Hello,
everyone.
My
name
is
Zhiwu
Liang,
statistician
from
Procter
&
Gamble
Company.
I'm
support of the
business
in
Brussels
Innovation
Center
for
P&G.
My
main
job
is
doing
the
consumer
survey
data
analysis.
Today,
Narayanan
and
I
will
present
the
G
rowth Curve Modeling
to
Measure
Impact
of
the
Temperature
and
Usage A
mount
on
Detergent
Performance.
Next
slide,
please.
Here
is
the
contents
we
will
cover
today.
First,
I
will
give
the
brief
introduction
about
the
structural equation models
and
a
bit
about
the
data
we
will
be
using
for
our
modeling.
Then
I
will
turn
to
Narayanan
to
introduce
the
growth curve modeling,
model
building
process
plus
the
JMP
demo.
Without
showing,
I
will
present
the
conclusion
and
next
steps.
Next
slide,
please
.
The
structural equation modeling
is
a
multivariate
technique
that
is
used
to
test
a
set
of
the
relationship
between
the
observed
and
the
latent
variables
by
comparing
the
model
predicted
covariance
matrix
and
observed
covariance
matrix.
In
SEM,
what
we
have
done
is,
observed
variables
are
manifest
variable
as
the
indicator
for
latent
variables,
which
is
using
the
measurement
model
to
construct.
Latent
variables
form
a
regression
model
to
build
a
network
which
we
call
the
structure
model.
Here
is
an
example
with
the
three
latent
variable,
eight
o
bserved
variable
in
JMP,
so
the
SEM
structure.
As
you
can
see
in
the
button
left
chart,
the
circle
represent
the
latent
variable,
which
is
calculated
through
the
indicators
like
cleaning,
as
the
latent
variable
is
indicated
by
the
full
square
represent
the
manifest
variable
overall
cleaning,
stain
removal,
whiteness
and
brightness.
Same
as
the
freshness,
latent
variable
indicated
by
the
three
manifest
variable.
If
you
look
at
the
right
side
of
the
window,
the
loading
window
show
the
structure
for
the
measurement
model
how
this
individual
latent
variable
relate
to
the
indicator.
The
button
of
the
regression
window
show the
two
regression
model:
cleaning
drive overall rating,
freshness
dry
overall rating.
This
is
the
structure
for
the
structure
equation
model.
Next
slide,
please.
The
data
we
use
for
our
growth curve modeling
is
the
survey
data
we
conduct
in
the
France
with
the
119
consumer.
We
divide
this
119
consumer
into
groups.
Sixty
of
them
use
control
products,
which
is
the
Ariel,
soluble
unit
dose,
the
pods,
in
our
data
set,
marked
as
0.
Another
59
consumers
use
test
product
is
the
Ecolabel
product,
code
as
1.
Each
consumer,
during
the
12
weeks
of
the
test,
first
four
weeks,
they
use
their
own
products.
Then
they
will
go
to
the
eight
week's
test
week,
use
one
of
our
assigning
products,
either
use
the
Ariel
SUD
or
Ecolabel.
Then
for
each
time
of
the
wash,
the
consumer
will
fill
in
the
questionnaire,
provide
some
information
about
their
washing
behavior,
such
as
the
washing
temperature,
number
of
the
pods
used,
soil
level
of
the
fabric,
how
dirty
it
is,
and
overall
rating
of
the
performance
for
the
product.
Our
modeling
objective
is
try
to
test
if
there
is
a
product's
effect
on
the
overall
performance
rating,
washing
temperature
on
the
overall
performance
rating,
number
of
the
pods
used
for
overall
rating
for
each
of
the
wash.
Next
slide,
please.
Since
every
consumer,
they
have
a
different
washing
habit,
they
have
different
condition,
not
all
of
the
consumer
has
the
same
number
of
wash
during
the
test
week.
Therefore,
to
make
every
consumer
the
weight
equal
in
our
model
building
data
set,
we
first
aggregate
the
consumer
data
by
the
panelist
level
by
weekly
basis.
You
take
the
average
washing
temperature
during
that
week
for
the
particular
consumer,
number
of
pods
used,
and
the
overall
rating
for
each
load
during
that
week.
After
this
aggregate
data,
we
use
the
exploratory
tool
like
JMP
Graph
Builder
to
identify
if
there's
any
linear
trend
for
overall rating,
for
temperature
trend
during
the
test
week,
and
the
number
of
the
pods
using
trend
during
the
test
week.
Since
the
exploratory
stage
,
OAR
is
pretty
stable
in
the
week
9
to
week
12,
we
use
the
intercept
only
model
for
OAR.
Then
for
the
temperature
for
the
product
and for
the
number
of
the
pods
used
from
this
exploratory
stage,
we
found
there
is
either
increasing
or
decreased
trend.
Therefore,
we
use
the
linear
growth
model
to
describe
the
temperature
indicator
and
the
number
of
pods
indicator.
To
explain
the
product
impact,
we
also
including
the
product
manufactured
variable
in
our
model.
Then
we
first
build
a
growth
curve
model
for
temperature
number
of
the
pods,
then
add
this
latent
variable
to
build
a
regression
model
from
products
variable,
intercept
of
temperature,
slope
of
temperature,
intercept
of
the
number
of
pods
used,
slope
of
the
number
of
pods
used
to
intercept
of
the
OAR
to
build
multivariate,
the
growth curve model.
Now I
would
turn
to
Narayanan
to
introduce
latent
growth curve model.
Narayanan,
it's
your
turn.
Thank
you,
Zhiwu,
for
the
great
[inaudible 00:06:49].
Hi,
everyone.
My
name
is
Narayanan.
I
am
an
Adjunct
professor
at
the
University
of
Cincinnati,
but
I
teach
courses
on
data
mining
using
JMP.
I'd
like
to
start
by
giving
a
very
broad
definition
of
what
is
latent
growth curve modeling.
As
we
go
along,
I
may
use
the
letters
LG
CM
to
represent
latent growth curve modeling,
and
SEM
to
represent
structural equation modeling.
Latent growth curve modeling
is
basically
a
way
to
model
longitudinal
data
using
the
SEM
framework.
Because
it
is
built
in
the
SEM
framework,
it
has
all
the
advantages
of
specifying
and
testing
relationship,
as
Zhiwu
was
explaining
with
the
example
of
structural equation modeling.
A
s
a
side
note,
I
would
like
to
mention
that
LGCM
is
actually
an
application
of
confirmatory
factor
analysis,
which
is
actually
a
submodel
within
structural equation modeling
with
the
added
mean
structure,
and
this
will
be
explained
when
we
get
into
JMP.
One
of
the
benefits
of
using
the
SEM
framework
is
that
we
are
able
to
evaluate
model
fit.
Let
us
look
at
the
statement
there,
which
says,
every
model
implies
a
covariance
matrix
and
mean
structure.
What
this
really
means
is
that
the
observed
covariance
matrix
and
the
mean
vector
can
be
actually
reproduced
by
the
model
parameter
estimates
which
are
estimated
using
the
latent growth curve modeling.
The
equality
between
the
two
is
what
many
of
these
fit
indices
are
actually
testing.
One
of
the
oldest
one
is
the
chi-square
test
and
the
hypothesis
it
is
testing
is
actually
listed
there:
the
equality
between
the
population,
and
the
model
predicted
covariance
matrix,
and
the
mean
vectors.
However,
this
test,
which
is
one
of
the
oldest,
has
some
watch-
out.
One
is
that
the
test
statistic in a
function
is
sample
size,
which
means
that
larger
sample
size
will
tend
to
reject
the
model
even
for
trivial
differences.
The
other
one
is
that
the
test
is
global
and
does
not
reflect
the local fit
such as
could
be
measured
by
R-square.
A
lso,
the
fit
is
too
exact
as
specified
in
the
hypothesis.
We
know
from
the
famous
box
statement
that
all
models
are
wrong.
Our
models
are
only
just
an
approximation.
Because
of
this,
there
have
been
several
alternative
fit
measures
that
have
been
proposed.
I'd
like
to
mention
three
of
them
here.
The
first
is
the
Root
Mean
Square
Error
of
Approximation.
This
is
actually
measuring
model
misfit,
adjusting
for
the
sample
size,
which
was
an
issue
with
the
chi-square
test.
This
is
actually
a
badness-
of-
fit
measure,
so
lower
numbers
are
better.
But
one
of
the
advantages
of
using
this
fit
measure
is
that
we
have
a
confidence
interval
for
it,
and
the
suggested
threshold
for
this
fit
measure
is
that
the
upper
bound
of
the
confidence
interval
is
less
than
0.10.
The next
is
a
Comparative
Fit I
ndex
and
Non-Normed
Fit
Index.
These
are
relative
estimates,
and
they're
actually
testing
how
good
is
your
proposed
model
compared
to
a
baseline
model,
which
is
usually
a
model
of
no
relationship.
This
is
a
goodness-
of-
fit
measure,
and
so
the
suggested
criteria
here
is
that
these
fit
measures
cross
a
threshold
of
at
least
0.95.
The
last
one
is
a
Standardized
Root
Mean
Squared
Residual.
This
is
actually
an
average
squared
residual
of
all
the
elements
in
the
covariance
matrix.
This
is
a
badness-
of-
fit
measure.
Again,
we
are
looking
for
smaller
numbers,
and
the
suggested
threshold
here
is
that
this
value
is
less
than
0.08.
On
top
of
all
this,
finally,
do
not
forget
to
check
the
actual
residuals,
the
standardized
residuals.
What
we
are
looking
for
here
is
numbers
which
are
beyond
minus 2
and
plus 2
threshold.
The
idea
here
is
to
look
at
the
totality
of
fit
and
not
just
any
one
measure.
Having
discussed
fit
measures,
now let
us
look
at
the
longitudinal
process
we
want
to
study.
Zhiwu described
three
different
processes.
First
one
is
success
criteria
as
measured
by
overall
satisfaction
rating
from
week
9
to
week
12.
Then
we
have
got
two
time vary
ing
covariates.
That
means
these
are
varying
over
time.
One
is
the
temperatures
setting
in
which
the
product
was
used
from
week
5
to
week
12,
and
then
the
amount
of
product
used
also
from
week
5
to
week
12.
Then
finally,
we
have
an
indicator
variable
indicating
what
type
of
product
it
is,
and
this
is
a
time invariant
covariate
doesn't
change
with
time.
The
modeling
strategy
we
are
going
to
use,
first,
we're
going
to
visualize
data
using
Graph
Builder.
Then
we
are
selecting
a
univariate
latent
growth
curve
model
for
each
of
the
processes.
Then
we
combine
all
of
them,
put
together
as
a
multivariate
LGCM.
Then
we'll
finally
test
the
hypothesis
that
Zhiwu
proposed,
which
is
how
well
the
product
and
other
growth
factors
impact
overall
satisfaction.
We
will
choose
the
simplest
model
when
we
build.
I
am
going
to
get
into
JMP.
I
am
running
JMP
18,
which
is
an
early
adopter
version,
and
I
am
going
to
show
some
scripts,
and
I
will
show
you
how
I
got
to
some
of
these
from
the
JMP
platforms.
The
first
thing
I
want
to
do
is
visualize
the
overall
satisfaction,
and
these
are
trajectories.
What
these
are, are
basically
individual
on
each
line
from
week
9
to
week
12.
Here,
the
overall
satisfaction
plotted
here
for
each
of
the
119
consumers.
They're
basically
one
trajectory
for
each
consumer.
If
you
look
at
this
particular
consumer,
row
number
16,
that
person's
trajectory
is
on
a
downward
trend
from
week
9
through
week
12.
They
started
somewhere
in
the
mid-50s,
and
by
the
time
they
are
in
week
12,
their
satisfaction
measure
has
come
down
to
about
37.5
on
a
scale
of
0-100.
Let
us
look
at
another
person.
This
person
here
who
used
the
Ariel
product,
their
trajectory
is
on
an
upward
swing
going
from
the
mid-70s
probably
to
the
early
90s
by
the
time
they
reach
week
12.
They
are
getting
more
and
more
satisfied
week
over
week.
Sorry
for
that.
A
bubble
screen
showing
up.
What
we
want
to
do
is
we
want
to
understand
how
different
consumers
are
experiencing
satisfaction
over
the
weeks,
and
the
change
in
these
processes
for
these
consumers
is
what
we
want
to
model
using
LGCM.
What
I'm
going
to
do
is
I'm
going
to
turn
on
the
script,
LGCM
of
overall
satisfaction.
I
have
built
here
three
different
models.
What
these
are
basically
the
latent
variable
corresponds
to
an
intercept
for
these
repeated
measures
of
the
overall
satisfaction
from
week
9
through
week
12.
I've
built
three
different
models.
I've
built
a
fourth
model,
which
is
a
simplification
of
the
first
model.
I've
built
a
no-growth
model,
which
means
different
people
have
different
levels
of
satisfaction
in
the
beginning,
which
is
week
9,
but
then
their
trajectories
flatten
out
and
does
not
grow
over
time.
Second
model
is
a
linear
growth
model,
which
means
that
trajectories
do
change
in
a
linear
fashion
over
time.
The
third
model
is
a
quadratic
model,
which
means
their
trajectories
change
in
a
quadratic
fashion
over
time.
Then
finally,
I've
got
a
simplification
of
the
first
model,
but
I'm
assuming
almost
elasticity
or
no
change
in
the
variance
across
time.
I'm
going
to
look
at
these
fit
measures
that
I
talked
about
and
choose
the
model
that
fits
the
best.
What
I'm
looking
for
is
low
values
of
chi-square,
high
values
of
CFI,
which
means
CFI
goes
on
a
scale
from
0-1
and
low
values
of
RMSEA,
which
also
goes
on
a
scale
from
0-1.
It
looks
like
all
my
models,
no-
growth,
linear
growth,
and
quadratic
growth,
fit
the
data
equally
well.
But
however,
I'm
going
to
take
the
simplest
of
the
models
because
if
I
look
at
the
estimates
as
I
can
in
the
path
diagram,
many
of
these
coefficients
relating
to
the
slope,
the
linear
slope
or
the
quadratic
slope,
are
actually
not
significant
as
shown
by
the
dotted
lines.
In
this
linear
growth
model,
what
we
have
is
an
intercept,
which
measures
the
initial
level
of
satisfaction,
and
slope,
which
measures
the
rate
of
increase
of
the
satisfaction
over
time
or
rate
of
decrease
of
satisfaction
over
time.
S
lope
measures
that,
intercept
measures
the
initial
level.
We
can
see
all
the
estimates
related
to
the
slope
are
actually
not
significant
as
indicated
by
dotted
lines.
The same
is
the
situation
for
the
quadratic
model
also.
Therefore,
I'm
going
to
take
the
simplest
of
the
model,
which
is
the
no-
growth
model
for
this
process,
which
is
overall
satisfaction.
Let
me
show
you
how
I
do
this.
In
JMP,
go
under
the
Analyze
and
pick
Multivariate
and
choose
the S
tructural Equation Model
platform.
Choose
the
repeated
measures,
in
this
case
is
OAR
from
week
9
through
week
12.
Drop
them
in
Model
Variables
box
and
click
OK.
We
have
got
these
four
repeated
measures
available
as
modeling
variables
in
the
path
diagram
area.
I
can
build
this
model
from
scratch
using
the
path
diagram,
but
JMP
has
made
it
easier
by
using
shortcuts.
I'm
going
to
go
under
the
Model
Shortcut,
red
triangle,
choose
Longitude
Analysis,
and
check
the
linear
latent
growth
curve
or
the
intercept-only
model.
If
I
choose
the
intercept-only
model,
I
get
this
path
diagram
which
you
saw
in
my
script.
If
I
run
the
model,
you
will
get
the
estimates
and
the
fit
statistic
for
this
model.
If
you
want
to
add
the
linear
growth
model
to
do
the
same
thing,
come
under M
odel
Shortcuts,
Longitudinal
Analysis,
and
Linear
G
rowth Curve Model.
Now we
have
got
not
only
an
initial
level
as
represented
by
the
intercept
latent
variable,
we've
got
the
rate
of
growth
of
this
process
as
represented
by
the
slope
latent
variable.
We
can
run
this
model.
Click
on
Run,
and
you
get
the
model
estimates,
as
I
showed
you
before,
which
are
not
significant
for
the
slope
latent
variable.
You
get
the
fit
statistics
right
here
under
the
Model
Comparison
table.
T
hese
models
are
easy
to
fit
in
JMP
using
the
model
shortcut
menu
available
under
the
Model
Shortcut.
I'm
going
to
close
the
one
I
just
created.
We
have
so
far
built
a
univariate
LGCM
for
a
single
process.
I'm
going
to
repeat
the
same
thing
for
the
other
two
growth
process
we
have,
and
we're
going
to
look
at
the
wash
temperature
trajectories.
Let
me
show
you
how
to
do
this
in
JMP.
In
JMP,
in
Graph,
click
on
Graph
Builder
and
open
up
the
temperature
variables.
We
want
to
look
at
temperature
from
week
5
through
week
12.
Drop
them
on
the
x-axis.
For
the
type
of
graph
you
want,
choose
the
last
icon
in
the
bar
at
the
top.
This
is
a
parallel
plot.
There
will
be
some
smoothness
associated
with
this.
Drag
this
letter
bar
all
the
way
to
the
left.
There
should
be
no
smoothness
at
all.
Take
the
product
variable,
which
is
an
indicator
variable,
put
them
on
Overlay.
Now you
get
individual
trajectories.
If
you
want
to
add
the
average
trajectory,
choose
the
sixth
icon
on
this
toolbar
from
left.
Click
on
the
Shift
key
and
click
on
this.
Now you
get
that
average
trajectory
of
temperature
used
over
these
eight
weeks.
Click
on
Done
to
get
the
plot
with
more
real
estate.
This
is
exactly
the
plot
that
I
showed
using
the
script.
You
can
clearly
see
that
from
week
7
onwards,
there
might
be
a
growth
in
the
temperature
setting.
It
looks
like
people
are
increasing
the
temperature
as
time
progresses
from week 7
through
week
12.
I'm
going
to
close
this.
We
have
a
graph
to
visualize
the
trajectories
of
the
temperature
setting.
We
repeat
the
same
thing.
We
want
to
choose
a
model
for
that
process.
A
s
before,
I
built
the
same
three
models:
a no-growth,
a
linear
growth,
and
a
quadratic
growth.
I'm
going
to
look
at
the
fit
statistic
here.
This
time,
we
see
definitely
a
significant
improvement
in
going
from
the
no-
growth
to
linear
growth
in
terms
of
the
fit
statistics.
The
quadratic
growth
is
a
marginal
increase
over
the
linear
growth
model.
Again,
for
the
same
reason
as
before,
all
the
estimates
in
the
quadratic
slope
are
actually
not
significant.
To
keep
things
simple,
I'm
going
to
choose
the
simpler
model,
which
is
the
linear
growth
for
temperature.
The
last
process
is
the
pod
usage.
This
is
the
number
of
pods.
Now
we
can
see
clearly
an
increasing
trend,
more
so
for
the
Ecolabel
product,
which
means
people
are
using
more
and
more
products
when
they
use
Ecolabel
as
compared
to
Ariel,
which
is
a
P&G
product.
I
want
to
model
this.
Let
me
close
that.
Click
on
the
script
for
LG
CM
of
pod
usage.
I'm
going
to
look
at
the
fit
statistic.
A
gain,
I
see
a
good
model
fit,
especially
the
linear
and
the
quadratic.
For
the
same
reason
as
before,
I'm
going
to
choose
the
linear
model.
Here
I
want
to
look
at
the
estimates
for
the
quadratic
slope,
and
this
is
what
I
mean
by
not
choosing
the
quadratic
slope
because
you've
got
all
the
parameters
point unit
to
that
to
be
not
significant.
Now we
have
got
a
model
for
each
of
the
three
processes.
We
chose
a
no-growth
model
for
overall
satisfaction.
We
chose
a
linear
growth
model
for
low
temperature.
Now I'm
going
to
put
them
all
together
using
a
multivariate,
latent
growth curve model.
This
is
basically
all
the
three
processes
put
together.
Here
, I
want
to
show
you
the
similarity
between
a
confirmatory
factor
analysis
model
and
latent
growth curve model
as
was
pointed
out
in
the
previous
slide.
You
can
see
that
there
is
a
mean
structure
added
to
it
with
a
triangle
with
a
number
one,
and
there
are
lines
going
from
that
to
each
of
the
latent
variables.
If
I
right-click
and
use
the
Show
option
and
not
show
the
mean
structure,
you
can
see
the
familiar
confirmatory
factor
analysis
model
with
latent
variables
and
the
indicators
associated
with
each
one
of
them.
We
have
a
single
latent
variable,
intercept
for
the
overall
satisfaction.
We
have
two
latent
variables
for
the
temperature,
which
is
initial
intercept
and
the
slope.
We
have
the
same
two latent
variables
indicating
the
pod
usage.
Initial
level
as
represented
by
the
int
pods
and
the
rate
of
change
of
product
usage
as
indicated
by
the
slp
pods,
which
is
basically
the
slope
of
pods.
Let
me
put
back
the
means
activated.
Now we
can
actually
look
at
the
estimates
of
these,
which
are
really
one
of
the
important
pods
of
the
latent
growth curve model.
What
we
have
here
is
an
estimate
of
the
initial
level
of
satisfaction
at
week 9
because
that
was
the
starting
time
period
for
overall
satisfaction.
That's
about
71
on
a
scale
of
0-100.
This
is
the
average
temperature
setting
at
week 9,
which
is
36
degrees
Celsius.
Here
is
the
product
usage,
1.4
pouches.
Here
is
the
rate
of
change
of
product
usage
because
there
is
a
slope
of
product
usage,
the
latency
variable,
which
is
about
0.02.
People
are
using
slightly
more
as
time
goes
on.
That
is
what
we
get.
The
overall
fit
of
this
model
is
also
fairly
good.
I
think
we
saw
that.
CFI exactly
at
the
threshold
0.95,
and
our
upper
bound
of
the
RMSEA
is
definitely
less
than
0.1.
Now we
go
to
the
last
model,
which
is
the
hypothesis
that
Zhiwu
wanted
to
test,
where
we
want
to
see
if
product,
the
indicator
variable,
and
the
other
growth
factors
have
a
significant
impact
on
overall
satisfaction.
In
order
to
remove
the
clutter,
I
have
not
shown
all
the
indicators.
All
we
are
seeing
is
only
the
circles,
which
represent
the
latent
factors
for
each
of
the
growth
curve
models
and
a
single
product
variable
indicating
what
type
of
product
it
is.
Again, let
us
look
at
the
fit
of
this
model.
Fit
of
this
model
is
indeed
good.
We
have
a
0.95
for
the
CFI.
We
have
less
than
0.1
for
the
upper
bound
of
the
RMSEA.
We
will
look
at
more
fit
indices
after
we
interpret
some
of
the
estimates
here.
I'm
going
to
interpret
the
solid
lines
which
are
significant
coefficients.
We
have
a
significant
product
effect
from
the
product
variable
to
the
intercept
of
overall
satisfaction.
This
can
be
interpreted
basically
as
a
regression
coefficient,
which
is
the
average
level
of
satisfaction
for
product
coded
1
minus
the
average
level
of
satisfaction
for
product coded
0.
Ariel
is
coded
as
product
0,
so
we
have
much
more
satisfaction
with
Ariel,
a
delta
of
negative
9 in
favor
of
Ariel
on
a
scale
of
0-
100.
That
is
a
big
change.
Delta
in
favor
of
the
Ariel
product.
Let
us
look
at
the
product
effect
on
pods.
Again,
the
same
way,
average
amount
of
product
used
for
product
coded
1
minus
product
coded
0.
This
time,
we
are
using
more
of
the
Ecolabel
product.
If
you
are
a
manufacturer
of
Ariel,
this
is
good
news
for
you.
A
lso,
the
rate
of
change
of
product
use
is
also
more
for
Ecolabel
compared
to
Ariel,
or
0.02
pouches
from
week
to
week.
Finally,
we
have
the
intercept
of
temperature
having
a
negative
impact
on
the
overall
satisfaction,
which
means
higher
temperatures
lead
to
less
satisfaction.
Remember,
these
are
products
which
are
marketed
as
cold-wash
products.
That
means
they
should
work
better
in
cold
temperatures
and
not
higher
temperatures.
I
also
want
to
show
you
where
you
can
look
for
other
fit
statistics
beyond
what
is
coming
out
in
the
model
comparison
table.
Under
the
S
tructural Equation Model
in
red
triangle,
if
you
check
on
Fit
Indices,
which
I've
already
checked,
there
are
more
fit
indices
that
can
be
shown
at
the
bottom.
We
want
to
look
at
CFI
and
RMSEA,
which
we've
already
seen,
and
here
is
the
Standardized
Root
Mean S
quare
Residual,
which
I
discussed.
This
is
also
exactly
at
the
threshold
of
0.08.
All
in
all,
in
terms
of
fit
indices,
our
model
does
fit
quite
well.
Finally,
I
told
you
not
to
forget
the
residuals.
These
are
normalized
residuals
in
terms
of
the
measured
variables.
We
have
21
measured
variables,
eight
for
pods,
eight
for
temperatures,
four
for
overall
satisfaction,
and
one
for
the
product
variable.
This
is
a
21
by
21
matrix.
What
we
are
looking
for
is
numbers
which
are
outside
the
plus
2
minus
2
range.
There
are
just
too
many
numbers
to
look
at
in
the
table,
but
JMP
produces
a
heatmap.
Heatmap
option
is
also
under
the
red
triangle.
What
we
are
looking
for
is
dark
red
or
dark
blue.
Here,
we
have
two
dark
reds
which
are
relationship
between pod
usage
at
week 6
,
temperature
at
week
12,
pod
usage
at
week
6,
and
temperature
at
week 9.
Finally,
we
have
one,
because
this
is
just
a
mirror
image
of
the
one
that
is
here.
This
is
the
relationship
between
temperature
at
week
9
and
temperature
at
week
10,
which
is
not
modeled.
This
could
actually
be
modeled
by
adding
an
error
covariance,
which
I
did
not
do.
If
I
did
this,
the
model,
in
fact,
would
be
even
better.
I
want
to
go
back
to
the
presentation
and
summarize
what
we
have
found.
Oops, sorry,
wrong
slide.
In
terms
of
conclusion,
we
started
the
Graph
Builder
to
visualize
our
trajectories,
and
we
built
latent
growth
curve
model
using
the
SEM
platform.
We
extended
from
univariate
to
multivariate
models.
A
ll
our
models,
including
the
last
one,
had
acceptable
fit,
in
fact,
good
fit.
Product
had
a
significant
impact
on
OAR,
which
means
Ariel
is
better
than
Ecolabel
in
terms
of
its
overall
satisfaction
and
significant
impact
on
the
number
of
pods,
which
means
less
product
was
used
for
Ariel
compared
to
Ecolabel,
and
also
from
week
to
week.
Intercept
had
a
negative
impact
on
OAR,
which
means
people
prefer
lower
temperature
setting
than
higher
temperature
setting.
If
you
are
a
P&G
manufacturer,
this
is
good
news
for
you
because
Ariel
works
better
than
Eco
label
in
this
modeling
framework
that
we
have
done.
I'm
going
to
turn
it
over
to
Zhiwu
to
see
what
the
next
steps
are
from
this
model
results.
Zhiwu?
Thank
you
very
much.
Thank
you,
Narayanan,
and
very
excellent
presentation
and
wonderful
demo.
As
Narayanan
mentioned,
the
modeling
results
prove
the
product
has
a
significant
impact
to
the
overall satisfaction
of
the
performance
of
the
detergent
products
in
our
test.
This
result
provides
us the
confidence
we can make
a
very
clear
claim,
Ariel
products
is
a
favor
to
the
cold wash
can
be
used
less
than
the
normal
products.
This
is
also
modeling
confirm
the
consumer
behavior
change.
If
you
use
Ariel
product,
you
will
have
more
washing
loads
go
to
the
cold wash,
use
less
energy
and
use
less
product.
Also,
we
plan
to
conduct
bigger
size
consumer
study
for
including
the
more
covariates
variables
in
the
future
modeling
stage
like
the
additive
usage
and
the
washing
cycle
of
every
wash
and
the
low
size
per
wash.
This
is
our
next
step.
Next
slide.
Now we
would
like
to
take
question
if
you
have
any.
Thank
you
very
much
for
attending
the
presentation.
We
look
forward
to
your
questions
probably
in
the
JMP
Summit.
