rtmhs

Regression to the mean at selected hot spots

R

rtmhs(x1, x2, cut, w = NULL)

Python

crimlab.rtmhs(x1, x2, cut, w=None)

Command line

crimlab rtmhs --x1 VALUE --x2 VALUE --cut VALUE [--w VALUE]

Places chosen because their count in a first period exceeds a cut show a fall in the next period even with no treatment and no trend: if the two periods are exchangeable, the selected places’ mean change is never positive, and places chosen for being low never fall on average. This reports the change at the selected places next to the same statistic on the data together with its period-swapped copy, which is exchangeable by construction and so never positive; the excess of the first over the second is the part of the fall that selection alone does not explain. A treatment effect needs a control group selected the same way. See proof("rtmhs").

Parameters

x1

Counts by place in the first period: finite numbers.

x2

Counts by place in the second period: same length; when x1, x2 (and w) are all named with unique names, they are matched by name.

cut

The selection cut: places with x1 > cut are selected.

w

NULL for equal weights, or one non-negative weight per place.

Returns

A named numeric vector: nsel (the weight selected), change (the weighted mean of x2 - x1 at the selected places), mirror (the mean of x1 - x2 at places with x2 > cut), sym (the change in the data with its swapped copy; never positive), excess (change - sym), low (the mean change at places with x1 < cut) and lowsym (its swapped-copy version; never negative). NaN where no place qualifies.

References

Barnett, A. G., van der Pols, J. C. and Dobson, A. J. (2005). Regression to the mean: what it is and how to deal with it. International Journal of Epidemiology, 34(1), 215-220. doi:10.1093/ije/dyh299

Examples

set.seed(5)
mu <- rgamma(300, 2, 0.5)
x1 <- rpois(300, mu)
x2 <- rpois(300, mu)
rtmhs(x1, x2, cut = quantile(x1, 0.9))

Generated from the R help page: rtmhs in the R reference.