Wk 5 - CFA

Question 1

What are the 3 main purposes of CFA?

Answer 1

ID latent psych constructs that account for correlations among sub-sets variables
Assess how strongly each variable is associated with factors
Test hypotheses about factor structure underlying set of variables

Question 2

What are the 2 main diffs between EFA and CFA? (x2, x2)

Answer 2

EFA looks for structure of data set
Is data-driven

CFA tests specific hypotheses about structure
Is theory driven

Question 3

Explain how CFA works (x4)

Answer 3

Based on theory, predict which co-variances among vars should be low
Constrain them to zero in analysis
Predict zero correlation between variables and OTHER factor/s
Test how accurately model fits the data

Question 4

What are model parameters in CFA? (x1)

Answer 4

Factor loadings

Question 5

How does CFA use model parameters? (x2)

Answer 5

Pattern chosen predicts parameters

Iterative process adjusts free parameter loadings to max similarity between predictions and data

Question 6

How are model predictions evaluated in CFA? (x2)

Answer 6

Chi-square test used to test diff between observed and predicted data
Significance = (unwanted) diff between model and data

Question 7

What 2 important things do CFA results reveal? (x4, x3)

Answer 7

‘Quality’ of theory:
o Hypothesized structure ignore anything important (poor fit)?
o Closely capture data (good fit)?
o Parsimony? (minimum psych constructs, not just fit)

Separates in/essential:
o What factors/loadings are needed to describe data structure?
o Which aspects of data can we ignore?

Question 8

When should we choose EFA? (x3)

Answer 8

To explore a set of variables
o Newly developed variables/measures
o No clear ideas about constructs underlying the variables

Question 9

When should we choose CFA? (x3)

Answer 9

To test a priori hypotheses derived from:
o Existing theory
o Previous research using the same variables

Question 10

What are the 4 steps in conducting a CFA?

Answer 10

Preliminaries
Evaluate model fit
Evaluate parameter estimates (pattern of factor loadings and correlations)
Evaluate alternative models

Question 11

What are 4 preliminary considerations (step 1) for running a CFA?

Answer 11

Check assumptions
Specify the model
Model parameters
Sample size?

Question 12

What assumptions should be checked before running a CFA?

Answer 12

Interval scales
Good variance in scores
LInear correlations between variables
Generally normally distributed

Question 13

What are the considerations for specifying the model in CFA? (x1, x3)

Answer 13

Theory driven assumptions of number/pattern of factors
Capturing most important aspects of data:
 What is essential for explaining the data?
 What can be ignored?

Question 14

What are the considerations when deciding on model parameters in CFA? (x2)

Answer 14

Which should be fixed (at correlations of zero)?

Which should be free (estimated from the data)?

Question 15

What do free parameters do for CFA? (x2)

Answer 15

Add greater flexibility:

Model can account for more patterns in data

Question 16

What is the benefit of the added flexibility brought by free parameters in CFA? (x2)

Answer 16

Better account of wider range of data

*Explain specific features in data, that aren’t zero correlations

Question 17

What is the downside of the added flexibility brought by free parameters in CFA? (x2)

Answer 17

Model that accounts for everything doesn’t give insight:

* More freedom = more noise explained
* Model predicts 'anything could happen'

Question 18

Why is it important to consider sample size for CFA? (x2)

And we should aim for? (x1)

Answer 18

Stability of model: small samples = unreliable estimates
Statistical power - detect smaller effects

5 - 10 per parameter

Question 19

In what ways is model fit evaluated (step 2) in CFA? (x3)

Answer 19

Against a null hypothesis
In terms of absolute fit
And relative fit

Question 20

What test is used to assess similarity of estimated and observed covariance matrices in CFA? (x1, explain x3)

Answer 20

Chi-square test:
Null hypothesis of no diff between model and data
Significance means poor fit
ns means acceptable fit

Question 21

What are the limitations of chi-square test? (x2)

Answer 21

Very sensitive to large samples (as used in CFA)

Assumptions of multivariate normality often not met

Question 22

What is the accepted convention for dealing with significant chi-square results in CFA? (x2)

Answer 22

Evaluate the importance:

*If chi-square over df > 2, misfit can be downplayed/dismissed

Question 23

What are alternative indices (to chi-square) used for in CFA? (x4)

Answer 23

Assess how much observed co/variance matrix accounted for by model
Absolute fit, and relative, against baseline model
Range 0 - 1 (no NHST)
*higher is better (goodness of fit)

Question 24

What 6 alternative indices are used in CFA?

And you should… (x1)

Answer 24

Normed fit index (NFI)		
Non-normed fit index (NNFI)
Incremental fit index (IFI) 	
Comparative fit index (CFI)
Goodness-of-fit index (GFI)    	
Adjusted goodness-of-fit index (AGFI)

Report 2 chosen a priori

Question 25

What are residual fit indices used for in CFA?

Answer 25

Assess amount of co/variance matrix not accounted for by model
    *Extent of model mispredictions
    *Diff between theory and data
Range 0 - 1 (no NHST)
    *Lower is better (badness of fit)

Question 26

What 2 residual fit indices are used in CFA?

And we should… (x1)

Answer 26

SRMR = standardized root mean squared residual
RMSEA = root mean square error of approximation

Report both

Question 27

What does a good model fit imply in CFA? (x3)

Answer 27

Hypothesised model/theory gives accurate account of the data
Theory-driven constraints on parameters were appropriate
*O/wise, poor fit…

Question 28

What doesn’t a good fit imply in CFA? (x3)

Answer 28

That the model is ‘correct’
That factor loadings are high (only that they’re not zero)
That factors explain lotsa variance - error terms are estimates

Question 29

What does a poor fit imply in CFA? (x3)

Answer 29

Model doesn’t adequately account for the data
Fails to capture underlying correlational structure
One of constraints/fixed parameters should be relaxed

Question 30

What could be producing a poor model fit in CFA? (x3)

And need to consider that… (x1)

Answer 30

Incorrect prediction of how DVs relate to factors?
*May need allowance to load onto others
May need to introduce between-factor correlations

Tinkering detracts from a priori theory testing

Question 31

What is involved in evaluating parameter estimates (step 3) in CFA? (x3)

Answer 31

Are significant loadings consistent with hypotheses?
Estimates for free parameters tested for significance
Against null hypothesis of factor loadings/correlations = zero

Question 32

What is involved in evaluating alternative models (step 4) in CFA?

Answer 32

Evaluating fit of simpler (factors nested) model

Does more parsimonious model give comparable fit?

Question 33

What can we conclude if alternative models give a poorer fit in CFA? (x2)

Which is determined by calculating… (x2)

Answer 33

Fails to accurately account for data
Original model better

Chi-square difference between model significance
*significant means poorer than original

Question 34

What can we conclude if alternative models give a better fit in CFA? (x2)

Which is determined by calculating… (x2)

Answer 34

That there are multiple plausible accounts for data
*Have to decide what to argue for…

Chi-square difference between model significance

* ns means as good as original
* choose most parsimonious

Question 35

What are the 2 important questions answered by CFA?

Answer 35

o How do variables correlate with factors?

o How do factors correlate with one another?

Question 36

What is 1 main con and 1 main pro in CFA over EFA?

Answer 36

More restrictive

But allows stronger conclusions

Question 37

What are 2 potential causes of misinterpretation of CFA results?

Answer 37

o Tension between multiple fit indices

o Potential to neglect and/or misevaluate relevant alternative models