FA; Lec 3 & 4; Lab 2 & 3

Question 1

Give an example of CFA.

Answer 1

Given a set of data you could determine which factor theory of personality best represents the data

Question 2

In the FA output, what should you be able to tell from the second column in the table ‘Total Variance Explained’?

Answer 2

How much of the variance is explained by the factors with an Eigenvalue above 1

Question 3

What is a problem with the Kaiser Guttman criterion?

Answer 3

It is sensitive to the number of items. Therefore, an increase in items = increase in eigenvalue.

Question 4

The Kaiser Guttmann needs to fulfill one of two criteria to be valid - what are they?

Answer 4

1. Either there must be <30 variables and ALL communalities >.7

OR

2. The sample size must be greater than >250 and AVERAGE communality must be >.6

Question 5

How does the Kaiser Guttman criterion work?

Answer 5

Generated factors with eigenvalues above 1 are removed as real factors.

Question 6

One purpose of FA is to show how many distinct common factors are measured by a set of test items - give an example of this.

Answer 6

Are the supposed different constructs: neuroticism, anxiety, hysteria, ego strength, self-actualisation, and locus of control, 6 independent entities or would they be better described as only 2 factors? (Elements of pathology: neuroticism, anxiety and hysteria; Healthy mechanisms: ego-strength self-actualisation and locus of control)

Question 7

Rotation has no impact on the overall variance explained - why do we do it?

Answer 7

Because we are searching for a simple structure and it helps us with this; it moves loadings around and cleans up the output. This aids our interpretation of the latent constructs.

Question 8

What is the most common orthogonal rotation?

Answer 8

Varimax

Question 9

One purpose of FA is to determine whether tests that purportedly measure the same thing in fact do so - give an example of this.

Answer 9

3 tests that claim to measure anxiety - FA may produce more than one factor indicating something in addition to anxiety is being measured.

Question 10

How do you conduct PCA (a type of EFA) with a correlation matrix and Varimax rotation in SPSS?

Answer 10

Analyse –> Dimension Reduction –> Factor –> Move all variables to ‘Variable’ box –> Extraction –> Scree plot –> Deselct ‘Unrotated Factor Solution –> Continue –> Descriptives –> KMO and Bartlett’s test of sphericity –> coefficients (for correlation matrix) –> Rotation –> Varimax –> Continue

Question 11

How do you interpret factors?

Answer 11

You use the factor loadings - anything >.3/>.32

Question 12

Why does the button ‘Eigenvalues over’ automatically become deselected when you indicated how many factors you want to be selected from the ‘Extraction’ dialogue box - why?

Answer 12

Because you aren’t using Eigenvalues anymore, you are forcing the result into a specific number of factors.

Question 13

What is an identity matrix?

Answer 13

When the R-matrix has no correlations/all correlations are 0

Question 14

If it is debatable whether, for example, a 2 or 3 factor solution makes more sense, what should you do?

Answer 14

Report the results of both interpretations and then follow one based on theoretical disposition. Since all the results will be reproduced enough information is available for someone with a different theoretical disposition to interpret the data in an alternative fashion.

Question 15

In the FA output, what does the table labelled ‘communalities’ tell us?

Answer 15

The first reads ‘Initial’ and indicates from a theoretical position that the communality of any item is potentially one.

The second, labelled ‘Extraction’ gives a different value for the communalities of the items after extraction has taken place.

Question 16

For data to be suitable for FA, should Bartlett’s be significant or not?

Answer 16

Significant

Question 17

What are the assumptions re variance of principal components analysis (PCA)?

Answer 17

• All variance explained by the factors

Question 18

In these two questions:
1. What is the capital of Spain?
2. What is the capital of Italy?
What is the common factor

Answer 18

Geographical knowledge

Question 19

How do you report Bartlett’s

Answer 19

Χ2(df) chi sq value, p><0.05

Question 20

Are loading factors with PAF going to seem less or more impressive than PCA?

Answer 20

PAF = Less impressive loading factors, because it allows for specific variance

Question 21

What must KMO value be for data to be suitable for FA?

Answer 21

Above 0.5

Question 22

What are the 4 parametric assumptions?

Answer 22

1. Must be continuous
2. Variables much be normally distributed and outliers must have been appropriately dealt with
3. Relationship between all variables appear to be linear, or at least not U-shaped or J shaped
4. All variables must be independent

Question 23

How do you estimate communality for PCA and PAF?

Answer 23

1. PCA - it is assumed to be 100% and therefore there is no estimation required
2. With PAF there is no agreed way to do this

Question 24

Whilst there are 7 steps to conducting PCA, this can be simplified to 3, what are they?

Answer 24

1. Determine the suitability of the data
2. Factor extraction
3. Rotation and interpretation

Question 25

One purpose of FA is to check the psychometric properties of a questionnaire - give an example of this.

Answer 25

Would a different population made of Chinese identify the constructs of extraversion-introversion and neuroticism which have been found in European cultures? Note: this would need to be done through confirmatory factor analysis

Question 26

When conducting FA you should look at the R-matrix for two potential problems, what are they?

Answer 26

1. Correlations are too low - variables with lots of correlations .9 for two variables or >.6 among many variables also possibly a problem)

Question 27

specific variance

Answer 27

variance that cannot be explained by the factors - fluke knowledge (e.g. knowing the capital of Spain because you went there, but not actually having good geographical knowledge)

Question 28

If you decide that the weakest factor is not worth retaining, how do you get rid of it in your SPSS output?

Answer 28

Go to the Factor Analysis 'Extraction' dialogue box and in the Box labelled 'Number of Factors' type in the number of factors you want to retain.

Question 29

How do you read a scree plot?

Answer 29

Going from left to right draw the first straight line that shows the data leveling off (elbow). No. factors above th line = number of factors to be retained

Question 30

In the FA output, what does the Rotated Component Matrix tell us?

Answer 30

It shows which items load heavily onto which factors based on the rotated solution

Question 31

Aside from parametric assumptions, how do you know if data are suitable for EFA?

Answer 31

1. There must be at least some correlations in the matrix that are above .3 2. There must be at least 100 participants and more participants than items; although partly a function of the 'strength' of the data

Question 32

What is an eigenvalue? Therefore, what does a scree plot indicate?

Answer 32

An indication of the amount of variance explained by any one factor. The scree plot graphically indicates how much variance is explained by the removal of successive possible factors.

Question 33

What is the simplest form of structural equation modelling?

Answer 33

CFA

Question 34

What is the most common oblique rotation?

Answer 34

Direct Oblimin

Question 35

What does factor rotation do?

Answer 35

It changes the position of the factors to ease interpretation. Each factor should have some large loadings and some small ones (simple structure). Large numbers of mediocre loadings should be avoided.

Question 36

FA will produce a correlation matrix. However, if we want to run this in SPSS beforehand how would we do it?

Answer 36

Analyse --> Correlate --> Bivariate --> Move the variables we are interested in correlating to the 'Variables' box --> OK

Question 37

What is the difference between exploratory factor analysis and confirmatory factor analysis?

Answer 37

EFA seeks to determine the number and nature of factors which underpin a set of data; while CFA allows you to choose between alternative hypotheses which purport to represent your data.

Question 38

What are the 4 basic purposes of FA?

Answer 38

1. To show how many distinct common factors are measured by a set of test items 2. Shows which items relate to which common factors 3. Determines whether tests that purportedly measure the same thing in fact do so 4. Checks the psychometric properties of questionnaire - with a different sample do the same factors materialise (CFA only)

Question 39

In the FA output, what should you be able to tell from the third column (Rotation Sums of Squared loadings) in the table 'Total Variance Explained'?

Answer 39

This column identifies the percentage of variance which each of the rotated factors now explains.

Question 40

A person's score on a factor can be calculated from what?

Answer 40

Their responses to items that load onto that factor. Items with greater loadings have higher weighting. You can then use factor scores for subsequent tests.

Question 41

If you expect your factors to be uncorrelated which kind of rotation should you use?

Answer 41

orthogonal - look at the rotated component matrix

Question 42

What do we usually use the Kaiser criterion to identify factors, and not the Joliffe criterion?

Answer 42

Joliffe retains too many factors

Question 43

In the FA output where do you look for the rotated solution?

Answer 43

'Rotated component matrix'

Question 44

What is a scree test?

Answer 44

It is based on eigenvalues of an unrotated solution

Question 45

What is a simple structure?

Answer 45

When a factor only have substatial loadings on a few item

Question 46

How does Bartlett's test of sphericity tell you if the R-matrix is an identity matrix?

Answer 46

If it is all correlations will be zero. A result with significance

Question 47

What is the difference between principal axis factoring and principal components analysis?

Answer 47

Principal components analysis (PCA) does not discriminate between common and specific variance, while principal axis factoring (PAF) does.

Question 48

SPSS sometimes produces strange numbers, if it produces a number with an E and a minus number after it e.g. 1.24E-02, what should you do?

Answer 48

Move the decimal place to the left the stipulated number of places. In this instance: 0.0124

Question 49

Large correlations between factors should be considered as what?

Answer 49

suspect

Question 50

Is there much difference between PCA and PAF?

Answer 50

They seem to produce very similar results; so much so that some researchers do not identify which one they are carrying out (although not good practice). However, since PAF allows for specific variance then an item's communality is necessarily going to be less than one; therefore, loading factors for items are going to appear less impressive with PAF as opposed to PCA.

Question 51

SPSS sometimes produces strange numbers, if it produces a number with an E and a positive number after it e.g. 1.24E02, what should you do?

Answer 51

Move the decimal place to the right the stipulated number of places. In this instance: 124.00

Question 52

Once you have your FA output, what 6 things should you look for to know that the data is suitable for FA?

Answer 52

1. Correlation matrix - some of the variables must be above .3 2. Bartlett's test - if its significant this means it is different from data selected at random 3. KMO - The least you should accept is .5 (.9 is superb) 4. Communalities - you want some above .4 5. The relationship between variables should be largely linear. But FA is robust so as long as it isn't J or U shaped you are okay 6 scree plot - interpret left to right as elbow to get initial idea of no. of factors

Question 53

What are two formal tests to assess data suitability for FA?

Answer 53

1. Kaiser-Meyer-Olkin (KMO) is a measure of sampling adequacy and addresses if the sample is big enough 2. Bartlett's test of sphericity - measures if the R-matrix is an identity matrix

Question 54

How would you clean up your component matrix if there were too many small values and it is hard to read?

Answer 54

Go to the Factor Analysis 'Options' and 'suppress small coefficients' This will get rid of values below .3

Question 55

Correlations detected from Bartlett's are unlikely to be...?

Answer 55

The product of chance

Question 56

In the FA output, what does the Component Matrix tell us?

Answer 56

It shows intial correlations between the items and the proposed factors. NOTE: Usually we don't use this

Question 57

When you report factor analysis what 5 things should you include?

Answer 57

1. Table of factor loadings 2. Extraction 3. Rotation methods 4. Rationale for the number of factors 5. Bartlett's and KMO

Question 58

What are the two questions that need to be asked in determining the suitability of a set of data for FA?

Answer 58

1. Is the sample big enough? 2. Are there at least some correlations between items in the sample (above .3 in magnitude) that would suggest that there might be underlying factors that could summarise some of the items used?

Question 59

1. What are the two types of exploratory factor analysis? | 2. How are they different from one another?

Answer 59

1. Principal components analysis and Principal axis factoring 2. They make different assumptions regarding unexplained variance

Question 60

When reporting FA what eight details should you include?

Answer 60

1. packages used (e.g. SPSS) 2. Presence of correlations with values .3 and above 3. KMO 4. Bartlett's 5. Inspection of scree plot (sometimes) 6. Number of factors with Eigenvalues exceeding 1 and how much variance (%) each one explains 7. Justification for removal of any factors and how much variance is explained by each of remaining factors 8. What kind of rotation was performed and whether this yielded a simple structure

Question 61

When factors are uncorrelated and commonalities are moderate, what does PCA produce?

Answer 61

Inflated values of variance accounted for by the components

Question 62

In the FA output, the table Total Variance Explained has three columns: 'Initial Eigenvalues', 'Extraction Sums of Squared Loadings' and 'Rotation Sums of squared loadings', what is the difference between these two?

Answer 62

The second column ignores potential factors that have an eigenvalue below 1

Question 63

According to PCA, what is 'total variance' equal to?

Answer 63

Total variance = common factor variance + measurement error

Question 64

What does variables being independent mean?

Answer 64

That they cannot be calculated from other variables - e.g. if item A was height and B was weight, then it would be inappropriate for C to be a height to weight ration since it would necessarily be correlated to both A and B

Question 65

What does varimax do?

Answer 65

Tries to equalise variance across all the factors

Question 66

What are 4 possible errors in factor analysis?

Answer 66

1. Interpreting the unrotated solution (SPSS spits this out by default) 2. Applying rigid rules to the extraction of factors (KG vs scree method) 3. Replication is very important 4. Factor validity is not attested to only by item content (face validity), it must also be compared with some other measure

Question 67

What you rotate a solution what changes? What doesn't?

Answer 67

The communality of each variable remains the same. The eigenvalues of factors do not

Question 68

What is regression and what is it used for?

Answer 68

It is a weighted sum of the factor loadings, used to calculate the factor scores.

Question 69

What is a varimax rotation?

Answer 69

An orthogonal rotation - tries to make factors independent by turning them to 90 degrees

Question 70

If you expect your factors to be correlated which kind of rotation should you use?

Answer 70

Oblique - look at the pattern matrix

Question 71

Why does the sample size have to be big enough?

Answer 71

Because FA is easily influenced by error variance

Question 72

Which is the simplest form of FA and suitable for undergraduate level?

Answer 72

Principal components analysis (PCA)

Question 73

According to principal components analysis (PCA), all items have a communality of what?

Answer 73

1 | Therefore the factors will, between them, account for 100% of the variation among the items.

Question 74

KMO is a measure of sampling adequacy and addresses if the sample is big enough. What are its ranges?

Answer 74

``` >.5 min .5-.7 mediocre .7-.8 good .8-.9 great .9< superb ```

Question 75

What are the 7 stages of carrying out exploratory factor analysis?

Answer 75

1. Ensure that data are suitable 2. Decide on the model - PAF or PCA 3. Decide how many factors are required to represent the data 4. When using PAF estimate the communality of each factor 5. Factor extraction 6. Rotate the factors ensuring that simple structure has been reached 7. Compute factor scores

Question 76

According to principal axis factoring (PAF), what is 'total variance' equal to?

Answer 76

Total variance = common factor variance + specific item variance + measurement error

Question 77

Is the scree plot alone enough to identify latent constructs?

Answer 77

No. FA should always be conducted in light of psychological theory - how many factors does it make sense to extract from a psychological point of view.