Various notes and Stata programs to aid in power analysis.

I write the notes mainly to explain to myself how to write power_reg and simci. The former can compute parametric power with clustering and stratification. The latter can simulate it. I wrote them mainly because I could not figure out how to do either for the simple (OLS) case with built-in Stata commands.

I only have access to Stata 13.1, so I impose that to be the minimum. The command is really simple, however, so I would not be surprised if it worked with earlier versions. The exception would be the fast option, which was compiled using C and v2.0 of the Stata Plugin Interface (SPI). This might be tied to Stata 13.1. See how to recompile below.

net install power_tools, from(https://raw.githubusercontent.com/mcaceresb/stata-power/master/)

To update, run

adoupdate, update

To uninstall, run

ado uninstall power_tools

sysuse auto, clear
tempfile auto
save `auto'
qui forvalues i = 1 / 20 {
    append using `auto'
}
replace price = price + runiform()

local depvar      price
local controls    mpg rep78
local cluster     rep78
local stratum     gear_ratio
local categorical foreign

* Parametric power
power_reg `depvar' `controls'
power_reg `depvar' `controls', cluster(`cluster')
power_reg `depvar' `controls', cluster(`cluster') strata(`stratum') nstrata(2)

* Simulate a CI
simci `depvar' `controls', reps(1000)
simci `depvar' `controls', reps(1000) cluster(`cluster')
simci `depvar' `controls' `stratum', reps(1000) cluster(`cluster') ///
    strata(`stratum') nstrata(2)
simci `depvar' `controls' i.`categorical', reps(1000) ///
    strata(`categorical') nstrata(0)

* Simulate MDE given power
simci `depvar' `controls', reps(1000) power(kappa(0.8) direction(neg))
simci `depvar' `controls', reps(1000) cluster(`cluster') ///
    power(kappa(0.8) direction(neg))
simci foreign  `controls' `stratum', reps(1000) strata(`stratum') nstrata(2) ///
    power(binary dir(pos))
simci `depvar' `controls', reps(1000) cluster(`cluster') strata(`stratum') ///
    nstrata(2) power(dir(pos))

* Simulate power given MDE
simci foreign  `controls', reps(1000) effect(effect(-0.5) ///
    bounds(-0.2 0.2) binary)
simci `depvar' `controls', reps(1000) cluster(`cluster') ///
    effect(effect(-0.5) bounds(-0.2 0.2))
simci `depvar' `controls', reps(1000) strata(`stratum') nstrata(2) ///
    effect(effect(-0.5) bounds(-0.2 0.2))

* Simulate a CI using C plugin (only tested under Linux)
simci `depvar' `controls', reps(1000) fast

* You can check it's actually faster
net install benchmark, from(https://raw.githubusercontent.com/mcaceresb/stata-benchmark/master/)
benchmark, disp reps(10): qui simci `depvar' `controls', reps(1000)
benchmark, disp reps(10): qui simci `depvar' `controls', reps(1000) fast

Note that the fast option depends on a plugin. The only non-standard library is the GNU Scientific Library (GSL), which is statically linked, so there shouldn't be any problems on most systems. However, if any of the dynamically linked libraries are missing, you may need to add their path (assuming they are somewhere in your system) to LD_LIBRARY_PATH; e.g.

LD_LIBRARY_PATH=LD_LIBRARY_PATH:/usr/local/lib
export LD_LIBRARY_PATH

before starting Stata. If this fixes the issue, you can add those lines to ~/.bashrc to avoid having to do that every time you log into a session.

The fast option uses a Stata plugin (compiled in C). To compile in Linux/Unix:

git clone https://github.com/mcaceresb/stata-power
cd stata-power
make SPI=3.0 # SPI v3.0, Stata 14 and later
make SPI=2.0 # SPI v2.0, Stata 13 and earlier

The advantage is twofold

1. First, C runs much faster than mata, which is how the function is implemented.
2. Second, C allows parallel loop execution. Since the simulation computes regression coefficients reps times, using N threads should result in an approximately Nx speed improvement. This works even with Stata/IC.

Note Mata runs faster than Stata's reg largely because this simulation uses just the regression coefficients; reg computes a lot of additional elements that the program does not use.

• The GNU Scientific Library (GSL)
• OpenMP
• Stata Plugin Interface (SPI version 2.0 for Stata < 14; version 3.0 for Stata >= 14)

I have only tested this in Linux so far. See Stata's plugin documentation for instructions on how to build the plugin in other platforms.

• Add documentation for simci
• Add documentation for power_reg
• Add examples for power_reg
• Compile fast option for Windows and OSX.
• Finish writing fast plugin so it works for clustering and stratification.
• Finish writing fast plugin so it works with effect() and power().

MIT