Hi,
everyone.
I'm
Laura
Castro-
Schilo.
I'm
a
senior
research
statistician
developer
working
with
the
Structural Equation Models
platform.
I'm
really
excited
today
to
show
you
some
of
the
new
features
that
we
have
in
JMP
Pro
17.
One
of
the
big
ones
is
going
to
allow
us
to
explore
group
differences.
We're
going
to
talk
about
that
a
lot
today.
Our
plan
for
today
is,
hopefully,
we'll
spend
most
of
the
time
in
a
demo,
really
showing
you
those
new
features.
But
very
briefly,
before
we
get
into
that,
I
want
to
remind
you
what
Structural Equation Modeling
is,
why
you
might
want
to
use
it,
and
then
hopefully
through
the
demo,
I'll
show
you
how
to
use
it.
Now,
our
presentation
today
is
not
very
long.
What
I
also
want
to
do
is
show
you share
with
you
some
additional
resources from
previous
discovery
presentations
and
developer
tutorials
where
you'll
learn
a
lot
more
detail
on
how
to
use
SEM.
Now,
the
overview
of
new
features
we're
going
to
cover,
we're
going
to
first
talk
about
multiple
group
analysis
and
then
some
improvements
that
we've
done
for
longitudinal
modeling
within
SEM
and
for
survey
development.
After
we
go
over
those,
we'll
go
straight
into
the
demo
and
really
show
you
how
all
of
those
are
used.
Structural Equation Modeling
is
a
very
general
analysis
framework
for
investigating
the
associations
between
variables.
Now,
this
is
a
very
broad
definition,
and
that's
purposeful, because
Structural Equation Modeling
is
a
very
broad
technique
where
a
number
of
different
models
can
be
fit.
Here
I've
listed
a
few
of
the
models
that
you
could
fit
within
SEM,
but
this
is
not
an
exhaustive
list.
It
really
is
a
a
very
flexible
framework.
A
natural
question
that
might
come
to
mind
is,
if
I
can
do
some
of
these
analysis
somewhere
else,
then
why
would
I
want
to
use
a
SEM?
Sometimes
you
might
not
need
to
use
it,
right?
That
would
be
just
fine.
But
there
are
some
circumstances
in
which
SEM
would
be
particularly
helpful.
I've
included
here
a
list
of
what
those
circumstances
might
be.
The
first
is
sometimes
you
might
be
interested
in
understanding
the
mechanisms
by
which
things
happen.
This
is
a
circumstance
where
SEM
can
be
very
useful.
Oftentimes
when
you
want
to
understand
mechanisms,
that
means
that
you
have
variables
that
are
both
predictors
and
outcomes.
Yet,
not
many
statistical
techniques
allow
you
to
specify
models
where
you
can
have
a
variable
be
both
a
predictor
and
an
outcome.
That's
actually
something
that
is
very
natural
in
SEM.
If
this
is
something
that
you're
working
on,
SEM
could
be
very
helpful
for
you.
You
really
want
to
leverage
your
domain
expertise
if
you're
using
SEM.
The
reason
is
because
in
order
to
specify
your
models,
you
really
need
to
think
about
what
are
your
theories?
What
is
it
that
you
know
about
your
data?
You
come
up
with
those
theories,
you
translate
them
into
a
testable
model,
and
then
when
you
fit
your
models,
you
see
whether
or
not
there's
support
for
those
ideas
that
you
have.
Now,
a
very
important
use
case
for
SEM
is
when
you're
working
with
variables
that
cannot
be
measured
directly.
So
late-
in
variables
are
very
important
in
a
number
of
different
domains.
If
you're
interested,
for
example,
in
looking
at
customer
satisfaction
or
quality
of
a
product
in
the
social sciences.
There's
so
many
late-
in
variables,
personality,
intelligence,
those
are
some
of
the
cliche
things
that
you
would
hear.
But
really,
late-in variables
are
all
over
the
place.
If
you
work
with
those,
if
you
have
research
questions
that
entail
late-
in
variables,
then
you're
really
going
to
benefit
by
using
SEM.
A
somewhat
related
reason
to
use
SEM
is
that
if
you
have
variables
that
have
measurement
error
and
you
actually
want
to
account
for
that
measurement
error,
SEM
can
also
be
very
helpful.
I
say
that
this
is
related
to
the
late-in variables
because
the
way
in
which
we
account
for
the
measurement
error
is
by
specifying
late-in variables
in
SEM.
Measurement
error
can
have
sometimes
unexpected
consequences
on
our
inferences.
It
can
be
quite
useful
to
account
for
it.
Another
benefit
of
SEM,
and
this
is
one
thing
that
is
very
practical
really,
is
when
it
comes
to
having
missing
data,
which,
of
course,
are
all
over
the
place,
the
most
popular
estimation
algorithm
for
SEM
handles
missing
data
in
a
seamless
fashion
such
that
the
user
doesn't
really
need
to
do
anything.
Missing
data
are
handled
with
a
cutting
edge
algorithm
and
you
really
don't
have
to
worry
about
it
as
much.
If
you
have
missing
data,
sometimes
I
tell
people
even
if
you
just
have
a
simple
linear
regression,
you
can
benefit
from
using
SEM
just
because
missing
data
are
handled
and
it's
easy.
Lastly,
Path
Diagrams
are
a
critical
tool
for
Structural Equation Models.
Those
diagrams
are
very
helpful
because
sometimes
even
the
most
complex
statistical
models
can
be
conveyed
in
a
very
intuitive
fashion
by
relying
on
these
diagrams.
In
JMP,
we
use
these
diagrams
to
facilitate
the
specification
of
our
models,
but
also
to
convey
the
results
of
models.
Those
diagrams
can
be
very
helpful
when
you're
presenting
your
results
to
any
type
of
audience,
really.
All
right,
so
this
is
just
a
very
brief
list
of
why
you
might
want
to
use
SEM.
I
do
want
to
share
a
link
here
to
a
presentation
that
I
gave
along
with
James Cuffler,
who's
also
in
job
development.
We
did
a
developer
tutorial
where
we
actually
went
into
a
much
more
depth
about
the
reasons
why
you
might
want
to
use
SEM.
If
you
want
to
check
that
out,
I
just
wanted
to
share
this
link
here.
If
you
download
the
slides
from
the
community,
you
don't
have
to
type
this
long
link.
You
can
just
click
on
that
and
check
that
video
out.
All
right,
so
how
to
use
SEM.
Again,
I'm
going
to
go
into
a
demo
and
I'll
show
you
how
to
use
SEM,
but
my
demo
is
not
going
to
be
too
focused
on
a
tutorial
type
of
presentation,
mostly
because
of
time
constraints.
We
want
to
keep
this
short
and
sweet.
What
I
want
to
do
in
this
slide
is
share
with
you
additional
video
presentations
where
you
can
go
and
learn
more
in
a
tutorial
form
how
to
use
Structural Equation Models
for
a
few
different
case
studies,
basically.
Here,
this
first
video
is
a
link
where
I
covered
how
to
model
survey
data
and
latency
variables.
We
cover
things
like
confirmatory
factor
analysisand
path
analysis
with
and
without
latency
variables.
If
you
have
longitudinal
data,
this
video
can
be
quite
helpful.
Here
I
went
over
how
to
fit
late-in growth
curve
models
and
how
to
interpret
those
results.
We'll
do
a
little
bit
of
longitudinal
modeling
here
today
in
the
demo,
but
we
won't
be
able
to be
able
to
go
into
the
details
again
in
a
tutorial
way.
I
definitely
encourage
you
to
watch
that
if
you
are
interested.
If
you
don't
have
prior
SEM
experience,
I
very
much
encourage
you
to
watch
this
other
video
where
James
Cuffler
and
I
talked
about
building
Structural Equation Models
in
JMP
Pro.
This
one
is
very
introductory,
and
so
you
might
want
to
start
with
that
one
prior
to
going
to
the
others.
Okay,
so
now
it's
time
to
get
into
a
little
overview
of
the
new
features
in
JMP
Pro
17.
Multiple
group
analysis
is
a
feature
that
I've
been
really
looking
forward
to
presenting
on
because
this
is
something
that
extends
all
of
the
models
that
can
be
fit
within
SE
M.
It
does
so
by
allowing
us
to
investigate
similarities
and
differences
across
sub-populations.
We
do
this
by
incorporating
a
grouping
variable
into
our
analysis.
Now,
the
most
popular
multiple
group
analysis
examples
usually
show
a
grouping
variable
that
has
few
levels.
Things
like
demographic
variables
are
used
very
often.
Indeed,
in
the
demo
I'm
going
to
do,
I'm
also
going
to
use
a
simple
demographic
variable.
But
really,
there's
no
limit
to
how
many
levels
you
really
should
have.
What
really
matters
is
how
many
observations
do
you
have
for
each
level.
You
want
to
have
a
relatively
good
sample
size
for
each
of
those
subgroups.
Now,
there
is
a
general
strategy
for
the
analysis.
We're
going
to
see
this
in
practice,
but
I
want
you
to
start
thinking
about
how
this
really
works.
It's
actually
quite
simple.
What
we
do
in
multiple
group
analysis
is
fit
two
models.
One
of
those
models
is
going
to
be
a
more
restricted
version
of
the
other.
Once
we
fit
both
of
them,
we'll
be
able
to
do
a
likelihood
ratio
test
or
a
high
square
difference
test
in
order
to
make
an
inference
about
whether
the
restrictions
that
we
imposed
in
one
of
the
models
are
in
fact
tenable.
This
is
how
we
figure
out
whether
there
are
statistically
significant
differences
across
groups.
Again,
we'll
see
that
play
out
in
the
demo
.
In
terms
of
longitudinal
data
analysis,
we've
made
it
a
lot
easier
to
interpret
the
results
from
your
models
by
looking
at
the
model
implied
trajectories
through
a
new
predicted
values
plot.
We
also
have
made
it
a
lot
easier
to
specify
multivariate
growth
curves.
If
you're
familiar
with
these
models,
they
allow
you
to
investigate
the
association
of
multiple
processes
over
time.
They
can
be
very
helpful,
but
it
used
to
be
a
little
tedious
in
terms
of
how
to
specify
those.
Now
we've
done
that
very
easy
and
fast
through
the
use
of
model
shortcuts.
For
some
advanced
applications,
we've
also
made
it
easier
to
define
an
independence
model
based
on
what
users
want
to
have
as
the
independence
model.
There
are
also
some
improvements
for
surveys.
This
really
is
mostly
focused
on
streamlining
your
workflow
for
developing
surveys.
Usually
the
analytic
workflow
starts
by
using
exploratory
factor
analysis,
and
then
you
take
those
results
and
confirm
them
with
an
independent
sample
using
confirmatory
factor
analysis
in
SEM
.
What
we've
done
with
the
help
of
Jianfeng
Ding,
who
is
the
developer
for
Exploratory
Factor
Analysis,
we've
been
able
now
to
link
the
two
platforms
by
basically
allowing
you
to
copy
the
model
specification
from
exploratory
factor
analysis
and
then
paste
that
into
SEM
so
that
you
can
easily
and
quickly
confirm
your
results.
We
also
have
a
new
shortcut
for
switching
the
scale
of
your
late-in
variables.
Sometimes
this
is
helpful
when
you're
developing
surveys
for
specifying
models.
We
also
have
a
number
of
more
new
heat
maps
that
are
just
going
to
make
it
easier
to
interpret
the
results
of
your
analysis.
Now,
last
but
not
least,
our
platform
has
always
been
very
fast.
But
in
this
release,
Chris
Gotwell
put
a
lot
of
awesome
effort
toward
improving
even
more
the
performance
of
our
internal
algorithms.
If
you
have
lots
of
variables
or
lots
of
data,
definitely
give
it
a
shot.
I
am
very,
very
impressed
and
excited
about
what
we
have
to
offer
in
terms
of
the
performance
of
the
platform
as
well.
Okay,
so
it's
time
for
the
demo.
Let's
go
ahead
and
show
you
what
I
have
over
here.
I
have
a
journal
where
I'm
going
to
work
through,
hopefully
we
have
enough
time
to
work
through
three
examples.
The
first
one
here,
perhaps
not
surprisingly,
uses
our
big
class
data
table.
It's
going
to
be
a
very
simple
example
just
to
introduce
the
notions
behind
multiple
group
analysis.
Now,
what
I'm
going
to
do
here,
we
have
two
variables,
right?
Height
and
weight.
What
I
want
to
do
is
investigate
the
association
between
these
two
variables
by
sex.
I'm
going
to
go
to
the
Analyze
menu,
go
down
to
Multivariate
Methods,
and
then
Structural
Equations
Models.
I'm
going
to
use
both
of
those
variables
and
click
on
Model
Variables.
Now,
the
brand
new
feature
of
multiple
group
analysis
can
be
found
in
this
launch
dialog
under
this
Groups
button.
This
button
is
new
and
that's
what's
going
to
allow
us
to
select
our
grouping
variable
and
click
on
groups
in
order
to
use
that
as
our
grouping
variable.
We're
going
to
look
at
how
males
and
females
and
whether
they
differ
basically
on
their
association
between
height
and
weight.
We're
going
to
click O
kay.
Now,
this
is
the
platform.
You
can
see
if
you
have
seen
our
platform
before,
it
looks
very
similar
as
before,
with
the
exception
of
these
new
tabs
right
here.
The
tabs
are
there
to
tell
us
about
the
different
groups
that
we
have
in
our
analysis.
In
this
case,
there's
only
two
levels
for
our
grouping
variables.
We
have
a
tab
for
the
females
and
a
tab
for
males.
One
of
the
things
you'll
notice
is
that
the
Path
Diagrams
have
a
model
already
as
a
default
for
each
of
those
groups.
Those
default
models
are
the
same.
That's
why
when
I
switch
tabs,
nothing
really
changes.
The
Union
tab,
as
the
name
implies,
it
shows
us
what's
in
common
across
all
of
our
grouping,
well,
the
levels
of
our
grouping
variable.
Here,
this
is
why
this
diagram
also
looks
the
same.
In
order
to
specify
a
simple
linear
regression
in
SEM
,
here,
I'm
just
going
to
select
in
this
From
List
the
height
variable,
and
then
in
the
to
list,
I'm
going
to
select
weight.
I'm
going
to
link
those
two
variables
with
a
one
headed
arrow,
which
is
what
adds
that
regression
path
to
my
model.
This
is
just
a
simple
linear
regression
where
height
is
predicting
weight.
Now,
sometimes
I
like
to
right-click
on
the
canvas
of
the
Path
Diagram
and
I
go
to
customize
diagram
just
to
make
the
nodes
a
little
bit
larger
because
I
find
that
sometimes,
especially
when
the
diagrams
are
small,
that
looks
a
lot
nicer.
This
is
just
a
simple
linear
regression.
Now,
notice
that
because
I
did
my
model
specification
under
the
Union
tab,
both
the
females
and
the
males
inherited
those
same
changes
and
specifications
to
the
model
that
I
made.
If
I
make
any
changes
within
a
group
specific
tab,
then
those
changes
will
only
apply
to
that
group.
But
in
this
case,
what
I
want
to
do
is
fit
an
initial
model
where
both
males and
famales
and
females
get
their
own
estimates
for
this
linear
regression.
Now,
keep
in
mind
that
the
estimation
of
this
model
is
all
done
simultaneously.
We're
not
separately
fitting
this
model
for
females
and
for
males.
Everything
is
done
simultaneously,
but
I'm
still
able
to
allow
each
of
the
groups
to
have
their
own
estimates
for
the
model.
I'm
going
to
click
on
Run,
and
we'll
see
there's
a
model
comparison
table
where
we
can
learn
a
lot
about
the
fit
of
the
model.
But
now,
something
that's
new
in
our
report
is
that
we
have
these
tabs
for
each
of
our
groups.
We
have
a
tab
for
the
females
and
a
tab
for
the
males.
Now,
if
you
focus
on
the
regression
coefficient,
for
example,
I
can
go
back
and
forth
and
realize
that
I
do
have,
in
fact,
a
different
estimate
for
that
coefficient.
Now,
the
coefficient
looks
different,
but
I
don't
have
a
test,
a
formal
statistical
test
that
tells
me
whether
or
not
that
association
is
statistically
significant.
The
difference
and
the
association
is
different.
At
any
rate,
the
males
here
have
about
3.4,
female
have
a
little
bit
larger
value.
But
what
we
really
want
is
to
fit
a
second
model
where
we
force
an
equality
constraint
on
that
parameter
estimate,
and
then
we
can
use
that
to
compare
against
this
model.
Let's
go
ahead
and
do
that.
I'm
going
to
be
on
the
Union
tab
and
I'm
going
to
select
that
regression
path
and
I'm
going
to
click
the
button,
Set
Equal.
This
is
going
to
bring
up
this
dialog
which
is
just
going
to
ask
me
to
confirm
that
I
do
want
to
apply
this
equality
constraint
across
all
of
my
groups,
which
I
do.
I'm
going
to
click
Okay.
Now
notice
that
I
have
this
new
label
that
was
put
here
on
the
edge.
If
I
look
at
the
female
tab
and
the
male
tab,
that
label
is
still
showing
up
on
that
edge
on
that
arrow.
That
is
our
way
to
convey
to
you,
the
user,
that
the
same
parameter
estimate
is
going
to
be
used
basically
to
describe
that
association.
Okay,
so
let's
go
back
and
model
name.
We're
going
to
change
this
to
be
regression
effect
is
equal.
We
force
that
to
be
equal
in
this
model.
We're
going
to
go
ahead
and
click
on
Run.
Now,
again,
we
could
look
at
our
model
comparison
to
look
at
the
fit
of
my
different
models.
I
can
select
the
two
models
that
I
just
fit,
and
because
one
of
those
models
is
a
restricted
version
of
the
other,
we
call
this
that
the
models
are
nested,
we
can
actually
do
a
likelihood
ratio
test.
That
is
done
very
easily
in
our
platform
simply
by
selecting
the
two
models
and
clicking
on
Compare
Selected
Models.
We
will
obtain
a
difference
in
the
Chi
square,
which
represents
the
change
in
the
misfit
of
the
model.
We
also
look
at
the
difference
in
degrees
of
freedom
between
the
two
models
and
the
differences
in
the
Fit
according
to
some
of
the
most
popular
Fit
statistics
in
SEM.
Now,
according
to
this
specific
test,
it
appears
that
the
change
in
Chi
square,
the
increase
in
misfit
is
not
statistically
significant.
If
we
use
just
this
Chi
square
difference
test,
we
would
then
come
to
the
conclusion
that
even
though
those
two
values
are
different,
they're
not
statistically
different.
Now
we
could
go
back
down
here
to
our
tab
results
and
you
can
see
that
the
regression
coefficient
is
the
same
even
when
I
go
across
the
tabs.
We
could
then
say,
well,
there's
no
difference
between
males
and
females
in
terms
of
how
height
predicts
weight.
This
is
a
very
simple
example
of
how
we
could
use
equality
constraints
across
groups
in
order
to
test
a
specific
hypothesis.
Now,
as
you
can
imagine,
I
could
go
back
into
my
model
specification
and
I
could
put
equality
constraints
also
on
the
variance
of
height
and
on
the
residual
variance
of
weight.
If
that
is
something
that
is
of
interest
to
me,
if
I
want
to
test
those
differences,
this
framework
allows
me
to
do
that.
Now,
a
lot
of
times
you're
going
to
have
more
complicated
models
well
beyond
linear
regression,
or
you
might
have
more
levels
of
your
grouping
variable,
and
that's
totally
fine.
This
is
a
simple
example
that
hopefully
you
can...
That
allows
you
to
see
how
you
could
extend
this
into
a
more
complicated
setting.
Okay,
so
that
is
this
example.
I
want
to
move
on
to
an
example
that
uses
longitudinal
data.
Now,
we're
not
going
to
move
away
from
multiple
group
analysis
entirely.
We're
basically
going
to
highlight
some
of
those
longitudinal
analysis
improvements,
but
then
still
bring
back
the
notion
of
multiple
group
analysis.
For
this
example,
I
want
you
to
imagine
that
we
have
data
table
where
we
have
data
from
students
that
have
taken
an
academic
achievement
test
for
four
consecutive
years.
Perhaps
what
we
really
want
to
find
out
from
these
data
is
whether
student's
achievement...
How
is
it
developing
over
time?
Whether
males
and
females
differ
in
their
trajectories
over
time?
These
are
going
to
be
the
two
questions
that
we're
going
to
focus
on
for
this
particular
example.
Now,
there
is
a
sample
data
table
that
you
will
find
within
our
sample
data
folder.
It's
called
Academic
Achievement.
You
could
use
that
to
follow
along
with
this
example.
In
this
data,
we
have
100
rows.
Each
row
represents
a
different
student
that
took
this
academic
achievement
test.
You
can
see
that
here,
these
four
columns
represent
the
scores
on
that
multiple
choice
test
that
was
taken
for
years
in
a
row.
Those
are
the
data
that
I'm
going
to
focus
on
for
fitting
a
longitudinal
model.
I'm
going
to
go
to
the
Analyze
menu,
Multi
Variate
Methods,
Structural Equation Models,
and
those
four
variables
are
selected.
I'm
just
going
to
click
on
Model
Variables
in
order
to
use
those
in
SEM.
I'm
going
to
click
Okay.
Remember,
the
first
question
was,
how
do
students'
academic
achievement
develop
over
time?
We
want
to
characterize
that
growth
or
figure
out
whether
there
is
growth
indeed.
We
have
our
model
shortcut
down
at
the
bottom
left,
and
you
can
see
that
under
the
Longitude
analysis
menu,
we
have
a
new
option.
We're
going
to
get
to
this
option
later
today,
multivariate,
late
in
growth
curves.
But
we
also
have
had
a
few
other
options
here
that
make
longitudinal
modeling
very
quick
and
simple.
For
this
example,
I'm
going
to
use
the
Fit
and
Compare
Growth
models.
When
I
do
that,
three
different
models
are
fit.
I
obtain
a
Chi
square
difference
test
for
all
of
the
possible
combinations
here.
If
I
look
at
the
Fit
indices
and
also
the
results
from
this
Chi
square
difference
test,
I
will
recognize
that
the
best
fitting
model
here
is
the
linear
growth
curve
model.
In
other
words,
it
appears
that
the
scores
on
this
academic
achievement
test
over
time
can
be
best
characterized
by
linear
growth.
Based
on
that,
I
will
go
ahead
and
focus
on
interpreting
the
results
from
this
linear
growth
curve
model.
I'm
going
to
open
that
and
recall
that
that
one
of
the
new
features
for
longitudinal
modeling
is
a
new
predicted
values
plot
that
allows
us
to
interpret
the
results
of
our
models
a
lot
more
easily.
If
you're
familiar
with
growth
curve
models,
you
know
that
some
of
the
key
parameter
estimates
are
these
right
here.
They
tell
us
on
average
how
our
students
where
do
they
start
and
how
are
they
changing
over
time
and
how
much
variability
there
is
in
those
trajectories.
Under
the
red
triangle
menu
of
this
particular
model,
if
I
scroll
down,
I'm
going
to
find
an
option
called
predicted
values
plot.
If
I
click
on
that,
you
will
see
that
as
a
default,
we
show
you
box
plots
of
the
predicted
values
for
all
of
the
outcome
variables
in
the
model.
Now,
when
you
have
longitudinal
data,
we
have
a
very
convenient
option
here
that
allows
you
to
connect
the
data
points
and
actually
obtain
a
spaghetti
plot
that
shows
you
each
of
the
individual
predicted
trajectories
by
the
model.
Now,
it's
pretty
cool
because
the
plot
is,
in
fact,
linked
to
the
data
table.
Whatever
selections
you
have
here
on
the
plot,
you
can
also
see
those
in
your
data
table,
which
is
something
that
you
know
to
expect
from
JMP.
In
terms
of
interpreting
the
results
of
the
model,
it's
no
surprise
that
these
are
all
straight
lines
because
we
fit
a
linear
model.
But
you
can
certainly
see
that
there
is
a
lot
of
variability
in
the
way
these
students
are
changing.
Some
students
start
on
the
top
at
the
beginning
and
are
still
increasing.
Other
students
are
starting
low
and
are
actually
exhibiting
a
little
bit
of
decline
over
time.
But
we
also
see
an
average
trajectory
here
that
seems
to
show
a
little
bit
of
increase
over
time.
On
average,
there
is
some
increase,
but
there's
a
lot
of
variability
on
how
people
are
changing.
Of
course,
one
of
the
natural
questions
you
might
have
is,
what
factors
predict
those
different
trajectories,
like
the
variability
in
that
intercept
slope,
that's
something
that
I've
covered
in
other
presentations,
so
I'm
not
going
to
talk
about
that
now.
But
again,
I
encourage
you
to
use
the
predictive
values
plot
to
better
interpret
your
longitudinal
analysis.
We
talked
about
users
being
able
to
specify
their
own
independence
model.
That
is
something
that
we
do
here
in
the
model
comparison
table
and
can
be
very
useful
for
longitudinal
analysis.
We
do
have
an
independence
model
that
is
fed
by
default,
but
if
you
choose
to
change
that,
then
you
could
always
right-click
on
any
given
model
that
you
want
to
set
as
the
independence
independence
model,
and
we
will
take
care
of
that
change
for
you.
That
is
an
advanced
technique.
I
very
much
advise
you
to,
if
you're
not
familiar
as
to
what's
the
proper
independence
model
for
your
analysis,
you
should
really
take
a
look
at
the
literature
to
make
sure
that
you're
using
a
good
independence
model
because
it
really
varies
sometimes
by
context.
I'm
sitting
next
to
this
beautiful
window
and
the
sun,
it's
a
gorgeous
day
so
I'm
going
to
have
to
adjust
here
my
computer
so
that
I
don't
have
all
the
light
on
my
face.
I
apologize
for
that.
Okay,
so
let's
get
back
to
this
question.
We
said
that
how
do students
achieve
and
develop
over
this
period
of
time?
We
now
have
an
understanding
that
it
develops
in
this
linear
fashion
and
that
there
is
substantial
variability.
That's
the
answer
to
that
question.
Well,
the
next
thing
is,
do
males
and
females
differ
in
these
trajectories?
The
way
we're
going
to
acknowledge
and
address
that
question
is
by
using
multiple
group
analysis.
T
his
could
be
back
in
the
platform,
we
could
use
the
main
triangle
menu
to
redo
and
relaunch
our
analysis.
Now
what
we're
going
to
do
is
bring
this
grouping
variable,
I
have
a
sex
as a
groups
variable.
Just
by
doing
this,
we'll
be
able
to
invoke
our
multiple
group
analysis
functionality.
I'm
going
to
click
Okay,
and
now
you
can
see
that
our
report
for
the
platform
has
the
levels
of
our
grouping
variable
here
as
tabs.
Just
as
before,
you
can
see
that
the
males
and
the
females
have
the
same
model
as
a
default,
but
we
can
make
changes
to
that.
We're
going
to
work
within
the
Union
tab
because
I
want
the
changes
that
I'm
about
to
do
to
the
model
specification,
I
want
them
to
apply
for
both
males
and
females.
I
will
also
highlight,
and
this
is
just
a
little
side
note,
that
under
the
Status
tab,
you're
going
to
find
group
specific
information
that
we
didn't
have
before
when
we
didn't
have
multiple
group
analysis.
You
can
have
some
information
about
your
data,
missing
data,
and
so
on
that
is
specific
to
the
groups.
Okay,
so
let's
go
ahead
and
answer
this
question.
Do
males
and
females
have
differences
in
their
trajectories?
Well,
I
already
know
that
the
linear
model
fits
best,
so
I'm
going
to
go
to
our
model
Shortcuts,
Longitude
Analysis,
and
I'm
going
to
click
on
the
linear
latency
growth
curve.
The
Shortcuts
very
quickly
set
up
the
model
for
me,
make
it
very
simple,
and
they
do
that
across
all
of
the
levels
of
the
grouping
variable.
I
have
the
linear
growth
curve
model.
Notice
that
these
key
aspects
of
the
model,
the
estimates
that
really
characterize
the
change
in
our
data,
don't
have
any
labels
on
those
edges,
which
means
that
they're
freely
estimated
across
males
and
females.
My
first
model
here
is
a
linear
growth
curve
model.
I'm
just
going
to
put
a
little
keyword
here.
Oops,
I
erased
it.
Linear
growth
curve.
But
I
wanted
to
include
here
that
this
is
freely
estimated
right
across
the
groups.
I'm
going
to
click
on
run.
Excellent.
We
can
see
here
some
Fit
indices.
In
my
report,
I
can
see
a
tab
for
the
males
and
for
the
females.
Of
course,
as
you'd
expect,
if
I
go
back
and
forth,
I
could
take
a
look
at
the
results
for
the
females
and
then
go
back
and
look
at
how
those
results
are
perhaps
different
for
the
males.
This
is
interesting.
There
appear
to
be
some
differences,
but
again,
we
might
want
to
figure
out
whether
the
differences
that
we
observe
just
from
looking
at
these
estimates
but
those
are
in
fact,
statistically
significant.
What
I'll
do
is
I'm
going
to
go
back
to
my
model
specification
and
I'm
going
to
do
an
OmniVis
test.
In
other
words,
rather
than
just
putting
an
equality
constraint
on
one
of
these
estimates,
I'm
actually
going
to
do
that
for
all
of
these
estimates,
the
intercept
mean,
the
mean
for
the
slope,
and
the
covariance
of
the
intercept
and
slope,
and
their
variances.
You
don't
have
to
do
it
this
way,
but
really
it's
your
research
question
that
should
be
guiding
where
do
you
place
those
equality
constraints?
In
my
case,
I
just
want
to
do
an
omniVis
test
where
I
figure
out
whether
the
trajectories
for
males
and
females
are
different
and
whether
or
not
I
need
a
separate
estimate
for
those
parameters.
I
have
all
of
those
edges
selected
and
I'm
going
to
click
on
set
equal.
Here
I
confirmed
that
I
do
want
those
equality
constraints
across
both
groups.
This
is
actually
quite
helpful
when
you
have
more
than
two
levels
in
your
grouping
variable.
It
might
be
that
you
want
equality
constraints
across,
say,
two
groups
but
not
the
third.
You
can
uncheck
some
of
those
groups
here
if
you
needed
to.
I'm
going
to
click
Okay.
Now
all
of
those
edges
got
a
different
label.
You
can
see
that
if
I
go
and
look
at
the
males
and
the
model
for
the
females,
those
labels
are
the
same.
Again,
just
to
remind
us
that
we're
going
to
estimate
only
one
estimate
for
each
of
those
edges
across
groups.
Okay,
so
this,
once
again,
is
a
linear
growth
curve,
but
I
have
equal
growth
estimates.
Let's
go
ahead
and
run
that
model.
We
can
see,
again,
we
could
focus
on
the
fit
of
this
model.
It
doesn't
seem
to
be
as
good
as
the
previous
one.
Because
this
second
model
is
a
restricted
version
of
the
first,
we
can
actually
select
those
two
models
and
do
a
meaningful
comparison
by
clicking
on
Compare
Selected
Models.
As
before,
we
are
able
to
see
here
the
change
in
the
Chi
square
along
with
the
change
in
the
degrees
of
freedom.
This
tells
us
how
much
increase
in
misfit
is
there
in
our
model,
and
is
that
increase
in
misfit
statistically
significant?
If
it
is,
which
in
this
case
it
is,
then
we
basically
are
saying
that
those
equality
constraints
are
not
tenable.
It
was
not
a
good
idea
to
place
those.
Now
we
can
say
with
a
formal
statistical
test
that
there
are
statistically
significant
differences
in
the
trajectories
across
males
and
females.
Now,
you
might
want
to
look
at
those
differences
by
using
the
predicted
values
plot.
That's
something
that
we
can
do
just
by
going
into
the
red
triangle
menu.
But
what
I'm
going
to
do
first,
actually
is
I
don't
really
want
to
look
at
the
model
that
has
the
equal
growth
estimates
because
we
just
realized
that
those
equality
constraints
were
really
not
a
good
idea.
I'm
not
going
to
look
at
that.
Instead,
I'm
going
to
look
at
the
first
model
we
fit,
and
I'm
going
to
do
the
same
for
the
males
here.
Under
the
red
triangle
menu,
I'm
going
to
click
on
Predicted
Values
Plot,
and
I'm
going
to
connect
those
points
because
I
know
my
data
are
longitudinal.
This
is
the
plot
that
is
specific
to
the
males,
to
the
male
sample.
But
it
would
be
really
helpful
to
look
at
this
plot
side
by
side
with
the
plot
for
the
females.
It's
actually
quite
nice
that
all
of
our
red triangle
menu
options
here
are
automatically
turned
on
across
all
of
your
groups,
so
you
don't
have
to
go
group
by
group
turning
on
the
things
you
want
to
see.
But
another
trick
that
I
really
like
is,
when
you
have
a
tabbed
report,
you
can
always
right-
click
on
it
and
change
the
style
of
the
report
so
that
it's
on
a
horizontal
spread.
This
is
going
to
allow
you
to
see
the
tabs
side
by
side,
the
content
of
them.
I'm
going
to
click
on
H
orizontal
Spread.
Now
notice
that
I
have
the
males
and
the
females
side
by
side.
I'm
going
to
use
the
red
triangle
menu
along
with
the
option
or
Alt
key
in
order
order
to
turn
off
the
summary
of
fit,
the
parameter
estimates,
and
the
diagram.
Really,
all
I
want
to
see
is
the
predicted
values
plot.
I'm
going
to
click
Okay.
Perfect.
Now
I
can
see
the
predicted
values
plot
for
the
males
and
for
the
females.
I
can
see
that
side
by
side.
Very
purposefully,
we
have
here
the
Y
axis
in
the
same
scale
so
that
these
plots
are
comparable.
Now
you
can
see
how
the
trajectories
differ.
We
see
that
there's
a
lot
more
spread
for
the
sample
for
the
females.
There
also
seems
to
be
a
little
bit
of
a
difference
on
that
average
trajectory
in
the
amount
of
growth.
Again,
there's
many
more
follow
up
tests
that
we
could
do
here
in
order
to
figure
out
where
the
specific
differences
lie.
If
we
wanted
to
test
that,
we
could
say,
well,
is
there
a
difference
specifically
in
the
variance
of
the
slope?
We
could
put
that
equality
constraint
and
do
more
specific
tests
as
followups.
But
for
now,
I
hope
that
just
showing
you
this
example
really
allows
you
to
see
how
multiple
group
analysis
can
be
used
in
a
more
complex
setting
and
how
this
new
predictive
values
plot
can
be
used
to
really
facilitate
the
interpretation
of
your
longitudinal
models.
All
right.
We're
almost
at
the
end
of
the
demo
and
what
I
want
to
do
very
quickly
with
the
same
data,
I
really
wanted
to
highlight
the
multivariate
growth
curves
shortcut.
L
et
me
go
ahead
and
go
back
here
to
the
Structural Equation Models
platform,
and
this
time,
imagine
that
we
have
two
sets
of
scores
over
time.
So
we're
going
to
be
looking
at
two
processes.
We
don't
just
have
academic
achievement
on
that
one
test.
We
have
it
on
two
different
tests
and
we
want
to
see
how
those
two
processes
are
changing.
How
are
they
related
over
time?
I'm
going
to
use
all
of
these
variables
here,
click
on
Model
Variables
and
Okay.
U
nder
the
model
shortcut,
remember
that
longitudinal
analysis
multivariate latent
growth
curve,
that
shortcut
allows
me
to
select
variables
for
one
specific
process.
Here,
I
might
have
those
first
four
variables.
That
was
my
first
process
I
want
to
look
at.
Let's
just
say
that
those
were
math
scores.
I'm
going
to
call
that
math.
Y
ou
get
to
choose
here
what
type
of
growth
you
want
to
specify
for
that
specific
process
for
that
set
of
variables.
We're
going
to
stick
to
a
linear
growth,
and
then
we
can
click
the
plus
button
in
order
to
have
that
done
for
us
right
away.
Y
ou
can
see
the
preview
in
the
background
here.
W
e
have
an
intercept
and
a
slope
for
math.
T
hen
we
can
change
the
name
here.
Maybe
the
second
process
is
science,
and
now
we
can
select
the
variables,
the
repeated
measures
for
that
science
test
over
the
four
years.
A
gain,
we're
going
to
stick
to
the
linear
model,
and
we're
going
to
click
the
plus
button.
V
ery
quickly,
that
model
is
changing
there
on
the
background.
We're
done
now.
So
I'm
just
going
to
click
Okay.
A
gain,
now
I
could
just
click
Run
and
very
quickly
get
the
results
for
that
model.
This
is
an
advanced
application,
but
it
is
a
really
interesting
one
because
it
allows
you
to
look
at
how
the
initial
time
point,
the
intercepts
across
two
processes
in
this
case,
how
are
those
intercept
scores
related?
Are
they
associated?
A
lso
the
rates
of
change
over
time.
If
you
have
a
higher
score
in
math,
do
you
also
tend
to
have
not
just
a
higher
score,
but
a
higher
slope
over
time
in
math?
Does
that
mean
you
also
have
a
higher
rate
of
change
in
science?
A
ccording
to
this,
you
do,
because
we
have
a
positive
association
between
those
two
factors.
Again,
just
highlighting
some
of
that
new
functionality.
My
very
last
example
is
for
survey
development.
This
is
going
to
be
very
brief,
I
promise.
Let's
just
say
here
that
we
want
to
figure
out
what
are
the
key
drivers
of
customer
satisfaction?
W
e
know
that
perceived
quality
of
our
product
and
the
reputation
of
our
brand
are
really
important.
But
really,
before
we
can
even
answer
any
questions
about
customer
satisfaction,
we
really
need
to
make
sure
that
we
have
a
valid
and
reliable
way
to
assess
those
variables.
Because
these
are
variables
that
are
not
observed
directly,
they're
latent
variables,
and
therefore,
it's
difficult
to
make
sure
that
we
are
measuring
them
in
a
reliable
and
valid
way.
S
urvey
development
is
all
about
achieving
that
goal.
I
have
an
example
here
that
is
going
to
allow
us
to
see
how
exploratory
factor
analysis
is
now
linked
to
SEM
so
that
you
can
do
survey
development
in
a
really
streamlined
fashion.
I
have
843
rows
in
this
data
table.
Each
row
represents
an
individual
who
filled
out
a
survey.
In
that
survey,
they
gave
us
ratings,
answered
questions
about
the
perceived
quality
of
our
product.
They
also
gave
us
different
answers
for
the
perceived
brand
of
our
brand.
T
hen
they
also
answer
questions
about
their
satisfaction
with
the
product.
This
could
be
things
like,
how
likely
are
you
to
recommend
our
product
to
someone
you
know?
Those
types
of
questions.
I
already
have
a
saved
script
for
the
factor
analysis
platform.
I'm
not
going
to
get
into
the
details
of
how
you
use
this
platform,
but
I
do
want
to
focus
on
the
fact
that
the
results
from
this
analysis
are
right
here
in
the
rotated
factor
loading
matrix.
That
is
the
key
result
from
this
analysis.
U
sually,
what
we
want
to
see
here
is
that
the
questions
that
are
supposed
to
measure,
in
this
case,
satisfaction,
that
they
are
in
fact,
loading
into
the
same
factor.
In this
case
they
are,
and
that's
good
news.
We
see
the
same
pattern
for
quality.
The
more
substantial
loadings
are
for
these
first
three
questions
of
quality.
Notice
that
there
is
one
quality
question
that
doesn't
seem
to
have
a
good
high
loading
in
any
of
the
factors.
So
maybe
we
would
go
back
and
make
sure
that
the
wording
of
that
question
is
good,
or
we
might
just
want
to
throw
out
that
question
altogether.
There's
also
a
couple
of
questions
for
perceptions
of
our
brand
that
didn't
seem
to
do
very
well.
A
gain,
usually
you
do
very
careful
selection
of
your
questions.
You
would
go
back,
read
what
were
those
questions,
is
there
something
we
should
tweak,
or
shall
we
just
get
rid
of
them?
Now,
for
the
time
being,
the
feature
I
want
to
highlight
is
that
under
the
red
triangle
menu
of
this
model,
there
is
a
new
option
for
copying
the
model
specification
for
SEM.
I'm
going
to
click
that.
W
hat
it
does
is
that
the
loadings
that
are
bold
here
in
our
final
rotated
factor
loading,
those
loadings
are
going
to
be
stored
so
that
we
can
use
them
in
the
SEM
platform.
Normally,
you'd
want
to
collect
a
new
independent
sample
so
that
you
can
confirm
these
exploratory
results.
Now,
let's
just
assume
for
a
minute
here
that
this
data
table
is
my
new
independent
sample,
and
I
would
now
go
to
Analyze,
Multivariate
Methods,
Structural Equation Models,
and
I
can
use
all
those
same
variables,
like
on
model
variables,
and
then
Okay
to
launch
the
platform.
Normally,
again,
you
want
to
confirm
the
results
that
you
found
with
an
independent
sample.
What
you
can
do
is
in
the
main
red
triangle
menu,
you
can
click
on
paste
model
specification.
N
ow
notice
that
the
factor
loadings
from
the
factor
analysis
platform
were
rescaled
by
the
standard
deviations
of
the
indicators.
I'm
going
to
click
Okay,
and
you
can
see
now
that
the
values
here
are
fixed
for
the
loadings
of
those
late
in
variables.
They're
fixed
to
correspond
to
the
values
from
the
factor
analysis
platform.
Now,
again,
they
have
to
be
rescaled
beause
the
variance
of
the
variables
is
taken
into
consideration.
That's
the
proper
way
to
specify
the
model.
But
it's
really
nice
to
be
able
to
streamline
this
workflow
because
normally,
if
you
really
want
to
fit
a
confirmatory
factor
model
based
on
an
exploratory
factor
analysis,
you
would
have
to
put
these
constraints
by
hand. T
hat's
really
tedious.
So
we've
made
it
very
easy.
These
latent
variables
have
loadings
that
are
fixed
to
known
values
from
a
previous
study,
from
a
previous
exploratory
analysis,
and
we
can
now
confirm
whether
or
not
that
factorial
structure
still
holds
with
a
new
sample.
One
thing
I
should
clarify
is
that
the
three
variables
that
did
not
have
substantial
factor
loadings
in
the
report
are
not
being
linked
to
any
of
the
latent
variables.
R
eally,
we
don't
want
these
to
be
here
in
the
analysis.
W
hat
I
can
do
is
the
red triangle
menu
also
has
an
option
for
removing
manifest
variables
from
the
analysis.
I'm
going
to
use
that
so
that
I
can
quickly
just
find
quality
3,
brand
3,
and
brand
5 a
nd
I
can
just
click
Okay
to
get
rid
of
those
variables
because
I
don't
really
want
to
fit
my
model
with
them
in
there.
A
gain,
now
I
can
just
run
this
model,
assess
the
fit,
and
figure
out
whether
I
can,
in
fact,
confirm
my
results
from
exploratory
factor
analysis
using
confirmatory
factor
analysis
in
SEM.
T
hat
is
all
I
have
for
this
demo.
I
hope
that
this
is
helpful
and
I
look
forward
to
answering
all
your
questions
during
the
live
Q&A.
Thank
you
very
much.
