*! version 1.1.0 03Mar2013

*! version 1.0.0 11Feb2013
help rtmci

Title

rtmci -- Regression to the mean effects with confidence intervals

Syntax

rtmci pre-test post-test [if] [in] , cutoff [options]

pre-test is the pre-test variable, post-test is the post-test variable,
and cut-off is the cutoff value on the pre-test variable.

Main
periods(#) defines the number of periods that the pre-test variable represents

figure produces a plot of the expected pre- and post-test means and confidence intervals for values
above and below the cutoff

Bootstrapped CIs
seed(#) sets the random-number seed to #

reps(#) specifies the number of replications to be performed

size(#) draws samples of size #

level(#) sets the confidence level; default is level(95)

saving(filename, ...)
saves results to filename

by is allowed with rtmci; see [D] by.

Description

rtmci calculates the regression to the mean effect for a variable that is generally measured
at two points in time (i.e., "pre-test" and "post-test"), based on a defined cutoff value on the "pre-test" measure, and
estimates confidence intervals using bootstrap simulation; see bootstrap. If only summary level statistics are
available (e.g., as published in a journal article), the user may consider using rtmcii, an immediate form of rtmci.

Options

Main

periods(#) defines the number of periods that the pre-test
variable represents; default is per(1).

figure produces a plot of the expected pre- and post-test means and confidence intervals for values
above and below the cutoff. This option requires Roger Newson's xsvmat and eclplot packages to be
installed; both are downloadable from SSC

Bootstrapped CIs

seed(#) sets the random-number seed to #. Specifying this option
is equivalent to typing . set seed # before calling rtmci; default is seed(1234).

reps(#) specifies the number of replications to be performed; default
is reps(1000).

size(#) sets the number of observations drawn at each replication; default is _N.

level(#) specifies the confidence level, as a percentage, for confidence
intervals. The default is level(95) or as set by set level.

saving(filename, ...)
saves the bootstrapped results of the simulations to filename. See
prefix_saving_option for details about suboptions.

Remarks

Regression to the mean (RTM), originally termed “regression toward mediocrity”, was described over a century ago by Sir Francis Galton (1886)
upon discovering that on average, tall parents had children shorter themselves and short parents had
taller children. An excellent historical review of RTM is provided by Stigler (1997).

RTM poses a major threat to the internal validity of any study in which
subjects are initially selected for their extreme values. Upon remeasurement, the sample mean
from this outlier group is likely to be much closer to the overall population mean. This
statistical phenomenon can be easily confused with a treatment effect.

rtmci calculates the expected pre-test value, post-test value, and estimated RTM effects using
equations proposed by Gardner & Hardy (1973) and Davis (1976) for Normally distributed data. Importantly, rtmci provides
confidence intervals to indicate the precision (uncertainty) for these estimates. See Linden (2013) for the results of simulation
a more comprehensive discussion.

Examples

. rtmci pretest posttest, cutoff(44.25) period(1) fig

. rtmci pretest posttest, cut(44.25) per(1) reps(2000) seed(4321) size(50)

. estat bootstrap, all

. bys treat: rtmci pretest posttest, cut(44.25) per(1) reps(2000) seed(4321) size(50)

Output tables

rtmci produces standard bootstrap output tables. Below is a cross reference to the variables in the tables:

Variable Description

mu pre-test mean

sd pre-test sd

rho correlation between pre-test and post-test

firstval_high expected pre-test value above the cutoff

secondval_high expected post-test value above the cutoff

rtm_high RTM effect above the cutoff

pct_rtm_high percent RTM effect above the cutoff

firstval_low expected pre-test value below the cutoff

secondval_low expected post-test value below the cutoff

rtm_low RTM effect below the cutoff

pct_rtm_low percent RTM effect below the cutoff

References

Davis CE. The effect of regression to the mean in epidemiologic and clinical studies. American Journal of Epidemioliology 1976;104:493-498.

Galton F. Regression towards mediocrity in hereditary stature. Journal of the Anthropological Institute 1886;15:246-263.

Gardner MJ, Hardy JA. Some effects of within person variability in epidemiological studies. Journal of Chronic Disease 1973;26:781-795.

Linden A. Assessing regression to the mean effects in health care initiatives. BMC Medical Research Methodology 2013;13(119):1-7.

Stigler SM. Regression towards the mean, historically considered. Statistical Methods in Medical Research 1997;6(2):103-14.

Citation of rtmci

rtmci is not an official Stata command. It is a free contribution
to the research community, like a paper. Please cite it as such:

Linden, Ariel (2013). rtmci: Stata module for estimating regression to the mean effects with confidence intervals.
http://www.lindenconsulting.org

Author

Ariel Linden

President, Linden Consulting Group, LLC

Ann Arbor, MI, USA

alinden@lindenconsulting.org

http://www.lindenconsulting.org

Acknowledgments

I would like to thank Nicholas J. Cox for his never-ending support and patience with me while
developing both rtmci and its immediate form; rtmcii. He knows Stata better than Stata knows Stata.
I would also like to thank Roger Newson for his guidance in creating the figure option using his xsvmat
and eclplot programs.

Also see

Manual: [R] bootstrap, [D] by

Online: bootstrap, by, xsvmat (if installed), eclplot (if installed)