) sd(1)
Estimated power for a one-sample mean test
t test
Ho: m = m0 versus Ha: m != m0
Study parameters:
alpha = 0.0500
N = 74
delta = -0.0520
m0 = 0.0000
ma = -0.0520
sd = 1.0000
Estimated power:
power = 0.0726With newer versions of STATA this should work as well:
Code:
power oneslope 0 -.0519664, sdx(1) sdy(1)
Robust standard errors
Code:
regress mpg price headroom weight displacement gear_ratio, beta robust Linear regression Number of obs = 74 F(5, 68) = 27.11 Prob > F = 0.0000 R-squared = 0.6581 Root MSE = 3.5051 ------------------------------------------------------------------------------ | Robust mpg | Coef. Std. Err. t P>|t| Beta -------------+---------------------------------------------------------------- price | -.0001408 .0001909 -0.74 0.463 -.0717795 headroom | -.3553828 .445874 -0.80 0.428 -.0519664 weight | -.0061447 .0010529 -5.84 0.000 -.825451 displacement | .0099741 .0090296 1.10 0.273 .1583254 gear_ratio | .9957116 1.787227 0.56 0.579 .0785291 _cons | 36.81308 6.579494 5.60 0.000 . ------------------------------------------------------------------------------
How can I correct for robust standard errors?
0 Response to Power Analysis [power] in Context of Regression Analysis and Robust Standard Errors
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