Confidence intervals
Changing the plot type
By default coefplot draws confidence intervals as spikes. Use
ciopts(recast())
to change the plot type. For example, to use capped spikes, type:
. sysuse auto, clear (1978 automobile data) . regress price mpg trunk length turn if foreign==0 (output omitted) . estimates store domestic . regress price mpg trunk length turn if foreign==1 (output omitted) . estimates store foreign . coefplot domestic foreign, drop(_cons) xline(0) ciopts(recast(rcap))Code
Multiple levels
The default for coefplot is to draw 95% confidence intervals
(or as set by set level).
To specify a different level or to include multiple confidence intervals,
use the levels()
option. Here is an example with 99.9%, 99%, and 95% confidence intervals:
. sysuse auto, clear (1978 automobile data) . regress price mpg trunk length turn (output omitted) . coefplot, drop(_cons) xline(0) msymbol(s) mfcolor(white) /// > levels(99.9 99 95) legend(order(1 "99.9" 2 "99" 3 "95") rows(1))Code
Line widths are (logarithmically) increased across the confidence
intervals. To use different line widths specify the
lwidth()
suboption within
ciopts():
. coefplot, drop(_cons) xline(0) msymbol(s) mfcolor(white) ///
> levels(99.9 99 95) legend(order(1 "99.9" 2 "99" 3 "95") rows(1)) ///
> ciopts(lwidth(*1 *3 *6))
Code
Here is a further example inspired by Harrel (2001, Figure 20.4):
. coefplot, drop(_cons) xline(0) msymbol(d) mcolor(white) ///
> levels(99 95 90 80 70) ciopts(lwidth(3 ..) lcolor(*.2 *.4 *.6 *.8 *1)) ///
> legend(order(1 "99" 2 "95" 3 "90" 4 "80" 5 "70") rows(1))
Code
And here is an example inspired by Cleveland (1994, Figure 3.78):
. sysuse auto, clear (1978 automobile data) . regress price mpg trunk length turn if foreign==0 (output omitted) . estimates store domestic . regress price mpg trunk length turn if foreign==1 (output omitted) . estimates store foreign . coefplot domestic foreign, drop(_cons) xline(0) levels(95 50) ciopts(recast(. rcap))Code
How CIs are retrieved
To compute confidence intervals, coefplot collects the variances of the
coefficients from the diagonal of e(V) (or
e(V_mi) for estimates from
mi)
and then, depending on whether degrees of freedom are available in scalar
e(df_r) (or in matrix e(df_mi) for estimates from
mi),
applies the standard formulas for confidence intervals based on the
t-distribution or the normal distribution, respectively. Custom
degrees of freedom can be provided through option
df().
If variances are stored under a different name than
e(V), use the
v()
option to provide the appropriate name, or, alternatively use option
se()
to provide custom standard errors (in which case variances from
e(V) will be ignored). Likewise, if your estimation command
provides precomputed confidence intervals, use the
ci() option
to include them in the plot (see the example on
plotting bootstrap CIs below).
For example, in survey estimation, you might want compare the design-based
confidence intervals with the confidence intervals you would obtain
in a hypothetical simple random sample of the same size. The
svy command stores the
hypothetical SRS variances in e(V_srs). Hence, to display
design-based and SRS-based confidence intervals, you could type:
. webuse nhanes2f, clear . svyset psuid [pweight=finalwgt], strata(stratid) (output omitted) . svy: regress zinc age age2 weight female black orace rural (running regress on estimation sample) Survey: Linear regression Number of strata = 31 Number of obs = 9,189 Number of PSUs = 62 Population size = 104,176,071 Design df = 31 F(7, 25) = 62.50 Prob > F = 0.0000 R-squared = 0.0698 ------------------------------------------------------------------------------ | Linearized zinc | Coefficient std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- age | -.1701161 .0844192 -2.02 0.053 -.3422901 .002058 age2 | .0008744 .0008655 1.01 0.320 -.0008907 .0026396 weight | .0535225 .0139115 3.85 0.001 .0251499 .0818951 female | -6.134161 .4403625 -13.93 0.000 -7.032286 -5.236035 black | -2.881813 1.075958 -2.68 0.012 -5.076244 -.687381 orace | -4.118051 1.621121 -2.54 0.016 -7.424349 -.8117528 rural | -.5386327 .6171836 -0.87 0.390 -1.797387 .7201216 _cons | 92.47495 2.228263 41.50 0.000 87.93038 97.01952 ------------------------------------------------------------------------------ . coefplot (., label(design-based)) (., v(V_srs) label(SRS-based)) /// > , keep(female black orace rural) xlabel(,grid)Code
When computing the SRS-based confidence intervals you might also want to
take into account that in a hypothetical SRS the residual degrees of freedom
of the model would be different. By default, coefplot uses the information
in e(df_r), which is equal to 31 in the example.
In an SRS, however, the degrees of freedom would be
e(N) – e(df_m) – 1, which is equal to 9181
in the example. To use the corrected degrees of freedom for displaying the
SRS-based confidence intervals, you could type:
. local df_r = e(N) - e(df_m) - 1 . coefplot (., label(design-based)) (., v(V_srs) df(`df_r') label(SRS-based)) /// > , keep(female black orace rural) xlabel(,grid)Code
Comparing the two graphs you will see that, due to the increased degrees of freedom, the SRS-based CIs in the second graph are slightly narrower than in the first graph.
Plotting bootstrap CIs
Bootstrap estimates obtained by the
vce(bootstrap)
option or the
bootstrap
command provide normal-approximation, percentile, and bias-corrected
confidence intervals (for the confidence level specified at the time of
estimation) in e(ci_normal), e(ci_percentile),
and e(ci_bc). Use the
ci() option to plot
there confidence intervals:
. sysuse auto, clear (1978 automobile data) . regress price mpg trunk length turn, vce(bootstrap) (output omitted) . coefplot (., ci(ci_normal) label(normal)) /// > (., ci(ci_percentile) label(percentile)) /// > (., ci(ci_bc) label(bc)) /// > , drop(_cons) xline(0) legend(rows(1))Code
Smoothed CIs
Option cismooth
adds smoothed confidence intervals (inspired by code provided in a
post
by David B. Sparks). By default,
cismooth
generates confidence intervals for 50 equally spaced levels (1, 3, ..., 99)
width graduated color intensities and varying line widths, as illustrated
in the following example:
. sysuse auto, clear (1978 automobile data) . regress price mpg trunk length turn if foreign==0 (output omitted) . estimates store domestic . regress price mpg trunk length turn if foreign==1 (output omitted) . estimates store foreign . coefplot domestic foreign, drop(_cons) xline(0) cismooth grid(none)Code
The smoothed confidence intervals are produced independently from
levels() and
ci() and are not
affected by ciopts().
Their appearance, however, can be set by a number of
suboptions.
If cismooth
is specified together with
levels()
or ci(), then the
smoothed confidence intervals are placed behind
the confidence intervals from
levels() or
ci().
CIs for proportions
When plotting proportions you may want to apply option
citype(logit)
to ensure that the confidence limits stay within 0 and 1 (see
help proportion):
. sysuse auto, clear (1978 automobile data) . proportion rep78 if foreign==0 Proportion estimation Number of obs = 48 -------------------------------------------------------------- | Logit | Proportion Std. err. [95% conf. interval] -------------+------------------------------------------------ rep78 | 1 | .0416667 .0288424 .0100647 .1567801 2 | .1666667 .0537914 .0840476 .3035829 3 | .5625 .0716027 .4172638 .6977581 4 | .1875 .0563367 .0988312 .3268658 5 | .0416667 .0288424 .0100647 .1567801 -------------------------------------------------------------- . estimates store domestic . proportion rep78 if foreign==1 Proportion estimation Number of obs = 21 -------------------------------------------------------------- | Logit | Proportion Std. err. [95% conf. interval] -------------+------------------------------------------------ rep78 | 3 | .1428571 .0763604 .0434141 .3796739 4 | .4285714 .1079898 .2301427 .6529748 5 | .4285714 .1079898 .2301427 .6529748 -------------------------------------------------------------- . estimates store foreign . coefplot domestic foreign, xtitle(Repair Record 1978) ytitle(Proportion) /// > vertical recast(bar) barwidth(0.25) finten(60) /// > citop citype(logit) ciopt(recast(rcap)) rename(*.rep78 = "")Code
(Option rename() can be omitted in Stata 15 or lower, or if
version is
set to 15 or lower.)
Truncated confidence spikes
Sometimes it may make sense to truncate wide confidence intervals so that the
rest of the information in the plot is better visible. The following example
illustrates how such truncation can be achieved using the
transform()
option. When truncating the confidence intervals you want to make sure that the
truncated spikes go all the way to the edge of the plot region. This is why in
the example the margin of the plot region is set to zero:
. sysuse nlsw88, clear (NLSW, 1988 extract) . regress wage ibn.occupation, nocons (output omitted) . coefplot, transform(* = min(max(@,1.5),12.5)) /// > xscale(range(1.5 12.5)) plotregion(margin(zero))Code
An alternative might be as follows:
. coefplot, transform(* = min(max(@,2),12)) ///
> plotregion(color(gray) icolor(white)) grid(nogextend)
Code
Furthermore, here is a somewhat involved example that uses the
if() option to select
a different plot type depending on truncation:
. coefplot (., pstyle(p1) if(@ll>2&@ul<12)) ///
> (., pstyle(p1) if(@ll>2&@ul>=12) ciopts(recast(pcarrow))) ///
> (., pstyle(p1) if(@ll<=2&@ul<12) ciopts(recast(pcrarrow))) ///
> (., pstyle(p1) if(@ll<=2&@ul>=12) ciopts(recast(pcbarrow))) ///
> , nooffset transform(* = min(max(@,2),12)) legend(off)
Code