SEM Series (2016) 3. Exploratory Factor Analysis (EFA)

Summary

This video script details a comprehensive guide to conducting Exploratory Factor Analysis (EFA). It emphasizes the importance of reflective latent measures, excluding formative and categorical variables, and setting up the analysis with maximum likelihood extraction. The speaker discusses the significance of KMO and Bartlett's test, communalities, and factor extraction. They address issues like cross-loadings and low factor loadings, suggesting strategies for resolving them. The script concludes with reporting the final pattern matrix, factor correlations, and reliability analysis, ensuring convergent and discriminant validity.

Takeaways

• 📊 The speaker begins by emphasizing the importance of saving data sets after making changes, suggesting to save the data as 'trimmed and no missing'.
• 🔄 The process of reordering variables in the data set is discussed, with imputed variables being moved to the end and key demographic variables placed at the bottom.
• 🔍 The speaker conducts an exploratory factor analysis (EFA), highlighting the need to include only reflective latent measures and excluding formative measures, categorical variables, and demographics not part of a reflective latent construct.
• 🎯 The choice of extraction method is discussed, with the speaker preferring maximum likelihood estimation due to its use in subsequent confirmatory factor analysis (CFA).
• 🔄 The use of Promax rotation is mentioned, which is less forgiving but may be necessary if issues arise with the factor analysis.
• 📉 The speaker discusses the suppression of small coefficients, aiming to focus on loadings greater than 0.5 for meaningful results.
• 📊 The Kaiser-Meyer-Olkin (KMO) measure and the significance of the Bartlett's test are highlighted as part of assessing the adequacy of the factor analysis.
• 📈 The total variance explained by the factors is discussed, with the speaker aiming for over 60% as an ideal threshold.
• 🔍 The pattern matrix is scrutinized for high loadings and cross-loadings, with the speaker identifying and addressing issues such as low loadings and Haywood cases.
• 🔄 The speaker demonstrates how to refine the factor analysis by iteratively removing problematic items and rerunning the analysis until a satisfactory model is achieved.
• 📝 The final step involves reporting the KMO and Bartlett's test results, the total variance explained, non-redundant residuals, the pattern matrix, and factor correlations to assess convergent and discriminant validity.

Q & A

What is the first step the speaker takes in the exploratory factor analysis process?

The first step the speaker takes is to save the dataset with the changes made, renaming it to 'trimmed and no missing'.

Why does the speaker reorder the variables in the dataset?

The speaker reorders the variables to place the imputed variables at the end and to organize the dataset with age, ID, gender, frequency, and experience at the bottom for better analysis.

What type of measures should be included in an Exploratory Factor Analysis (EFA) according to the speaker?

The speaker emphasizes that only reflective, not formative, measures should be included in EFA. Categorical variables and demographics not part of a reflective latent construct should be excluded.

What extraction method does the speaker prefer to use in EFA?

The speaker prefers to use the maximum likelihood extraction method because it is the same algorithm used in Amos for confirmatory factor analysis.

What rotation method is suggested by the speaker for EFA?

The speaker suggests using the Promax rotation method as it is less forgiving and can help in resolving issues with factor loadings.

Why does the speaker choose to suppress small coefficients at 0.3 in the analysis?

The speaker suppresses small coefficients at 0.3 because they are not interested in loadings less than 0.5, which is a threshold for meaningful factor loadings.

What does the speaker look for in the KMO (Kaiser-Meyer-Olkin) measure to assess the adequacy of the factor analysis?

The speaker looks for a KMO value above 0.7 and ideally about 0.9 to ensure the factor analysis is adequate.

How does the speaker interpret the total variance explained by the factors in the analysis?

The speaker interprets the total variance explained by the factors as good if it is more than 60%, with 64.5% being a satisfactory result in this case.

What issue does the speaker identify with the pattern matrix and how does it affect the analysis?

The speaker identifies a discriminant validity issue between decision quality and information acquisition, which affects the convergent validity of information acquisition.

What action does the speaker take to resolve the discriminant validity issue between decision quality and information acquisition?

The speaker runs another factor analysis excluding all items except decision quality and information acquisition to isolate and resolve the issue.

How does the speaker address items with low loadings in the pattern matrix?

The speaker considers dropping items with low loadings, such as decision quality one and eight, and re-runs the analysis to see the impact on the pattern matrix and overall model.

What additional analysis does the speaker perform to assess the reliability of the items?

The speaker performs a Cronbach's alpha scale reliability analysis to assess the internal consistency reliability of the items.

Outlines

00:00

📊 Exploratory Factor Analysis Setup

The speaker begins by discussing the process of setting up an exploratory factor analysis (EFA). They emphasize the importance of saving the dataset with changes and reordering variables. The speaker then proceeds to conduct an EFA, highlighting the need to include only reflective latent measures and exclude formative measures, categorical variables, and demographics not part of a reflective latent construct. They also mention the importance of using maximum likelihood as the extraction method and Promax rotation. The speaker sets parameters for the analysis, such as suppressing small coefficients and allowing a certain number of iterations, and checks the Kaiser-Meyer-Olkin (KMO) measure and the significance value as part of the adequacy assessment. The goal is to identify the number of factors that explain the variance in the model.

05:02

🔍 Addressing Factor Analysis Issues

In this segment, the speaker identifies issues in the factor analysis, particularly cross-loadings between decision quality and information acquisition factors. They decide to rerun the EFA, focusing only on these two sets of items to resolve the issue. After rerunning the analysis and examining the pattern matrix, they find that certain items, such as decision quality six and one, are causing problems and decide to eliminate them. The speaker also discusses the concept of Haywood cases, where factor loadings exceed one, and their decision to ignore these until other issues are resolved. The goal is to improve the discriminant and convergent validity of the factors.

10:05

📉 Finalizing Factor Analysis and Reporting

The speaker concludes the EFA by rerunning the analysis with the revised set of items. They report on the KMO and communalities, indicating the adequacy of the analysis, and the total variance explained by the six-factor model. They also discuss the non-redundant residuals and the pattern matrix, noting improvements in factor loadings. The speaker addresses the issue of discriminant validity by examining the factor correlation matrix and ensuring that no factors share a majority of variance. They also perform a reliability analysis using Cronbach's alpha to assess the internal consistency of the scales. The speaker provides a detailed explanation of what to report from the EFA, including the pattern matrix, factor correlation matrix, and reliability analysis results.

Keywords

💡Exploratory Factor Analysis (EFA)

Exploratory Factor Analysis (EFA) is a statistical method used to identify underlying relationships between measured variables and group them into latent factors. In the video, EFA is applied to explore patterns in the dataset, aiming to extract factors that explain the variance among the observed variables. The speaker uses EFA to ensure that only reflective latent measures are included and discusses how it reveals issues like cross-loadings.

💡Reflective Latent Measures

Reflective latent measures refer to variables that are influenced by an underlying factor. In this video, the speaker emphasizes that only reflective measures should be included in the EFA. Reflective indicators are used to measure a construct that influences them, unlike formative measures, which are not suitable for factor analysis.

💡Formative Measures

Formative measures are variables that cause or contribute to a construct, rather than being caused by it. The speaker warns against using formative measures in EFA, as they do not fit the model of reflective latent variables. This distinction is key to performing proper factor analysis, which focuses on identifying reflective relationships.

💡Kaiser-Meyer-Olkin (KMO)

The Kaiser-Meyer-Olkin (KMO) measure is a statistic that assesses the adequacy of the data for factor analysis. The speaker mentions that a good KMO value should be above 0.7, ideally closer to 0.9, indicating that the variables are suitable for factor analysis. A high KMO suggests that there is sufficient correlation among variables for the analysis to produce meaningful factors.

💡Maximum Likelihood Extraction

Maximum Likelihood Extraction is a method used in factor analysis to estimate factor loadings. The speaker prefers this method because it aligns with the confirmatory factor analysis (CFA) that will be conducted later. It is used to optimize the likelihood of obtaining the observed data based on the proposed factor model.

💡Promax Rotation

Promax rotation is an oblique rotation method used in factor analysis to make the output easier to interpret by allowing factors to correlate. The speaker prefers Promax rotation over other methods like Varimax because it is less restrictive and can handle more complex factor structures, which often reveal underlying relationships more clearly.

💡Cross-Loadings

Cross-loadings occur when a variable has significant loadings on more than one factor. The speaker identifies cross-loadings as an issue, particularly between decision quality and information acquisition. Cross-loadings are problematic because they can indicate that a variable is not clearly associated with one specific factor, complicating the interpretation of the results.

💡Cronbach's Alpha

Cronbach's Alpha is a measure of internal consistency or reliability of a set of items in a survey or test. The speaker uses Cronbach's Alpha to evaluate the reliability of the factors extracted in the EFA. A value above 0.7 is considered acceptable, with the speaker achieving 0.901 for decision quality, indicating high reliability for that factor.

💡Convergent Validity

Convergent validity refers to the degree to which two measures of the same concept are correlated. In the video, the speaker checks for convergent validity by ensuring that all factor loadings are above 0.5, indicating that the items within a factor are strongly related to the underlying construct.

💡Discriminant Validity

Discriminant validity is the extent to which factors are distinct and not too highly correlated with each other. The speaker checks for discriminant validity by ensuring that the factor correlation matrix values are below 0.7, confirming that the factors are not sharing a majority of variance. This helps to establish that each factor measures a unique aspect of the data.

Highlights

Exploratory Factor Analysis (EFA) is initiated with saving the dataset after minor changes.

Variables are reordered to place imputed ones at the end for clarity.

Factor analysis is conducted with all reflective latent measures, excluding formative or categorical variables.

Descriptives, KMO, and extraction methods are set, favoring maximum likelihood estimation for consistency with Amos.

Promax rotation is chosen for its less forgiving nature in handling factor loadings.

Factor scores can be saved as new variables for further analysis.

KMO measure indicates the data's suitability for factor analysis, with a value above 0.9 being ideal.

Eigenvalues above 0.3 in the extraction column suggest sufficient communalities.

Six factors are extracted, aligning with the预先 expected model.

Total variance explained by the model is over 64%, exceeding the minimum threshold of 60%.

Reproduced values are below the 5% threshold, indicating good model fit.

Issues with discriminant validity between decision quality and information acquisition are identified.

A focused factor analysis is conducted on decision quality and information acquisition to resolve issues.

Items with cross-loadings or low factor loadings are considered for removal to improve model clarity.

Reliability analysis is performed to assess the impact of item removal on Cronbach's alpha.

Final model retains all items despite some low loadings, anticipating improvement in confirmatory factor analysis.

Reporting includes KMO, eigenvalues, total variance explained, non-redundant residuals, and pattern matrix.

Cronbach's alpha values are reported to assess the reliability of the factors.

Factor correlation matrix is examined for evidence of discriminant validity.

Transcripts

all right moving right along next is

exploratory factor analysis so what I

would do first things first I would go

back to the data set and save it we've

made several minor changes here and

there I mean who had save this as and

I'm going to save it as trimmed and no

missing let's see

no missing there we go save so now all

of our changes are recorded and if we

make a mistake somewhere we're good to

go and I'm going to go ahead and reorder

these variables look we have these guys

in the end here because we imputed them

we replaced the missing values I'm going

to resource this column sort ascending

smus a sure you want to do this the

answer is yes but do you want to save it

as a different thing no okay we're in

order now I'm just going to put age ID

gender frequency experience all at the

bottom again okay there we go

the next thing to do is a factor

analysis I'm excited I like factor

analyses so analyze dimension reduction

factor analysis what I'm going to stick

in there we're going to start with

everything throw it all in there all the

the reflective latent measures this is

critical to bear in mind you must have

reflective not formative reflective

latent meaning multi indicator measures

if you have formative measures don't

include them in the EFA if you have

categorical variables like gender don't

include them the EFA if you have

demographics that are clearly not part

of a reflective latent construct don't

include them in the EFA or CFA they

don't belong in a reflective measurement

model you're only going to include

reflective latent factors hope that was

clear enough cool throw this in here if

you're not sure what reflective versus

formative means please refer to my

YouTube video called formative versus

reflective measures and a factor

analysis I think it's called that

something like that okay throw these all

over descriptives I've done this

times before reproduced kmo continued

extraction I like to use maximum

likelihood why well that's the same

algorithm that Amos is going to use when

we do the confirmatory factor analysis I

like to do it based on I gain values

instead of a fixed number of factors at

least initially just to see what it's

going to give me how many iterations do

we want to allow 25 is fine continued

rotation I like to use Promax it's less

forgiving but we might have to switch if

we have issues continue noting in scores

although just FYI if you wanted to save

each of the factors as a variable is

called factor scores then you click here

and save variables and that'll give you

however many factors you came up with in

your pattern matrix it will create that

many more new variables to represent

each of those factors in it if set I'm

not going to check that okay cancel in

the options I am going to suppress small

coefficients at point three because I'm

really not interested in loadings less

than 0.5 and we need them to be at least

point to difference I've talked about

this in other videos I'm not going to go

into depth here okay this is more

procedural video anyway we want to look

at km okay Emily looks good 935 you want

this above 0.7 um ideally about 0.9

you're at the sig value to be

significant this is all part of adequacy

we're going to talk about adequacy

validity convergent discriminant and

reliability okay back here we look at

the extraction column and we want to see

if there's anything less than about 0.3

we're at point three a decision called

the eighth order the line dude do

looking pretty good okay moving on and

we have total variance explained that we

will look at this cumulative column it

came up with six factors how many were

we expecting well if we go back to our

model we were expecting one two three

four five six it came up with exactly

what we wanted this rarely happens so

I'm kind of surprised

and this doesn't provide us an

opportunity to do mitigation strategies

so maybe see my other videos for

mitigation strategies okay

it explains sixty four and a half

percent of the variance in the model

that's good we want more than sixty

percent at a minimum we want more than

fifty percent but again above sixty

percent is ideal skip the factor matrix

skip the goodness fit go down to the

reproduced we want a number here less

than about five percent we're looking

pretty good and pattern matrix is

looking stellar ish who actually we do

have some issues we have a few issues

this is fun I don't like it when just

works so let's do this one time

a typical use looks fabulous is there no

cross loadings anywhere um all the items

loaded on to a single factor factor five

decision quality not so fabulous

I'm still good but not fabulous look we

have 0.40 seven that's fairly low we

also have these two other items from

information acquisition that loaded with

all the decision quality items that's a

problem we'll have to resolve that

separately information acquisition

loaded onto its own factor but look at

those loadings they're awful so I'm not

sure what to do about that I'll have to

address that next joy looks joyful no

problems there whatsoever playfulness

looks incredible

and usefulness looks incredible as well

so the only real problem is this

discriminant validity issue between the

decision quality and information

acquisition which my guess is is causing

the convergent validity issue with

information acquisition so what would

you do here I would actually just run

another factor analysis but get rid of

everything except decision quality and

information acquisition there we go and

just run it again with just those two

sets of items and looking good looking

good really what I want to do is go down

to the pattern matrix good it did come

up with two factors that's what we

wanted but you can see there are some

issues decision quality six is loading

most equally on both sides that is the

first one I would delete so let's do

that factor analysis again decision

quality six sayonara K write it again

jump down to the pattern matrix decision

quality one loading on both sides hey

look at these loadings though those are

looking better okay this one no good

decision quality one you may say hey

James wait wait wait what is this

it's above one it was last time two

we're going to ignore what it is called

a Haywood case we're going to ignore

this Haywood case until we resolve other

issues because it'll probably just

resolve itself so decision quality one

you are gone kicked off the island there

we go jump down the pattern matrix

looking better but look at this decision

quality eight not really contributing

very well I'm going to drop decision

quality gate and pattern matrix much

better this is borderline we might keep

it this is also borderline we might keep

it what I'm going to do at this point is

I'm going to recreate the larger pattern

matrix and see if everything is resolved

if not we can see where we'll go

probably decision quality seven and into

acquisition five will be the next to be

eliminated so back to the full factor

analysis we're going to throw everything

in there except decision quality one six

and eight do yep run it again and I am

just going to do a few cursory things

I'm going to jump down here looks like

we still have six factors excellent good

variance explained actually better than

before and we have only three percent on

or doesn't residuals this time and

here's the pattern matrix and it already

looks better okay decision quality that

looks really good information

acquisition also very good Wow actually

I wasn't expecting it to be that good um

and everything else looks just as good

as before well I might do is drop

information acquisition five it is still

fairly low and you can see these

loadings here point seven point seven

point seven

6m4 these aren't going to average out to

above 0.7 which is problem if I want to

verify this what I might do is do

reliability analysis aniline is scale

reliability and just stick in those

information acquisition items here I'll

pull it over and then go to statistics

and do a scale of item deleted continue

and okay and what this is going to tell

us is if dropping that item will

actually do us any good so it was me go

back over here to the pattern matrix it

was information acquisition five now if

we go down to the reliability analysis

click here if you look at this last

column it says what our cronbach's alpha

would be if we deleted each of these

items the current convict self is 0.8 4

- but if we deleted information

acquisition 5 it would go up to point 8

4 6 this isn't a big difference and so

if I was struggling if I wanted to keep

all these items

I'm fully justified in keeping all these

items even though that is a low loading

most likely scenario is it will bump up

a little bit during the confirmatory

factor analysis in Amos so I can keep it

if I really don't care and these are

scales I made up myself and and I had

the liberty to do so then I might just

drop information acquisition 5 which is

what I am going to do at this point so

I'm going to run this one more time drop

into X 5 watch what happens to see makes

big differences that's an uptick which

is good 3 percents the same ooh ok so it

actually caused some problems it threw

in a new loading here above 0.3 what

what happened is information acquisition

5 helped distinguish us from decision

quality whereas now we're having a hard

time distinguishing yourself so I'm

going to retain information acquisition

5 even though this is a greater than 0.2

difference it did bring up that

discriminant sort of cost loading issue

so my final pattern matrix is actually

going to be the one with information

acquisition 5 still in it here we go run

it

what do I report I report the kmo say

it's awesome I report the cig say it's

awesome these are all under adequacy

under communalities this is this is

another adequacy measure I look at the

extraction column and I say all of mine

all my communalities were above 0.3

looks like they are the lowest one is

this one point three nine seven and then

I'd say the six factor model explains

sixty six point three percent of the

variance which is good and then I'd say

we had less than three percent non

redundant residuals which is great and

here's the pattern matrix and I'd say as

evidence of convergent validity we have

all the loadings above 0.5 except this

one point 4 which way which I'd mention

and then evidence of discriminant

validity is we had no strong cross

loadings another bit of evidence for

discriminant validity is this factor

correlation matrix we can look and see

at all these non diagonal values and

make sure they're not above 0.7 which

would indicate sharing a majority of the

variance so the closest one is this

factor for two factors six I'm guessing

that is information acquisition and

decision quality I'd go here check four

and six yep those are those two and they

are highly related but not so related

that they're sharing a majority of their

variance so that's the closest one

what would I report I would report the

pattern matrix at a minimum you may also

want to report this factor correlation

matrix okay that is adequacy convergent

validity discriminant validity if we

want to do reliability you just do like

I did before go do a cronbach's alpha

scale reliability analysis we did it for

information acquisition move those over

we'll do another one for decision

quality but not all decision quality

items will they have two three four five

and seven two three four five and do two

six eight loops so two three four five

and seven throw those in there okay and

report this number here 0.90 one

what I like to do is just stick it at

the top of my pattern matrix so this

point 901 I would go stick it right here

that was decision quality so I'd

replaced this 4 with 0.9 on one and that

put cronbach's alpha right over here

okay you want all those cronbach's

alphas to be greater than 0.7 if they're

not there's actually literature that

says it can get down 0.6 particularly if

you have only a few items 2 or 3 and

that is the EFA