SEM Series (2016) 4. Confirmatory Factor Analysis Part 1
Summary
TLDRThe video script offers a detailed tutorial on conducting a confirmatory factor analysis using Amos software. It guides viewers through the process of manually constructing a model, utilizing a plugin for efficiency, and importing data. The presenter demonstrates how to address common issues like missing data and error handling. Further, it covers model fit assessment, modification indices, and invariance testing by gender, providing practical insights into ensuring the reliability and validity of the analysis.
Takeaways
- 📕 The video script provides a step-by-step guide on conducting a confirmatory factor analysis (CFA) using the Amos program.
- 🔧 The script outlines both an easy method using a plugin and a more challenging manual approach to inputting a pattern matrix into Amos.
- 🔄 The manual method involves creating a model, adding latent factors, rotating them, and setting covariances manually within the Amos interface.
- 🔨 The video emphasizes the importance of correctly labeling variables and handling missing data to ensure the accuracy of the analysis.
- 🔇 It details the process of using plugins to simplify tasks in Amos, such as the pattern matrix model builder, and explains how to install and use these plugins.
- 🔬 The speaker discusses the process of checking model fit and validity, including looking at standardized estimates and modification indices.
- 🔅 The video highlights the significance of convergent and discriminant validity, explaining how to interpret the values and what thresholds to aim for.
- 🔍 The speaker provides insight into dealing with errors that arise during model fitting, such as missing observations and how to address them.
- 🔄 The script touches on multi-group analysis, explaining how to set up groups and conduct configural and metric invariance tests.
- 🔨 The video concludes with how to report the findings from the CFA, emphasizing the importance of providing evidence of model fit and invariance.
- 🔧 The script serves as an educational resource for users unfamiliar with Amos or those looking to refine their CFA techniques.
Q & A
What is the first step in conducting a confirmatory factor analysis according to the transcript?
-The first step is to put the pattern matrix into the Amos program.
What are the two ways to input the pattern matrix into Amos as described in the transcript?
-The two ways are using a plugin or building it by hand.
How does the plugin help in putting the pattern matrix into Amos?
-The plugin automates the process of creating the model by allowing users to paste the matrix directly into Amos.
What does the user need to do if the plugin does not work?
-If the plugin does not work, the user needs to build the model by hand, which involves opening Amos, creating a new model, and manually dragging and rotating the latent factors and observed variables.
How does the user ensure that all variables are covaried in the model?
-The user ensures all variables are covaried by manually selecting each one and applying the covariance, or by using the plugin's feature to automatically covariety them.
What does the user need to do to fix the labels in Amos?
-The user needs to go to view, interface properties, and then on the misc tab select 'don't display variable labels' to fix the labels.
Why is it important to name the latent factor variables without spaces according to the transcript?
-It is important because Amos automatically names them as 'f1' and 'f2' if not named properly, and renaming them afterward can be confusing.
What is the process of installing a plugin in Amos as described in the transcript?
-The process involves downloading the plugin, unblocking it if necessary, and then placing it into the Amos plugins folder.
What is the purpose of the Excel Stats Tools Package mentioned in the transcript?
-The Excel Stats Tools Package is used to help with the analysis and management of data in Excel, which can then be imported into Amos.
What does the user need to check for in terms of model fit when conducting the confirmatory factor analysis?
-The user needs to check the ACFI, RMSEA, and PCLOSE values to ensure the model has good fit.
What is the significance of the chi-square value in the context of the model fit?
-The chi-square value indicates how well the model fits the data. A large chi-square value can suggest a poor fit, but it can also be inflated by a complex model or large sample size.
Outlines
📊 Setting Up Amos for Confirmatory Factor Analysis
The speaker begins by outlining the steps to perform a confirmatory factor analysis using Amos software. They describe two methods for inputting a pattern matrix: using a plugin for ease or manually constructing it. The manual method involves opening Amos, creating a new model, and dragging to size for latent factors. The speaker then details adding items for 'decision quality' and 'information acquisition', arranging them, and covarying them clockwise. They mention using 'fire truck and balloons' to symmetrize the model. The process continues with importing data, adjusting view settings to hide variable labels, resizing observed variables, and naming latent factors without spaces. The speaker also guides on how to download and install the plugin from the Stat Wiki website, emphasizing the need to unblock the downloaded file before moving it to the Amos plugins folder.
🔧 Troubleshooting and Running the Model in Amos
In this section, the speaker addresses potential issues that may arise when running the model in Amos. They explain how to copy the pattern matrix, paste it into Amos, and deal with decimal or comma issues that could affect the model. The speaker also discusses the importance of ensuring variable names are used instead of variable labels. They guide on checking for missing data in SPSS, which could cause errors in Amos, and how to impute missing values to avoid such errors. After making corrections, the model is re-run in Amos, and the speaker reviews the model fit and validity, suggesting that values should average above 0.7 for good convergent validity and be less than 0.8 for discriminant validity. They also mention checking model fit statistics like ACFI, RMSEA, and SRMR.
🔎 Analyzing Model Fit and Modification Indices
The speaker proceeds to analyze the model fit, looking at the chi-square value and other fit indices. They discuss the implications of a large chi-square value, which could be inflated by sample size and model complexity, and suggest ways to improve the model by examining modification indices. The speaker demonstrates how to use modification indices to adjust the model by adding covariance between errors, which can improve the model fit. They also mention referencing Dave Kenny's website for justifications of such adjustments. The focus is on achieving fit indices close to or exceeding the desired thresholds, indicating a good model fit.
👤 Testing Configural and Metric Invariance by Gender
The speaker explains the process of testing for configural and metric invariance by gender. They guide on setting up two groups in Amos, one for each gender, and running a freely estimated model to obtain baseline model fit indices. The speaker then discusses how to perform a configural invariance test, emphasizing the importance of model fit indices like CFI, RMSEA, and SRMR. For metric invariance, they demonstrate how to constrain parameter estimates across groups and compare the chi-square values of the constrained and unconstrained models to assess invariance. The speaker concludes that the measures are the same across genders, indicating metric invariance.
📊 Reporting Results and Next Steps
In the final paragraph, the speaker summarizes the results of the configural and metric invariance tests, providing an example of how to report these findings. They mention that if the p-value for metric invariance were significant, it would indicate that the measures differ by gender, and further investigation would be needed. The speaker also hints at further videos that will cover additional aspects of the analysis, suggesting that the process will continue beyond this segment.
Mindmap
Keywords
💡Confirmatory Factor Analysis
💡Pattern Matrix
💡Amos
💡Plugin
💡Latent Factor
💡Covary
💡Model Fit
💡Modification Indices
💡Configural Invariance
💡Metric Invariance
💡Error Variables
Highlights
Introduction to confirmatory factor analysis using Amos program.
Two methods to input pattern matrix: using a plugin or building it manually.
Step-by-step guide on manually creating a model in Amos.
How to covary latent factors in Amos by manual selection.
Importing data into Amos and handling missing values.
Fixing variable labels for better visualization in Amos.
Renaming latent and error variables for clarity.
Using the Amos EFA plugin to simplify model building.
Instructions on downloading and installing Amos plugins.
Importing data and using the Pattern Matrix Model Builder plugin.
Analyzing model fit and validity in Amos.
Interpreting convergent and discriminant validity.
Addressing model fit issues by estimating means and intercepts.
Using modification indices to improve model fit.
Configural and metric invariance tests for multi-group analysis.
Creating groups for gender-based multi-group analysis.
Testing configural invariance and interpreting the results.
Conducting metric invariance test and comparing constrained vs. unconstrained models.
Reporting the results of invariance tests.
Transcripts
our next task is to do a confirmatory
factor analysis which involves a whole
bunch of stuff so let's get going
the first thing we need to do is put our
pattern matrix into our Amos program now
there's an easy way in a hard way the
easy way is to use my plugin the hard
way is to build it by hand if you were
to build it by hand here's how it would
go roughly um you would open Amos which
I need to open let's see Amos
there it is and let me go ahead and do a
new model okay and what you would do is
you get this candle opera thing single
click it and then out here drag click to
whatever size you feel is appropriate
for your latent factor and then single
click one two three however many we need
looks like we need for decision quality
we need one two three four five of these
items four five and then for information
acquisition we need five again one two
three four five click aw
one two three four five you get the idea
and then I rotate them do so they're all
to the left for now and then I covary
them easy way to do that is select each
one of them and do plug-in straw
covariances of course it makes it ugly
for us undo that and we'll just do it
manually okay
it only draws clockwise by the way and
make sure you get them all Co varied and
I'd move them all around we deselect all
use the fire truck and the balloons to
make them symmetric and I'd move them
all together like this something like
that might have my now then I got to be
this I have to go grab my data where's
that data downloads here we go trim - no
missing open okay and then I click on
this and I'd pull in each of those
things so a typical use would go here oh
and then it's ugly because it has all
those labels so I'd have to fix that it
is such a pain in the rear anyway how
you fix the labels is you go to view
interface properties
and then on the misc tab don't display
variable labels hit apply close it makes
it to those they're still too big so I'd
go plugins and I'd resize observed
variables there we go then I got to name
this as a tip use no spaces allowed in
Layton factor variable names and then
I'd have to name all of the error
variables which I better do after I name
all the other variables otherwise this
happens named unobserved and it's going
to name these f1 and f2 for you so you'd
have to rename these guys to whatever
they are anyway that's how you'd make it
by hand for those of you for whom the
plug-in does not work and for those of
you for whom it does not work I'm very
sorry I wish I knew why for the rest of
you lucky for you or lucky majority
hopefully you can use my plug-in on a
closed amis you're going to go to stat
wiki go to the home page or any page
really um and you're going to
right-click not left-click you're going
to right-click the Amos EFA to see if a
plug-in right click it save link as
yours might say download as or save as
or something like that
go save leg as and I'm going to save it
just in the Downloads folder let's see
downloads paid a pattern matrix model
builder and I'm going to get rid of this
one here there you ll save and then I'm
gonna go view that folder so go to my
downloads folder which is right here
and I'm going to right click it
properties and I'm going to unblock it
if you don't unblock it it will not work
some of you might not have this unblock
of option that means it's already
unblocked so you don't need to worry
about it
for those of you for whom this is an
issue unblock hit ok it's now unblocked
and now and only now after it's been
unblocked stick it in your Amos plugins
folder where is that you might say it is
over here in C program files 86 for the
most for most of you IBM
SPSS Amos and then whichever version
you're currently running I'm running
version 23 right now so I'm going to
open up 23 and there's the plugins
folder I'm going to drag this into that
plugins folder okay as long as I'm doing
this let me do it for these other few I
need to see a CLF plug-in as well so I'm
going to right-click CLF plug-in I'm
going to save link as same places before
CL effed-up VB save now this file
shouldn't be blocked so let me just
right-click it to make sure properties
oh it is blocked so unblock okay and
then drag it back into the plugins
folder and then the last one is the Amos
a and B estimate right click Save Link
As yep we'll call it that is fine save
and go back to that folder here it is
right here that this shouldn't be
blocked properties OBE is so I'm block
okay and where should you stick this
this shouldn't go in the plugins folder
because it's not a plug-in it should go
in somewhere else I I'm just going to
stick it in my Amos 23 folder okay so
now it's in there and now we're good we
have all the plugins
you might also now if you haven't yet go
download the excel stats tools package
if you just be able to left click this
one okay back to Amos SPSS so we have
this pattern matrix I'm going to right
click it and copy if for you the left
column is filled variable labels instead
of variable names this will pose a
problem these need to be variable names
move the way to switch this go to edit
options and in the variable lists do
names in the output do names and names
and the pivot tables and then hit OK
it's going to reset everything you have
to redo the the EFA just the final one
and then it should be good okay so copy
and then over in Amos let me open up
Amos
push this to the side I'm going to go to
data get the right data it's this one
missing and hit OK and then plugins I'm
going to do you should have new plugins
now let me do the pattern matrix model
builder I'm just going to paste all that
enters control V for me and hit create
diagram also if you have instead of
decimals you have commas that might
throw it off I know a lot of countries
use commas so that could be a problem
all right so it just builds it for you
and sizes it all for you in positions at
all for you it's very very nice the only
thing it doesn't do for you is guess the
variable names for the latent variables
so that's one thing we need to change so
I'm gonna double click this instead of
variable named one we're going to call
it useful because that's what these are
and then I'm going to click on the next
one instead of two it's going to be joy
okay now they're all named and we should
save let's save we're going to save this
let's just save it I'm the Downloads
folder right now I'm going to stay in
there for now downloads okay and this is
my CFA initial nothing changed no
special features just my initial CFA
alright the first thing we need to do is
listed right here okay obtain a roughly
decent model quickly so just look at
model fit look at validity see if
they're good and then move on so let's
do that to do that click on the analysis
properties and in the output we want
standardized estimates and modification
indices and that should be good for now
we then save and run and hope it runs an
error occurred haha and I record while
attempting fit the model these error um
boxes are really good usually actually
in Amos read them they'll tell you what
the problem isn't how to fix it so they
so this says that there was an error
because I'm missing observations so I
have to explicitly estimate means and
intercepts huh so if I want to just fix
this in Amos I just check the box for
estimate means intercepts in the
analysis properties window but I don't
want to do that I would like to have no
missing data
I thought we'd replace it all let's go
double check so in in SPSS first off
make sure it's been saved ooh that might
be the problem maybe we just didn't save
it so let's save it but just to
double-check let's go do frequencies
again and for all the variables with the
frequencies I don't need the frequencies
tables hit OK and I just get this right
here
and if I just scan across it dee dee dee
dee dee dee dee oh there it is that one
okay um I'll go back that's the only one
information acquisition 3 apparently I
didn't impute that did we catch that
before if I go back to here and boom
boom boom boom oh there it is
information acquisition 3 we just happen
to miss it so
I earn I'll go back and fix this and
we'll get going from there
okay and then save and then go back to
Amos and then make sure - after you save
the SPSS file
go read link it does look like this go
get that data again open because it will
need to update it then save again and
then run again and then ah it worked all
right so we're going to look at this
we're gonna eyeball it real quick
because we're just doing a rough model
to start and as we look at these we want
these values to average out above 0.7
looks like that one looks fabulous
that one looks fabulous if you can't see
these they're like pointing it's point
7s again twenty two point seven s the
one we were struggling with was
information acquisition I go down here
look at that that point for jump to a
point six that is awesome if you wanna
be able to see it a little bit better
you can use this little swervy thing
click that and click that there it is
it's a point six so we're looking pretty
good in terms of convergent validity if
we want to know about discriminant
validity let's look at these diagonal
covariance arrows or correlations in
this case and the correlations should be
less than about 0.8 and we're doing
pretty good everywhere the only high one
is point seven five and again that's
between decision quality information
acquisition which we expected so we're
doing pretty good there um that's good
let's check model fit to see if we have
a good model there go look at the output
and let me open this up go look at model
fit and we have ACF I of nine three four
not too bad and ap close not where we
want it to be rmsea is less than 0.06
but not less than 0.05 and this really
ought to be above 0.05
back up the CFI this ought to be greater
than point nine five but I should
mention that um these values do depend a
lot on the sample size we have a sample
size of 380 that's a large sample size
and so that's going to inflate the
chi-square if we go back to here you can
see the chi-square is a thousand twelve
is twelve hundred that's fairly large
chi-square also the
complexity of the model will inflate the
chi-square from our model as you can see
we it is fairly complex lots of
variables lots of parameters that
inflates the chi-square look at all
those degrees of freedom so I wouldn't
say that's bad that's pretty good
if I wanted to make it better I could go
look at the modification indices go look
for the biggest one that's a lot let me
narrow this down go back here analysis
properties in the output for
modification and C's changes from a4 to
like 20 and what that's going to do is
it's just going to set invisible any
modification indices that are less than
20 there we go now we see just the big
ones and the biggest one is ether teen
2e 14 well let's see ether teen D 14
means joy 6 and 7 most likely scenario
these are highly similar items and they
got to the end of that section of the
survey and they're like oh another joy
Adam just answer the same way so you can
either delete 7 or just co-vary these
errors so I'll just do that if you can
avoid it is good to not co-vary errors
although there is justification for it
if you look at the references section of
the stat wiki I have a reference for
that on Dave Kenny's website so back to
Muffet 0.94 modification indices I'm
really looking to push this up a both
0.95 and that will call it good the next
biggest one is this one 19 and 20 see if
we can cover those same issue here
they're right next to each other on the
survey and they're towards the end of
that set of questions in the survey so
there is a systematic reason for their
or there's a logical reason for their
systematic relationship model fit 0.94
800 I'm darn close and 45 III and 4 III
and 4 same issue here right next to each
other on survey similar similarly worded
questions no doubt and Moll fit 0.9 5.95
for good and P close looking fabulous at
Point a 1 7 and remember CA less than
0.05 we're doing great so we're going to
call that good um
we're not reporting any of that yet
we're just eyeballing it again if I want
to make sure validities are good now
that I've changed these little bits and
pieces here by adding covariance errors
I can go back and look at these nothing
looks to have changed drastically so
we're good
that is only the first item on this list
next configural and metric and variance
tests all right this is if we're using a
grouping variable for multi group
analyses later on which we are if we go
back to our model down here our multi
group is gender so we need to do a and
invariance test by gender now there are
several different types of invariants
there's scalar intercept configurable
metric all sorts of stuff we're just
going to do these two and call it good
to do configural invariance test let me
save this first okay now we're going to
create two groups one for each of those
genders so mail you the mail loop the
mail there we go and close again that
was just up here we need to set data for
both of those we already have it for
male let's set up a female same data set
and for the grouping variable it's
gender and the grouping value for male
is one grouping variable for females I
just click in here and hit G and it
jumps me data gender hit OK grouping
value is two we have far fewer females
than males in this case it okay just
something to note and hit OK and save as
okay save as instead of CFA initial we
are on CFA variants okay and to test
configurable and variants you have a
freely estimated model and you run it
and look at the model fit a freely
estimated model with two groups I should
mention and it gives you model fit
across the two groups so our model fit
will have changed you can see our
chi-square has inflated even more
because we have two groups now if we go
to model fit check the model fit 0.93 -
not too bad
go down to the ARMA c8 looks great P
close looks great I'm going to check
also the SR
are but these should be sufficient right
here I'm going to check the SR mark just
to be sure
plugins standardized RMR
nothing happens because you have to run
while that window is open and look at
this it is less than point zero eight
which I believe is a threshold but it's
it's definitely under whatever the
threshold is so we're good point zero
four one two we have good configural
invariance what would I report in this
case I would say we did a configurable
environments test and obtained adequate
goodness-of-fit when estimating a freely
or when when when analyzing a freely
estimated model across two groups and
then maybe a parenthesis I stick the CFI
and som är and arma CA and that's my
evidence of configurable variance now
for metric invariance you want to see if
forcing these groups together is
substantially substantially different
than letting be estimated freely so
freely we have a chi-square degrees of
freedom of 1905 and 1152 in the stats
tools package if you'd like to use that
you can you would go to the chi-square
difference tab and you'd stick those
values in those values
19:05 this is the unconstrained model
1905 and 1152 and then I'd go to a fully
constrained model I am going to save
this it's already saved there we go
plugins I'm going to name parameters
almost I'm actually going to move this
constraint double-click each latent
variable go to the parameters tab type 1
for the variance click one click one
click one click one click one and then
remove it from the regression line here
this will become important in just a
moment what it's going to do is we're
going to name what this does is that
allows us to name the regression lines
and then constrain them so we're going
to name parameters and we're going to
name the regression weights hit ok now
they're all named
force to be equal across groups you can
see their name the same thing across
groups which tells Amos that they are
the same ie constraining them to be
equal if we run this now we'll get a
different kind of your freedom here we
go 1930 and 11 88 so I'll stick those in
here 1930 and 11 88 and the answer is
they are not different they're so not
different metrically speaking so the
measures are the same across groups if
this p-value were significant then they
would not be invariant meaning they
would be different and then we'd have to
figure out why which is a pain in the
rear but essentially what we have to do
is go look at each of these paths and
see which one differs the most based on
gender by toggling back and forth year
or just go to the output and compare
those tables you can go click on
regression weights understand engine
very friendly it's copy this over to
excel do a new tab here paste that in
here that's for male and then I go click
down here on female grab the same table
copy it over nice to hear and then I do
a little different maybe call this Delta
and equals this minus this and see which
one is the most different in our case
there aren't going to be a lot real
different ones because these were
metrically in variant but if I want to
do I probably sort on this column let's
see sort will it let me if it did and
the biggest difference we have is on joy
3 and so if I were metrically in variant
I might go do a I might try or if you
are metrically not invariant if the
p-value here were significant I might go
and remove joy 3 and see if that fixed
the problem and go from there
okay that's metric and parents and I
think I'm gonna stop the video here and
then we'll do these last few in a new
video
actually first what would you report for
metric invariance you would say we did a
metric invariance test by constraining
the two models to be equal and did a
high score difference test between the
fully constrained and unconstrained
models and found them to be invariant
p-value equals whatever we had there
0.91 six tada
we are invariant both configure Lee and
metrically okay
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