SEM Series (2016) 4. Confirmatory Factor Analysis Part 1

Summary

The 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

00:00

📊 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.

05:02

🔧 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.

10:02

🔎 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.

15:02

👤 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.

20:03

📊 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.

Keywords

💡Confirmatory Factor Analysis

Confirmatory Factor Analysis (CFA) is a statistical technique used to validate the structure of a theoretical framework. It tests whether the observed variables actually measure their theorized latent constructs. In the script, CFA is the main focus of the video, where the speaker guides through the process of conducting a CFA using Amos software.

💡Pattern Matrix

A pattern matrix in CFA represents the relationships between observed variables and their underlying latent factors. It is a crucial component of the model specification in Amos. The script describes how to input the pattern matrix into Amos, either through a plugin or manually.

💡Amos

Amos is a structural equation modeling software used for analyzing multivariate data. It is central to the video's narrative as the tool through which the CFA is conducted. The speaker provides a step-by-step guide on how to use Amos for CFA.

💡Plugin

A plugin in the context of the video refers to an add-on software component that extends the functionality of a program. The speaker discusses using a plugin to simplify the process of inputting a pattern matrix into Amos.

💡Latent Factor

A latent factor is a theoretical construct that is not directly observable but is inferred through observable variables. In CFA, latent factors are central to the analysis as they represent the underlying dimensions being measured. The script describes how to represent these factors in Amos.

💡Covary

To covary in the context of CFA means that two or more variables are allowed to correlate with each other. This is done in Amos by manually connecting the variables or using a plugin, as mentioned in the script.

💡Model Fit

Model fit refers to how well a proposed model represents the data. It is assessed using various fit indices in CFA. The script includes a discussion on evaluating model fit and making adjustments to improve it.

💡Modification Indices

Modification indices in Amos suggest potential model improvements by indicating which changes would result in the greatest decrease in the model's chi-square value. The speaker discusses using modification indices to refine the CFA model.

💡Configural Invariance

Configural invariance is a type of measurement invariance that assesses whether the same factors are present across different groups. The script describes conducting a configural invariance test as part of a multi-group analysis.

💡Metric Invariance

Metric invariance is a stronger form of measurement invariance that tests whether the relationships between observed variables and their latent factors are the same across groups. The speaker explains how to test for metric invariance in Amos.

💡Error Variables

Error variables represent the random measurement errors in observed variables. The script mentions the need to name these error variables in Amos to complete the CFA model setup.

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