Okay,
so
welcome.
I'm
Phil
Kay,
and I'm joined
by
Hadley
Myers.
We're
going
to
talk
about
O
MARS Designs,
this
new
family
of
design of experiments
and
an
ad
d-in
that
gives you
a
gateway
into
that
world.
I'll
start
with
an
introduction,
and
I'm
going
to
give
you
a
motivating
case
study.
I'm
going
to
talk
about
how
these OMARS Designs
bridged
the
gap
between our
small,
efficient,
Definitive Screening Designs
that we're all
familiar
with,
and
the
larger,
high-
powered,
more
traditional
r
esponse surface designs
that
you
might
know
of.
Then
I'll
pass
over
to
Hadley
and
he'll
talk
about
how
you,
as
a
JMP
user,
can
create
and
evaluate
different
OMARS Designs
with
an
add-in
that
he's
been
working
on.
These
O
MAR Designs,
they
come
from
a
paper
by
Jose
Nunez
Ares
and
Peter
Goos.
I'll
just
show
you
that
briefly.
They've
worked
through
the
enumeration
of
thousands
of
such
designs,
and
we'll
introduce
you
to what these
designs
look
like.
I've
got
a
motivating
case
study
to
begin.
This
is
from
a
published
case
study.
This
was
published
in the
Journal
of
Clinical
Chemistry.
It's
a
response surface design.
It's
about
optimizing
clinical
chemical
methods,
so
an
assay,
in
this
case.
The
objective
was
to
optimize
an
assay
method,
maximizing
the
response,
which is called
Elevated
Serum
30 degrees
C.
They
had
six
factors,
each
of
which
was
a
quantity
of
a
different
reagent,
and
they
took
a
traditional
approach.
This
was
done
quite
some
time
ago.
They
generated
a
Central Composite Design,
which
is
a
very
traditional
response surface design
for
optimization
with
48-runs,
which
includes
four
center
points.
I've
used
this
to
motivate
the
use
of
O
MARS Designs.
As
an
alternative
to
this
48-
run
design,
I
generated
a
17-
run
Definitive
Screening
Designs
for
those
six
factors.
I
also
generated
an
alternative
31-
run
O
MARS Design.
I
took
the
model
from
the original
48-run
experiment.
So
use
that
data,
fit
a
model,
and
use
that
to
simulate
the
responses
that
we
might
expect
for
the
Definitive
Screening Design
and
fully
OMARS Design.
We
added
an
appropriate
amount
of
noise
to
that
to
give
us
a
realistic
response
simulation.
What
you're
going
to
see
through
this
example
is
that
the
Definitive
Screening
Design
is
effective
at
what
it
should
do,
which
is
finding
the most important
factors.
The
O
MARS Design
enables
us
to
optimize
the
process
by
identifying
and
estimating
all
of
the
important
effects
from
the
response
surface
model.
In
this
way,
we
are
saying
that
these
O
MARS Designs,
you
can
think
of
them
as
bridging
the
gap
between
Definitive
Screening
Designs
and
the
traditional
response
surface
method
designs,
like
the
Central Composite Design.
Here
is
that
Central Composite Design.
Here
are
our
six
factors,
and
this
is
our
response
of
interest.
These
are
some
of
the
models
that
we
fit,
and
we're
comparing.
It's
a
traditional
face-
centered,
Central Composite Design.
This
is
just
three
of
the
factors
visualized.
You
can
see
we've
got
our
axial
points here
on
the
face
of
the
cube
that's described
by
the
factor
ranges.
Those
kind
of
designs
are
very
good.
They've
got
lots
of
nice
properties
in
terms
of
the
correlations
between
effects.
You
can
see
lots
of
white
space
here,
which
means
zero
correlations,
orthogonal
effects.
They're
not
so
great
with
the
quadratic
effects.
There's
fairly
strong
correlations
between all of our quadratic effects
on
one
another,
which
does
reduce
the
power
of
our
ability
to
estimate
these
quadratic
effects.
Nevertheless,
we
can
fit
a
good
model
to
that.
This
is
the
model
fit
to
that
original
data.
We
identified
that
there
really
are
four
critical
factors
out
of
the
six
and
there
are
various
higher
order
terms
as
well
that
are
important.
Really
the
pH,
this
P
5P
OG,
and
MDH
are
very
important.
The
L-a
spartic
acid
and
this
Tris
buffer
are
much
less
important.
We
can
build
a
good model
using
that
design.
It's
quite
a
big
expensive
design,
though,
48-runs.
What
would
our
alternatives
be?
Well,
Definitive
Screen
Designs
are obviously
very
good
for
screening
these
kind
of
situations,
screening for
the
important
factors.
I've
generated
using
the
same
factors,
same
factor
ranges,
a
17-run
Definitive
Screening
Design
for
those
six
factors.
A
gain,
I've
simulated
the
response
data
there
based
on
the
model
from
the
published
data
from
the
big
experiment
there.
The
definitive
screen
design
does
what
it's
supposed
to
do.
It
finds
that
we've
got
these
four
important
factors,
the
pH,
P5
P,
OG, MDH.
It's
identified
those
and
it's
been
able
to
identify
some
of
the
higher
order
effects
that
are
important.
Now
at
this
stage,
what
you
could
do
is
augment.
Screening
design
is
all
about
screening
for the important factors
and
then
in
the
next
step
of
the
sequence,
experimental sequence,
we
can
augment
to
learn
more
about
the
higher order effects,
the
higher
order
terms
for
the
response
surface
model.
What
I'm
going
to
show
you
here,
though,
is an
alternative
approach
we
could
have
taken.
Here
is
an
experimental
design
with
31
runs.
Again,
same
six
factors,
the
same
factor
ranges.
You'll
notice
that
it
is
a
three-
level
design.
For
each
factor,
we've
got settings
at
three
levels.
It's
a
response surface design.
If
we
compare
it
using
the
compare
designs
platform,
then
we
can
compare
those
two
designs.
The
Definitive Screening Design
here
in
blue,
we're
looking
at
the
powers
versus
the
31
run
OMARS
Design.
Well,
it's
not
a
surprise
that the 31-run
design
has
higher
power.
Generally,
we've
got
more
runs,
so
we
would
expect
that.
We
can
see
significantly
higher
power
for
these
quadratic
effects,
though.
Another
thing
to
look
at
that might be of interest
is
the
color
map
on
correlations.
Here's
our
17-run
Definitive
Screening Design,
and
you
might
recognize
that
color
map,
if
you
know
anything
about
Definitive Screening Designs then.
This
color
map
is
really a key.
It demonstrates
a
key
property
of
Definitive Screening Designs,
which
is
that
all
of
our
main
effects
are orthogonal
to
one
another,
and
the
main
effects
are
also
orthogonal
to
the
second
order
effects,
the
quadratics
and the two-factor
interactions.
That's
what
all
that
white
space
there
means.
Then
within
the
higher
order
terms,
there
is
some
degree
of
correlation,
but
no
complete
correlation,
no
aliasing.
We
are
always
able
to
estimate
some
of
these
higher
order
terms,
and
those
higher
order
terms
are, at
least, orthogonal,
completely
separately estimated
from
the
main
effects
factors,
the
fact
ors
main
effects
rather.
Now if
we
look
at
this
31-run
O
MARS Design,
you
can
see
its
got
similar
properties.
Again,
we've
got
orthogonal
main
effects,
and
those
main
effects
are
orthogonal
to
the
second
order
effects.
You
can
see
we've
got
lower
correlation
between
the
quadratic
effects,
for
example.
Overall
with
the
two-
factor
interactions
as
well,
there
are
lower
correlations.
Why
are
these
things
called
OMARS?
Well,
OMARS
stands
for
Orthogonal
Minimally
Aliased
R
esponse Surface
designs.
Again,
we've
got
orthogonal
main
effects,
and
we've
got
minimal
aliasing
between
our
second
order
effects
as
well,
and it's
a
response surface design.
In
fact,
both
of
these,
both
the
Definitive
Screening
Design
and
the
31-
run
design
are
OMARS.
They
are
both
Orthogonal
Minimally
Aliased
Response Surface
Designs,
so
DSDs
are
a
subset
of
OMARS.
How
well
does
this
perform?
What
I've
done
is
I
fitted a model
to
that
simulated
data.
Again,
I
simulated
the
response
data
for
our
31-
run
O
MARS Design,
and
I've
compared
that
model
against
the
17-run
Definitive Screening Design.
17-run
Definitive Screening Design
is doing
a
reasonable
job
of
predicting
the
actual
data.
Here,
we're
comparing
how
well
our
two
models
from
the
Definitive
Screening Design
and
the
OMARS Design,
how
well
they
fit
against
the
actual
data
from
the
48-run
published
example.
You
can
see
a
much
improved
model
with
the
31-
run
O
MARS Design,
as
we
might
expect.
In
fact,
the
31-
run
O
MARS Design
has identified correctly
the
higher
order
terms
that
are
important,
as
well
as
identifying
the
important
factor
effects,
which
was
pretty
much
all the
Definitive Screening Design
was
able
to
do.
Again,
just
to
reiterate,
what
we're
showing
here
is
that
these OMARS Designs
are
really
an
extension
of
Definitive
Screening
Designs,
and
they
are
a
bridge
between
that
small,
efficient
Definitive Screening Design
and
the
larger
traditional
response surface designs.
At
this
point,
I'll
hand
you
over
to
Hadley,
who's
going
to
show
you
more
about
an add-in
that
he's
created
that
will
enable
you
to
actually
explore
this new class
of
designs
for
yourself.
All
right.
Thank
you
very
much,
Phil.
Hello
to
everyone
watching
this
online,
wherever
you
are.
Thank
you
very
much
for
clicking
on
this
talk.
Before
I
take
you
through
the
add-in
to
show
you
how
you
can
use
it
to
generate
these
designs
and
select
the
best
one
for
you,
I'd
like
to
say
that
the
add-in
itself
includes 7,886 files,
each
one
containing
a
design,
where
the
main
effects
are
orthogonal
to each
other
into
the
higher
order
terms.
The
add-in
not
only
gives
you
access
to
these
7,886
new
designs,
but
it
also
gives
you
access
to all of these
designs
with
an
added
center point.
How
can
we
select
from
among
these
almost
16,000
designs
the
best
one
for
us
in
our
situation,
while
the
add-in
provides
us
an
interface
to
allow
us
to
do
that?
I'll
show
you
how
that
works.
Right
now,
the
add-in
is called
OMARS
Explorer.
What
it
will
allow
us
to
do
is first indicate
the
number
of
factors
that
we
have,
and
the
add-in
at
this
moment
has the ability to generate designs
for
five,
six,
or
seven
continuous
factors.
We
can
write
the
maximum
number
of
runs
that
we
can
afford,
or
that
we'd
like
to
do,
as
well
as
whether
we'd
like
a
design
for
which
we
can estimate
all
main
effects
or
all
the
main
effects,
as
well
as
all
the
two-factor
interactions
or
the
full
response
surface
model.
We
have
the
option
of
generating parallel plots,
something
we
can
use
to
help
us
select
the
right
design.
I'll
show
you
how
that
works.
So
I'll
press
okay,
I
can
put
in
the
names
of
my
factors
as well
as
the
high
and
low
settings,
but
I'm
just
going
to
leave it
the
way
it
is
for
now.
I've
been
given
this
table
with
2,027
designs
that
satisfy
our
requirements.
Each
one
has
five
factors
less
than
or
equal
to
35
runs,
and
we
can
fit
a
full
response
surface
model.
So
how
can
we
now
select
the
best
one?
Well,
one
thing
we
could
use
is
the
local
data
filter,
where
we
can
select
runs
of
a
certain
design
of
a
certain
run
length
with or without
center points,
as
well
as
our
efficiencies.
The
average
or
max
variance
of
prediction
and
the
powers
for
the
intercept,
the
main
effects,
and
then
the
minimum
and
average
powers
for
the
two-factor
interactions
in
the
square
terms.
If
we
have
a
full
response
surface
model.
Because
we
generated
the
parallel
plots,
we
also
have
the
parallel
plot
here.
We
can
use
all
of
this
to
then
zero
in
on
designs
that
are
the
best
among all
the
ones
that
we've
chosen.
If
the
minimum
power
of
the
square
terms
was
something
that
was
important
to
us,
and
I
can
narrow
my
search
to
10
designs
rather
than
from
among
the
2,000 designs
that
were
possible,
once
I've
done
that,
I
can
press
this,
Get
Summary
Results
script
on
the
table,
and
then
generate
this
table
here
with
the
names
of
the
designs,
whether
the
design
includes
a
center
point
or
not,
the
number
of
runs,
as
well
as
all
of
the
metrics.
Let's
see,
I
think
I'll
go
ahead
and
just
choose
this
one
here.
I
can
press
make
design,
and
now
I've
been
given
this
design
a JMP.
One
thing
I'll
add
is
that
if
you
choose
a
design
with
the
center point,
it
adds
a
-0
at
the
end
to
indicate
that
the
center point
has
been
added
to
that
design.
I
can
now
go
ahead
and
add
my
response
column,
save
the
table,
and
I'm
ready
to
start
conducting
my
experiment.
As
Phil
mentioned
before,
Definitive Screening Designs
are
a
subset
of
OMARS Designs.
Of
course,
there
are
many
other
Orthogonal
Minimally
Aliased
Designs
that are
not
Definitive Screening Designs.
I'll
show
you
an
example
here
that
uses
six
factors
and
a
maximum
of
20
runs.
In
this
case,
we
only
have
eight designs
that
meet
this
criteria.
I'm
just
going
to
go
ahead
and
select
all
of
them
and
press
Get
Summary
Results.
Now,
this
13-
run
design
here
with
the
center point
is actually
the
Definitive
Screening
Design
for
six
factors.
You
can
see
that
this
design
is in every way
except
for
the
power for the intercept,
better
than
this
15-
run
O
MARS Design,
which
is
not
a
Definitive
Screening
Design.
But
I'm
going
to
go
ahead
and
select
both
of
these
so
that
I
can
compare
the
designs.
When
I
do
that,
it'll
open
both
tables
as
well
as
this
compare
designs
platform.
Scrolling
down
to
the
color
map
on correlations,
I
can
see
that
the
Definitive
Screening Design,
which
is
this
one
here,
looks
as
I
would
expect
it
to.
Of
course,
the
O
MARS Design
is also orthogonal
for
the
main
effects.
That's
what
defines
it
as
an
O
MAR Design.
But
you'll
also
notice
that
this
one
happens
to
be
orthogonal
for many of
the
higher
order
effects
as
well.
If
I
were
to
try
to
fit
the
full
response
surface
model
to
add
those
terms
to
this
model,
of
course,
I
won't
be
able
to
add
all
of
them,
but
I'm
able
to
add
one
additional
term
or to fit one
additional
term.
Using
my
O
MARS Design,
then
I
would
be
using
the
13-
run
Definitive Screening Design.
If
I
tried
to
do
that
,
so now you'll
notice
that
the
powers
for
the
intercept,
the
main
effects,
and
the
quadratics
are
all higher
for
the
O
MARS Design.
They
are
lower
than
the
Definitive
Screening
Design
for
the
interaction
terms.
Looking
at
the
fraction
of
the
design
space
plot,
you'll
see
that
the
OMARS
Design
has
a
higher
maximum
prediction
variance,
but
is
lower
than
the
Definitive
Screening Design over
more
than
80 percent
of
the
design
space.
Interestingly,
the
Definitive Screening Design
platform
doesn't
have
the
ability
to
generate
15-
run
six
factor
designs.
We
can
generate
13
or
17runs.
If
we
can't
afford
17-runs,
but can afford 15,
this
provides
us
perhaps
an
option
that may be suited to us
that
we'd
like
to
consider
or
explore
further.
Once
again,
thank
you all
for
your
attention.
At
this
point,
I'd
like
to
turn
things
back
over
to Phil.
Thanks,
Hadley.
Just
to
summarize
what
you've
seen there,
what
we've
shown
you,
hopefully,
you've
seen
how
these
Orthogonal
Minimally
Aliased
Response Surface designs
can
bridge
that
gap
between
the
small,
efficient
Definitive Screening Designs
and
large
high-
powered
traditional
response
surface
method
designs.
You've
seen
how
there's
more
flexibility.
There
are
Orthogonal
Minimally
Aliased
Designs
with
three
levels
for
different
numbers
of
runs
now.
If
a
Definitive
Screen
Design
doesn't
meet
your
needs
or
a
traditional
Response
Surface
Method
design
doesn't
meet
your
needs,
you
should
now
be
able
to
explore
these OMARS Designs.
Exploring
those
designs
is
now
made
easier
to
use
as
a
JMP
user
with
the
add-in
that
Hadley
has
created
for
you.
We'll
obviously
post
links
to
all
of
these
things
in
the
article
in
the
community,
and
that's
a
great
place
to
let
us
know
if you've got
any
questions
as
well.
Thanks
very
much
for
your
attention.
