Hello.
My
name
is
Bradley
Jones.
I'm
the
manager
of
the
JMP
DOE
Group,
and
what
I
want
to
talk
to
you
about
today
is
a
surprising
use
of
the
Fit
Definitive
Screening
Platform.
If
you
haven't
done
a
Definitive
Screening D
esign
and
analyzed
it
using
this
platform,
then
you
wouldn't
know
exactly
where
the
platform
was.
I'll
show
you
that.
But
what
I'm
going
to
show
you
is
that
you
don't
have
to
use
the
definitive
screening
fitting
platform
just
to
fit
definitive
screenings.
It
can
fit
other
stuff
as
well,
and
that's
a
surprise.
I'll
start
out
by
talking
about
what
the
main
idea
of
this
presentation
is,
and
then
I'll
review
how
Fit
Definitive
Screening
works.
Of
course,
I'm
going
to
show
you
by
hand,
but
the
platform
does
all
the
work
for
you,
so
you
don't
really
have
to
ever
do
all
this
tedious
stuff.
And
then
I'll
have
a
couple
of
examples
of
using
Fit
Definitive
Screening
to
analyze
other
designs
that
are
not
definitive
screening
designs.
And
I'll
make
some
recommendations
at
the
end.
To
start
out,
here's
a
definitive
screening
design.
And
if
you
look
at
the
first
pair
of
runs
at
the
top,
you
can
see
that
each
value
here
is
plus
or
minus
one,
and
each
value
here
is
minus
or
plus
one.
W
hat
it's
trying
to
show
there
is
that
whatever
value
the
top
number
has,
the
bottom
number
has
the
opposite
value.
If
this
is
plus
one,
then
that
will
be
minus
one.
If
this
is
minus
one,
then
this
will
be
plus
one.
And
the
fact
that
all
six
pairs
of
designs
for
this
example
are
mirror
images
like
this
means
that
the
Definitive
Screening
Design
is
a
Fold
over
design.
Let's
think
about
what
Fold
over
designs
are
and
what
it
means
to
have
a
Fold
over
design
in
terms
of
properties.
For
any
Fold
over
design,
the
main
effects
and
two-
factor
interactions
are
uncorrelated,
and
that
means
that
they're
statistically
independent.
Orthogonal
Fold
over
designs
exist
for
every
multiple
of
eight
runs.
However,
orthogonal
main
effects
are
not
as
important
as
the
orthogonality
of
main
effects
in
two-
factor
interactions.
You
may
choose
to
allow
for
some
non-
orthogonality
in
main
effects
in
order
to
get
this
nice
property
that
main
effects
are
not
correlated
with
two-
factor
interactions,
which
means
that
if
you
have
active
two-
factor
interactions,
they
won't
bias
the
estimates
of
any
main
effects.
I
want
to
show
you
how
to
make,
or
talk
about
how
to
make
a
Fold
over
design in
JMP,
and
you
can
do
this
in
the
Custom
Designer.
You
open
the
Custom
Designer.
You
add
two-
level
Categoricals
or
Continuous
factors.
By
default,
Continuous
factors
are
always
two
levels.
And
then
you
choose
a
model
that
only
has
main
effects,
which
is
Default,
again.
And then you
can
choose
a
number
of
runs
that's
a
multiple
of
two
where
the
multiple
of
two
has
to
be
at
least
as
big
as
the
number
of
factors
times
two.
Then
in
the
red
triangle
menu
on
the
Custom
Designer,
you
go
to
Optimality
Criterion,
and
look
at
the
sub
menu
and
choose
Make
Alias
Optimal
Design
from
the
red
triangle
menu.
Then
you're
done.
All
you
have
to
do
is
click
Make
Design.
And
then
after
you
see
the
design,
you
can
check
that
the
Alias
Matrix
contains
only
zeros
for
the
main
effects
and
two-
factor
interactions.
If
the
number
of
runs
in
your
design
is
not
a
multiple
of
eight,
then
you
may
see
some
correlations
between
two-
factor
interactions
and
the
intercept.
But
that
intercept
estimate
isn't
really
important
for
screening.
Let
me
give
you
a
JMP D
emo
of
that
process.
The
first
example
here
is
how
to
make
a
Fold
over.
And
I'm
going
to
create
a
six-
factor
custom
design.
And
in
this
design,
I
have
factors
A
through
F.
And
you
can
see
that
the
A through
F
factors
are
the
only
things
in
the
model
that's
the
Default.
Now
I'm
going
to
the
red
triangle
menu
and
I
choose
Alias
Optimal,
which
is
the
last
choice
here.
And
then
if
I
say, "Well,
let's
do
16
runs
instead
of
12,"
and
Make
Design,
it's
going
off
and
it's
going
to
compute
the
Alias
Optimal
design
for
six
factors
and
16
runs.
Now
I'm
going
to
check
by
looking
at
the
Alias
matrix,
and
you
can
see
that
everything
in
the
Alias
matrix
is
zero.
Another
thing
I
can
do
is
look
at
the
color
map
and
the
correlations,
and
I
can
see
that
the
main
effects
are
all
white,
and
the
rectangular
area
showing
main
effects
and
two-
factor
interactions
is
also
all
white,
which
means
that
this
design
is,
in
fact,
a
Foldover
design.
And
I
could
use
it
to
do
a
screening
experiment.
Let
me
go
back
to
my
slides.
All
that
the
Definitive
Screen
Design
platform
does
is
check
that
the
design
is
a
Foldover.
It
doesn't
actually
require
that
what
you
have
in
the
table
that
is
current
is
actually
a
DSD.
You
can
use
Fit
DSD
to
analyze
any
Fold
over
design.
And
that's
the
surprise.
And
that's
the
main
idea
of
this
is to
show
you
not
first,
that
you
can
create
Fold
over
designs
very
simply
using
the
Custom
Designer,
and
that
if
you
have
a
Fold
over
design,
you
can
use
Fit
Definitive
Screen
Design
to
analyze
the
data.
It
turns
out
that
since
main
effects
and
two-
factor
interactions
are
orthogonal
to
each
other
in
a
Foldover
design,
you
can
split
the
response
that
you
observed
into
two
new
responses.
One
response
you
use
for
identifying
main
effects,
and
you
could
call
it
YME.
And
the
other
response
you
can
use
to
identify
two-
factor
interactions,
and
you
could
call
that
Y2FI
.
And
it
turns
out,
because
the
main
effects
are
orthogonal
to
the
two-
factor
interactions,
the
two
columns
that
you
create
doing
this
will
be
orthogonal
to
each
other.
The
way
you
would
do
that
is
you
can
fit
the
main
effects
model
with
no
intercept
and
save
the
predicted
values
of
that
model.
And
then
after
doing
that,
and you
can
call
that
column
YME,
and
then
the
next
thing
you
do
is
save
the
residuals
from
that
fit,
and
those
residuals
are
in
the
space
of
the
two-
factor
interactions.
Now,
these
two
actions
are
unnecessary,
but
if
you
wanted
to
know
what's
behind
the
screen,
then
this
allows
you
to
do
all
these
actions
for
yourself
if
you
want.
But,
of
course,
you
can
use
the
Fit Definitive
Screening
platform,
and
it's
doing
this
behind
the
scenes.
Let
me
make
a
small
digression.
I
think
it's
valuable
to
use
the
Model
Heredity
Assumption,
which
is
that,
generally
speaking,
two-
factor
interactions
are
much
more
probable
to
occur
if
both
the
main
effects
that
compose
that
interactions
are
active
themselves.
For
example,
if
factor
A
and
factor
B
main
effects
are
both
active,
then
you
might
want
to
consider
fitting
the
two-
factor
interaction
of
A
B.
Now
this
is
not
a
physical
law.
Nothing
makes
it
absolutely
necessary
that
this
hold.
And
yet
empirical
evidence
has
shown
that
such
models
are
much
more
likely
than
having
interactions
be
active
when
the
main
effects
are
not
active.
Now,
everybody
who's
done
a
lot
of
experiments
has
counter
examples
to
this.
All
I'm
saying
is
those
counter
examples
are
comparatively
rare.
Now
why
would
you
make
this
assumption?
Well,
here's
the
reason.
If
you
use
the
Heredity
Assumption,
you
can
have
the
set
of
possible
models
being
much
smaller
than
if
you
don't
make
this
assumption.
In
the
example
that
I
showed
you
earlier
where
I
had
factors
A
through
F,
let's
suppose
that
it
turned
out
that
only
factors
C,
D,
and
F
were
active,
then
you
would
only
consider
the
three
two-
factor
interactions,
CD, CF,
and
DF.
And
since
there
are
three
of
these
interactions,
there
are
two
to
the
third
possible
models,
one
of
which
has
no
interactions,
and
you
have
three
with
one
interaction,
three
with
two
interactions,
and
one
with
all
three
interactions.
However,
if
we
wanted
to
look
at
all
the
two-
factor
interactions
among
all
the
factors
A
through
F,
then
there
are
six
choose
two
or
15
possible
two-
factor
interactions,
which
means
that
there
are
two
to
the
15th
or more
than
32,000
possible
models.
And
sifting
through
all
of
those
models
is
a
much
harder
model
selection
problem.
If
you
can
rely
on
the
Heredity
Assumption,
you
can
save
yourself
a
lot
of
work
and
also
a
lot
of
ambiguity
in
making
your
model
selections.
Now
going
back
to
how
you
do
this,
you
can
form
the
two-
factor
interactions
involving
the
active
main
effects
and
then
do
step
wise
regression
up
to
the
point
where
the
mean
squared
error
of
the
model
that
you
have
is
relatively
small.
If
you
have
an
estimate
of a
Sigma
squared,
if
they're
roughly
comparable,
then
that
is
the
time
to
stop.
But,
of
course,
this
still
is
not
necessary t
o
do
by
hand
because
Fit Definitive
Screening
is
going
to
do
it
for
you.
Let
me
show
you
a
couple
of
examples
of
this
process
and
I'll
start out
with
an
example
from
Doug
Montgomery's
Design
and
Analysis
of
Experiments
textbook,
the
eighth
edition.
And
he
did
this
as
first
running
a
resolution
three
fractional
factorial
with
seven
factors
and
eight
runs.
Let
me
show
you
that
design
and
how
that
is
analyzed.
Here's
a
resolution
three
design,
and
if
I
do
just
Fit
Screening,
what
you
see
here
is
that
our
B,
D, and A
are
the
active
effects
and
maybe
G
is
marginally
active
but
small
compared
to
the
effects
of
B, D, and A.
But
let's
evaluate
this
design.
I
just
click
the
Evaluate
Design
script
in
the
table.
And
if
I
look
at
the
Alias
matrix,
you
can
see
that
factor
A
is
confounded
with
the
BD
interaction.
You
could
also
learn
the
same
thing
by
looking
at
the
color
map.
And
you
can
see
that
the
correlation
between
A
and
the
BD
interaction
is
one,
which
means
that
I
don't
know
whether
what
I'm
seeing
is
actually
the
main
effect
of
A
or
the
two-
factor
interaction
of
B
and
D
or
any
linear
combination
of
those.
What
I
have
is
an
ambiguity
and
I
need
to
make
some
more
runs
in
order
to
resolve
that
ambiguity.
Going
back
to
my
example,
what
then
happens
in
the
textbook
is
that
the
design
is
folded
over.
Now
instead
of
eight
runs,
there
are
16
runs.
And
let
me
show
you
that
example.
Here's
the
folded
over
design.
If
I
do
Evaluate
Design
and
then
look
at
the
Alias
matrix,
I
can
see
that
the
Alias
matrix
is
identically
zero
for
every
possible
value.
And
I
can
learn
the
same
thing
by
going
to
the
color
map
on
correlations.
And
I
see
that
the
main
effects
are
orthogonal
and
all
the
main
effects
are
orthogonal
to
all
the
two-
factor
interactions.
I
now
know
that
I
have
a
Fold
over
design
and
that
my
main
effects
are
not
going
to
be
biased
by
two-
factor
interactions.
I
have
data
for
the
time
it
takes
for
the
eye
to
focus.
And
if
I
click
on
this
script,
I
see
the
result
of
having
done
the
Fold
over.
And
what
I
see
is
first
that
B
and
D
are
the
two
main
effects,
that's
as
before,
except
that
A
is
no
longer
there
because,
guess
what?
The
BD
interaction
is
massively
significant.
And
the
true
model
is
BD
and
the
BD
interaction.
And
now
we
can
run
this
model
and
we
can
see
that
first
our
actual
by-
prediction
plot
and
our
residuals
all
look
good.
And
then
playing
with
the
profiler,
we
can
see
that
as
I
move
B
from
one
end
to
the
other,
the
slope
of
the
line,
the
prediction
line
of
the
effect
of
D
on
time
changes.
And
that's
the
nature
of
interactions.
When
you
have
an
interaction,
the
slope
of
one
factor
depends
on
the
value
of
the
other
factor.
And
so
now
we
have
this
is
the
setting
that
you
would
use
if
you
wanted
to
maximize
the
time
that
takes
the
eyes
to
focus.
Generally,
you
would
want
to
minimize
the
time.
This
would
be
the
setting
that
you
wanted
to
use
to
minimize
the
eye
focus
time.
That's
the
end
of
that
example.
Let
me
now
go
back
to
my
slides
for
just
one
second
and
introduce
the
Peanut
Solids
example.
The
Peanut
Solids
example
was
an
example
that
my
friend
Chris
Nachtsheim
actually
did
in
a
consulting
environment
and
we
have
in
the
sample
data
library
and
the
Peanut
Solids
experiment
as
a
definitive
screening
design.
But
what
I
did
was
instead
I
created
a
two-
level
Foldover
design
and
used
the
same
model
to
create
data
for
that.
And
so
let
me
show
you
that
data,
which
is
my
second
example
here,
the
peanut
example.
And
notice
that
I
have
PH,
water
temperature,
extraction
time,
ratio,
agitation
speed,
and
two
categorical
factors,
whether
you
hydrolyze
the
peanuts
first
and
whether
you
presoak
the
peanuts,
and
then
what
are
being
measured
are
the
peanut
solids.
Notice
also
that
the
number
of
runs
here
is
22,
which
is
not
a
multiple
of
eight.
And
therefore,
when
I
look
at
Evaluate D
esign,
I
don't
expect
that
this
design
will
be
orthogonal
for
the
main
effects.
And
when
I
look
at
the
Alias
matrix,
you
can
see
that
the
intercept
is
correlated
or
aliased
by
a
very
small
amount
by
any
active
two-
factor
interaction.
And
again,
if
I
look
at
the
correlation
color
map
cell
plot,
you
can
see
that
the
main
effects
are
not
orthogonal
to
each
other,
but
their
correlations,
their
absolute
correlations
are
very
small
like
one
over
eleven.
And
again,
because
this
area
is
white,
main
effects
are
orthogonal
to
two-
factor
interactions.
And
this
is
what
we
wanted.
This
is
what
we
have
to
have
in
order
to
use
the
Fit
Definitive
Screening
platform.
Now
I'm
going
to
run
that
platform.
And
what
I
see
are
that
I
have
four
active
main
effects
and
that
means
that
I
have
as
many
as
four
choose
two
or
six
two-
factor
interactions
to
check.
And
it
looks
like
ratio
and
agitation
speed
is
a
term
that
I
don't
really
need,
very
small
estimate
of
the
example.
But
the
true
model
that
generated
the
data
involves
these
four
two-
factor
interactions
here.
Ratio
times
agitation
speed
turns
out
to
be
a
type
one
error,
except
we
would
probably
get
rid
of
it
anyway,
and
its
estimate
is
very
small.
Here
we've
used
the
Fit
Definitive
Screening
Design
and
also
this
assumption
of
heredity
of
the
main
effects
and
two-
factor
interactions
to
find
not
only
all
the
main
effects
but
four
active
two-
factor
interactions
among
the
two-
factor
interactions
that
are
related
to
the
active
main effects.
We
found
the
actual
data-
generating
model,
the
correct
model.
Okay,
so
what
do
I
recommend
that
you
do?
First,
I've
shown
you
how
to
use
the
optimal
design
criterion
in
the
Custom
Designer
to
create
Fold
over
designs
and
you
can
do
that
relatively
simply
and
you
don't
necessarily
have
to
create
orthogonal
Foldove
r
designs.
The
Fit
Definitive
Screening
Design
platform
doesn't
care
whether
the
design
is
orthogonal
or
not,
it
will
still
analyze
the
data
as
long
as
the
design
is
a
Fold
over
design.
And
then
once
you
have
this
Fold
over
design
and
the
data,
you
can
use
the
Fit
Definitive
Screening
Design
platform
to
analyze
the
data.
And
so,
in
the
words
of
Nike,
"Just
do
it."
Here
are
some
references.
The
first
two
are
referencing
the
original
paper
on
Definitive
Screening
experiments
and
then
the
paper
by
Xiao
and
co-
authors
shows
how
we
create
Definitive
Screening
Designs
nowadays
without
involving
optimizations,
just
by
direct
construction
using
conference
matrices.
Then
the
second
paper,
Miller
and
Sitter,
have
the
basic
idea
that
I've
introduced
here
to
analyze F
old
over
designs.
This
was
in
Technometrics
way
back
in
2005,
but
we're
using
slightly
more
current
model
selection
techniques
than
Miller
and
Sitter.
And
finally,
the
last
reference
there
is
telling
how,
again
in
Technometrics,
Chris
Nachtsheim
and
I
wrote
a
paper
to
basically
explain
how
to
use
this
Fold
over
technique
and
the analysis
to
do
model
selection
for
Definitive
Screening D
esigns
in
a
two-
step
method
that
I
talked
about
at
the
very
beginning
of
this
talk.
Thank
you
very
much
for
your
attention
and
I'll
be
at
the
talk
when
it's
finally
delivered
to
answer
questions.
