Week 5 - Structural Equation Modelling 1 (Confirmatory factor analysis)

Question 1

What is it about Structural Equation Modelling (SEM) that makes is particularly useful, relative to all the other techniques we’ve been taught (like regression, ANOVA, etc)

Answer 1

All those techniques are limited to looking at a single relationship at a time, where as SEM allows you to look at multiple relationships simultaneously.

Question 2

Confirmatory Factor Analysis and Path Analysis are both examples of what?

Answer 2

Structural Equation Modelling

Question 3

A Structural Equation Model typically has two ‘parts’. What are they?

Answer 3

1. The measurement model

2. The structural model

Question 4

What is the difference between Exploratory Factor Analysis and Confirmatory Factor Analysis?

Answer 4

EFA can impose two kinds of restriction:

• number of factors
• constrain the factor loadings to be uncorrelated (ie orthogonal rotation)

CFA can restrict factor loadings (or factor correlations or variances) to take certain values

• a common value: zero
• if a factor loading was set to zero the hypothesis sis that the observed variable score was not due to the factor
• we get a measure of model fit

Also the sense that CFA contains a hypothesis whereas EFA does not

Question 5

Confirmatory Factor Analysis is ultimately a measurement model, T/F

Answer 5

TRUE

Question 6

What are the seven issues that Geoff discussed in relation to CFA?

Answer 6

1. Sample size
2. Significance testing
3. Distribution
4. Identification
5. Estimation (methods of)
6. Assessment of fit
7. Specify the model

Question 7

In CFA, how should we think about SAMPLE SIZE?

Answer 7

In short, it depends. There are various opinions. But at very least, you need a decent sample size.

It’s ropey, but you can work with the idea of wanting more than 20 participants per survey item, and being in trouble if you have less than 10 per item.

Question 8

In CFA, how should we think about SIGNIFICANCE TESTING?

Answer 8

It’s not such a big deal in CFA.

CFA adopts a ‘higher level’ view.

Also significance testing is pretty suspect just generally

Question 9

In CFA, how should we think about DISTRIBUTION?

Answer 9

The default technique (maximum likelihood) assumes MULTIVARIATE normality

Widaman (2012): maximum likelihood estimation appears relatively robust to moderate violations of distributional assumptions.

CFA assumes CONTINUOUS variables

Question 10

In CFA, it is important that your model is IDENTIFIED.

What are the requirements for this?

Answer 10

1. Model degrees of freedom must be greater or qual to 0
2. All latent variables must be assigned a scale (don’t know what this means atm)
3. A number of equations must be solved

Question 11

With CFA, would we prefer our model to be UNidentified, JUST identified or OVERidentified?

Answer 11

Over

Question 12

For EFA, what are the three most commonly used methods of estimation?

And which one is preferred

Answer 12

1. Unweighted Least Squares
2. Generalised Least Squares
3. Maximum Likelihood**

Question 13

In EFA, when assessing model fit, do you want small or large p value?

Answer 13

LARGE!

Question 14

With EFA, what is the main model fit test statistic used?

Answer 14

Chi squared

Question 15

What’s the eccentric thing about using Chi Squared to test model fit for EFA?

(Hint: sample size)

Answer 15

It punishes large samples and rewards small samples

Question 16

What are the two types of EFA model fit test statistics/approaches?

Answer 16

1. The Model Fit indexes (always Chi squared)

2. Approximate Fit indexes (of which there are at least three)

Question 17

What are three types of approximate fit indexes Goeff mentioned?

Answer 17

Absolute (eg Standardised Room Mean square residual - SRMR)

2. Comparative (e.g. Comparative Fit Index - CFI)
3. Parsimony (e.g. Root Mean Square Error of Approximation - RMSEA)

Question 18

What are three types of approximate fit indexes Goeff mentioned?

Answer 18

Absolute (eg Standardised Room Mean square residual - SRMR)

2. Comparative (e.g. Comparative Fit Index - CFI)
3. Parsimony (e.g. Root Mean Square Error of Approximation - RMSEA)

Question 19

You want you factors to explain X% or more in each of your observed variables. What is X?

Answer 19

.50

Question 20

You do you do if you notice that your factors explains less than 50% of the variance of one of your observed variables, what should you do?

Answer 20

Discuss it qualitatively … pay attention to it.. have a look.. maybe delete it