Design of Experiments
Suppose we want to test alternative movie theater designs using three factors.
The factors to include in the analysis have 3, 2, and 3 levels so we
enter 3
in the Max levels
input.
Here we enter the factors of interest. For example, enter
price
as the variable name, $10 as level 1, $13, as level
2, and $16 as level 3. Then click the
icon. This will add
the provided information about the factor to the
Design factors
window in the format Radiant needs for
analysis. To remove the last line in the Design factors
window click the
icon.
After entering the required information for each of the three factors your screen should look as follows:
You are now ready to create an experimental design by clicking on the
Create design
button. This will generate the following
output.
For our example, the ideal design has 18 trials. However, this
implies that the partial and the full factorial are the same size. We’d
like to find out if it is possible to reduce the number of trials. See
# trials
below.
This input can be used to control the number of trials to generate.
If left blank Radiant will try to find an appropriate number of trials
using the optFederov
function in the
AlgDesign
package.
Lets review the output in Design efficiency
. For our
example, the goal is to find a design with less than 18 trials that will
still allow us to estimate the effects we are interested in (e.g., the
main-effects of the different levels of price, sight, and food). Notice
that there are several designs that are considered balanced
(i.e., each level is included in the same number of trials). We are
looking for a design that is balanced and has minimal correlation
between factors (e.g., a D-efficiency score above 0.8). You can think of
the D-efficiency score as a measure of how cleanly we will be able to
estimate the effects of interest after running the test/experiment. The
ideal D-efficiency score is 1 but a number above 0.8 is considered
reasonable.
The smallest number of trials with a balanced design is 6. This design is balanced simply because 6 is divisible by 3 and 2 (i.e., the number of levels in our factors). However, the D-efficiency score is rather low (.513). The next smallest balanced design has 12 trials and has a much higher D-efficiency. This design is a reasonable choice if we want to estimate the main-effects of each factor level on movie-theater choice or preference.
To generate the desired partial factorial design enter
12
in the # trials
input and press
Create design
. This will generate the following output.
The trial
column in the output shows which profiles have
been selected from the full factorial design. Note that the off-diagonal
elements of the (polychoric) correlation matrix for a partial factorial
design will all be equal to 0 only when D-efficiency is equal
to 1. The
polycor
package is used to the estimate the correlations between the
factors.
A partial factorial design may not be unique (i.e., there might be
multiple combinations of trials or profiles that are equally good). By
setting a random seed you ensure the same set of trials will be
generated each time you press Create design
. However, to
see alternative partials factorial designs empty the
Rnd. seed
box and press Create design
a few
times to see how the set of selected trials changes.
Note that we will not be able to estimate all possible interactions
between price
, sight
, and food
if
we use a design with 12 trials. This is the trade-off inherent in
partial factorial designs! In fact, if we do want to estimate even one
interaction (e.g., select price:sight
) the appropriate
design has 18 trials (i.e., the number in the full factorial design that
includes all possible combinations of factor levels).
Click on the Partial
or the Full
button to
download the Partial or Full factorial design in csv format .
To download the list of factors you entered click the
Download
button. To upload a previously created set of
factors click the Upload
button and browse to find the
desired file.
Add code to
Report
> Rmd to (re)create the design by clicking the
icon on the bottom
left of your screen or by pressing ALT-enter
on your
keyboard.
For an overview of related R-functions used by Radiant for experimental design see Design > Design of Experiments
The key function from the AlgDesign
package used in the
doe
tool is optFederov
.