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Statistics > Factor Analysis > Flashcards

Factor Analysis Flashcards

1
Q

What is the aim of FA

A

To reduce a larger set of variables into a smaller set of components

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2
Q

The ‘smaller set of components’ in FA aims to…

A

Account for most of the variance in the original variables

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3
Q

How is factor analysis done?

A

By analysing patterns of correlations between variables

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4
Q

Groups of variables that relate highly to each other…

A

Constitute a factor

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5
Q

What is one type of factor analysis?

A

Principle components analysis

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6
Q

Difference between PCA and FA?

A

FA is often used with a smaller set of variables

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7
Q

Idea underlying the PCA equation…

A

Equation that MAXIMISES the variance accounted for by a component

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8
Q

The second component should be ______ with the first

A

Uncorrelated

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9
Q

The second component should be uncorrelated with the first, yet still

A

Accounting for max amount of variance remaining

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10
Q

A Factor loading is…

A

The correlation between a variable and a component

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11
Q

“The correlation between a variable and a component” - What is this?

A

Factor loading

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12
Q

What would we do with factor loadings to tell us the variance this component explains over others?

A

Squaring and summing

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13
Q

Absolute loadings above >.3 are…

A

Salient and interpreted

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14
Q

Where do we find the factor loadings in SPSS?

A

Component matrix

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15
Q

The level of correlation considered worthy of a variables inclusion is usually…

A

> .3

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16
Q

You would examine the correlation matrix to see…

A

If there are any variables NOT strongly correlated with any other variable

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17
Q

Communalities are…

A

Proportion of variance in a variable accounted for by EXTRACTED COMPONENTS

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18
Q

If you were to retain all components in the analysis, you will be able to account for all the variance in the variables. Why don’t we just do this?

A

This not the purpose

Purpose is to explain as much variance as poss whilst using as few variables as poss

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19
Q

Total Variance Explained table…How many components are usually extracted?

A

Generally only the first few

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20
Q

What is an Eigenvalue?

A

The measure of VARIANCE accounted for by a COMPONENT

Sum of squared loadings within a component

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21
Q

An Eigenvalue of 1 represents the….

A

Variance of one variable

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22
Q

Eigenvalues

25 variables represents…

A

25 eigenvalues

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23
Q

What is the most popular method for choosing COMPONENTS to retain?

A

Eigen-value one criterion (Kaiser criterion)

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24
Q

What is Kaiser’s criterion recommendation?

A

Eigenvalue less than 1 should not be retained

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25
Q

Kaiser’s Criterion states that a variable less than one indicates…

A

That the component explains less than a variable would

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26
Q

How is an Eigenvalue calculate?

A

Sum of squared loadings within a component

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27
Q

Eigenvalues range between…

A

0-total number of components

28
Q

An Eigenvalue larger than ____ is GOOD

A

1

29
Q

An Eigenvalue larger than 1 indicates the factor…

A

Should be selected

30
Q

A communality of ____ suggests that the variable is _______ and should be _______

A

< .3
Unreliable
Removed

31
Q

Aside from Kaiser’s Criterion, what else can we use to decide which components to keep?

A

Scree plot

32
Q

What does a scree plot tell us

A

Total variance explained by each component against its respective component

33
Q

Scree plot

How do we know which components to retain

A

Those before last inflection point

34
Q

Scree plot

The inflection point represents

A

The point at which the graph begins to level out

Subsequent components add little

35
Q

“The point at which the graph begins to level out
Subsequent components add little”

What does this description refer to?

A

Inflection point

36
Q

A scree plot is another way of…

A

Deciding which components to keep/remove

37
Q

The first Factor Loading matrix SPSS will display is…

A

Unrotated

38
Q

What is one way of visualising the clusters of variables that form the components?

A

Plot variables in a factor space

39
Q

Our ideal result would be where each variable loads uniquely onto…

A

ONE COMPONENT ONLY

40
Q

Our ideal result would be where each variable loads uniquely onto one component only. However, what do we often find?

A

Cross-loading

41
Q

Two ways of solving cross-loading?

A

Orthogonal/oblique rotation

42
Q

What is orthogonal rotation?

A

Where we rotate the axis to fit the data we’ve got

43
Q

What is the difference between orthogonal and oblique rotation?

A

Oblique moves through each axes independently until they go through items

44
Q

Why are orthogonal/oblique rotations used?

A
  • Solves cross-loading

- Makes interpretation easier

45
Q

6 STEPS OF FACTOR ANALYSIS

A 
a) Matrix of Correlations 
B) Extract factors (Kaiser's) &amp; Scree plot
C) Examine FLs and communalities 
D) Do factors need rotating 
E) Check FLs again
46
Q

A PCA can be used to solve three major problems…

A

a) Removing unrelated variables
b) Reducing redundancy
c) Removing multicollinearity

47
Q

What is multicollinearity

A

Two or more variables that are highly correlated

48
Q

“Two or more variables that are highly correlated “ Whats this

A

Multicollinearity

49
Q

What does ‘redundancy’ refer to

A

Some of the variables are measuring the SAME UNDERLYING CONSTRUCT (not what you want)

50
Q

What do we look at: SPSS

A

M of Correlations
Communalities
Eigenvalues
Factor loadings

51
Q

Orthogonal rotation can sometimes create factors that are _______ or ________ with each other

A

Correlated

Uncorrelated

52
Q

The proportion of variance each variable explains in the principle (extracted) components

What is this describing

A

Communalities

53
Q

Comment on Factor Loadings

All items load highly onto the first component. Only some items load highly (both positively and negatively) onto the second factor.

Does this indicate a simple factor structure?

A

No - they need to be rotated

54
Q

Factor loadings are the

A

Correlation between variable and component

55
Q

“Correlation between a variable and a COMPONENT”

What is this

A

Factor loadings

56
Q

Communalities

What is the cut-off for removal

A

.3

57
Q

If there are 2 components making up the component matrix, this tells us…

A

2 components have been extracted

58
Q

Orthogonal rotation keeps the axes at ______ ________, whereas Oblique does not

A

Right angles

59
Q

How do you decide if it is complex structure when there are 3 components?

A

If there are items that load highly onto more than 1 component

60
Q

Inspection of the commonalities revealed that the two factors accounted for (>.30)

A

Sufficient amount of variance in all items

61
Q

Inspection of the commonalities revealed that the two factors accounted for sufficient amounts of variance in all items (>.30), indicating that

A

All items were reliable

62
Q

The rotated factor loadings were plotted, which confirmed the clear

A

X factor structure

63
Q

Write-up

Inspection of the FL’s indicated that all items loaded strongly (>.40) on both factors. The factor loadings were therefore

A

Plotted

64
Q

Write-up

The unrotated factor loadings were then plotted which indicated

A

The factors should be subjected to rotation

65
Q

Write-up

The rotated factor loadings were also plotted, which

A

Confirmed a clear two-factor structure

66
Q

Write-up

Inspection of the commonalities revealed that the two factors accounted for

A

Sufficient amounts of variance in the items (>.30)

Statistics (9 decks)

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