Stata plot of the week #3
Contents
Interaction charts are quite useful to assess the direction and magnitude of an interaction effect in the context of an analysis of variance. Here is one way to build an interaction plot in Stata, using builtin commands only.
The data we will be using come from Montgomery’s Design of Experiments: This is basically a $3^2$ factorial design where we study the effect of temperature (°F) and a design parameter with three possible choices. The aim is to design a battery for use in a device subjected to extreme variations of temperature. I struggled to build an interaction plot for these data while writting my Stata tutorials lately, so I thought it would be a good idea to summarize how I came to a working solution.
Here are the data that we can load into Stata using the folllowing instruction:
import delimited "battery.txt", delimiter("", collapse) varnames(1)
list in 1/3
A twoway ANOVA table can be builit using anova
:
. anova life temperature##material
Number of obs = 36 Rsquared = 0.7652
Root MSE = 25.9849 Adj Rsquared = 0.6956
Source  Partial SS df MS F Prob > F

Model  59416.2222 8 7427.02778 11.00 0.0000

temperature  39118.7222 2 19559.3611 28.97 0.0000
material  10683.7222 2 5341.86111 7.91 0.0020
temperature#material  9613.77778 4 2403.44444 3.56 0.0186

Residual  18230.75 27 675.212963

Total  77646.9722 35 2218.48492
Of course, marginsplot
will solve our problem directly, but let’s look at a manual solution. I know that there is anovaplot
or even the builtin serrbar command. However, let’s first create summary statistics for our dataset:
preserve
collapse (mean) mean=life (sd) sd=life, by(material temperature)
Now, we could use twoway line
instructions using an if
qualifier to subset data according to, say, material
levels and draw an overlaid scatter plot of means across temperature
levels. But let us reshape the data first, after we discarded the previously generated sd
variable since we can only reshape one response variable at a time:
drop sd
reshape wide mean, i(temperature) j(material)
twoway connected mean* temperature, legend(label(1 "#1") label(2 "#2") label(3 "#3")) ytitle(Mean life) scheme(plotplain)
This misses the error bars, though, but I can imagine that adding “low” and “high” values to the current aggregated table and then overlaying the current graph with grouped twoway rcap
could be one solution. Again, this is quite overkill since the marvelous margins
command will handle all that for us:
restore
margins temperature#material
marginsplot