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research methods 2 > Factor Analysis > Flashcards

Factor Analysis Flashcards

1
Q

what is factor analysis?

A

looking at the structure of a concept using data and simplying seeing if there’s any structure between variables

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2
Q

what is the importance of the structure?

A

should be psychologically meaningful

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3
Q

how do we conduct factor analysis?

A

take lots of data on different variables, look for a specific pattern and see if you can simply it down to one or two psychological meaningful elements which have the underlying structure of the concept

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4
Q

what is the definition of factor analysis?

A

powerful tool when you want to simplify complex data, find hidden patterns, and set the stage for deeper, more focused analysis

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5
Q

what is an example of a test using factor analysis?

A

WAIS-R -> measuring general intelligence

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6
Q

what do we want to figure out with tests like WAIS-R?

A
  • what the underlying structure of these tests
  • what the actual structure is when we look at the data underneath -> having psychologically meaningful elements that underline a score
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7
Q

what is factor analysis about?

A

simplification
* structure beneath two variables -> breaking it down into 1 or 2 meaningful psychological elements

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8
Q

what does orthogonal mean?

A

people can vary along them independently
(variation on one does not affect the variation on the other -> factors are uncorrelated and not related to each other)

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9
Q

elements of analysis

A
  • need a way to diagnose or find a structure underlying the data -> extract dimensions (or factors) from the data set
  • need a way of representing the structural elements within the analysis which allows us to make decisions into whether they are important or not -> need to be able to make judgments about the factors and relate it back to the individual item’s we’ve got (need to see how the individual elements we have relate to the structure)
  • some form of structural element that represent these factors
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10
Q

what does analysis allow us to do?

A
  • allows us to make judgements about the factors
  • information about how the individual item, score etc. relate to the structural dimension/factors
  • how much each item relate to the structural element
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11
Q

how should we extract dimensions (or factors) from data set?

A

using principle component analysis (incl rotation)

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12
Q

what are sone structural events that represent these factors (allowing us to make judgement about them)

A

eigenvectors and values

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13
Q

what are factor loading?

A

information about how the individual items, scores etc. relate to structural factor

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14
Q

what is principal component analysis (PCA)?

A
  • takes a cloud of data points and finds the ‘principal axes’ of that cloud -> which are at right angles to each other
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15
Q

what does PCA allow you to find?

A

factors (structure) in factor analysis
* PCA is a way of doing factor analysis
* principal axis underlie our data
* a way in which we extract structure from a cloud of data

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16
Q

what are principal components sometimes called?

A

eigenvectors (with associated eigenvalues)

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17
Q

PCA

A

a dimensionality reduction method that is often used to reduce the dimensionality of large data sets, by transforming a large set of variables into a smaller one that still contains most of the information in the large set.

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18
Q

what are eigenvectors?

A

a mathematical foundation of the factors / components

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19
Q

what does each eigenvector have?

A

an eigenvalue

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20
Q

what is an eigenvalue?

A

tells you how important each individual eigenvector (representation of the factors) is and therefore how important each factor is

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21
Q

how do we use the eigenvalues?

A
  • values tell you which factors are important
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22
Q

which eigenvectors can we ignore?

A

those with small eigenvalues (as they’re pointless)

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23
Q

which eigenvectors should we not ignore?

A

eigenvalues which are big/large as they are important/explain a lot of the variation (because of how strong they are)
-> will give you a graph like a positive correlation instead of no correlation

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24
Q

which two methods can we use to know which factors are important?

A

Kaiser’s Extraction and Screeplot

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25
Q

Kaiser’s Extraction (1960)

A

retain factors with Eigenvalues >1. (any eigenvalue over 1 is important, anything below 1 is less/ not important)
-> unless a factor extracts at least as much as the equivalent of one original variable, we drop it

26
Q

Scree Plot by Cattell (1966)

A
  • Uses ‘point of inflexion’ of the scree plot
  • interesting in the point at which it starts flattening out and there’s a point of inflexion
27
Q

what does the kink in a scree plot tell you?

A

how many factors (component number) you want to use
* one’s after the kink are pointless because the eigenvalue is much lower

28
Q

what are the pros and cons of a scree plot?

A
  • simple
  • subjective but will give you a way to see how many factors are important
29
Q

which method is more preferred?

A

Kaisser’s Extraction

30
Q

what is factor loading?

A
  • once we have our main factors extracted (and after rotation), we have loading
  • want to know how much each element relates to that factor -> element is said to be ‘loading on a factor’
  • individual elements can load on more than one factor
  • can be tricky to interpret -> but you’re trying to interpret what these factors are
31
Q

what do the factors in factor loading range from?

A

0 to 1
* loading can be negative or positive depending on the nature of the relationship to the element

32
Q

factor loading range

A
  • high loading above .5 (element highly related to that factor)
  • .3 (anything less than this is not really important)
33
Q

factor loading

A

the correlation coefficient for the variable and factor. Factor loading shows the variance explained by the variable on that particular factor. In the SEM approach, as a rule of thumb, 0.7 or higher factor loading represents that the factor extracts sufficient variance from that variable

34
Q

What is factor rotation?

A
  • way in which you can simplify your structure and association between the element you’ve got and the structure
35
Q

Why do we simply structure of analysis in rotation?

A

makes it easier to interpret (allows you to actually interpret what you get and the outcome of your results)

36
Q

To aid interpretation it is possible to maximise the loading of a variable on one factor while minimising the loading on other factors. What are two ways in which this can be done?

A

Orthogonal and Oblique

37
Q

Orthogonal

A

(factors are uncorrelated): Varimax

38
Q

Oblique

A

(factors intercorrelated): Oblimin
-> tend to be in the same sector of the grid

39
Q

what does rotation allow us to do?

A
  • see how loading works -> depending on the relationship of individual elements on the factors
  • allows us to understand / have a guess what the factor is / actually are (i.e. factor all problem solving tests, verbal comprehension, perceptual organisation, freedom from distractibility) -> naming variables as a guess
40
Q

what is the point of factor rotation?

A

simplification -> allows you to interpret what you get from the analysis visually
* trying to get factors lines to fit better with the data in a way which means you can interpret the outcome

41
Q

what assuring our data is suitable, what do we have to check for

A

the relationship between the variables -> our data has to be correlated
* variables / dimensions should be correlated together (r > .3)
* correlation matrix is the basis of analysis -> looking for commonalities using the correlation matrix if there is none, we won’t find any

42
Q

making sure data is correlated, r > ?

A

.3

43
Q

what happens if our data is not correlated?

A

you’re not going to find the structure

44
Q

what happens if the data is too correlated?

A

multicollinearity is an issue in PCA
-> correlation amongst variables cannot be too high because that affects analysis (because you’d just end up having one singular variable which you’ll continually testing)

45
Q

what do we want to avoid in data relationship?

A

avoid singularity (you don’t want to be testing the same thing over and over)

46
Q

what’s a blockak specific?

A

our variables are too highly correlated and all you ever extract is one factor
-> when we want our elements to be correlated but not too correlatied)

47
Q

How can we test the data to make sure it isn’t too correlated?

A

Barlett’s Test of Sphericity

48
Q

Barlett’s Test of Sphericity

A

checking for very low correlations across all variables
* testing null hypothesis that there is no correlation between the variables
* should be significant at p < .05 -> so we can reject the null hypothesis (that there is no correlations) - this is what we want

49
Q

Barlett’s Test of Sphericity: Determinant

A

tells you whether you have multicollinearity
* Indicator of mulitcollinearity and should be greater than 0.00001.
* If so your correlation are not too high
* if below that, your correlation is too high

50
Q

Another assumption is data sample size

A

YOU NEED A BIG SAMPLE -> the bigger the better
* 100 is low, 300 is good 1000 is great.
* There should be about minimum 2 participants per variable, but the larger the better (some recommend 10:1)
* will determine how reliable your factor structure is and to some extent how likely you are to find a structure

51
Q

How can ensure sample size is fine?

A

Kaiser-Meyer-Olkin (KMO)

52
Q

Kaiser-Meyer-Olkin

A
  • indicates how good/adequate your sample is based on the interrelation of the variables (and size of the sample)
  • should be > 0.5 (greater than) -> is adequate
  • 0.7 is very very good and means it’s big enough to do a factor analysis
  • If you’re getting 0.6, it may not be good enough for you to get a clear enough view of the structure
53
Q

In PCA factor rotation’s job is to..

A

aid the interpretation of the factor structure and clarify the factor structure

54
Q

Eigenvalues allow us to…

A

determine the importance of factors and reduce the number of factors in the final structure

55
Q

Checks

A
  • Determinant = 0.002
  • Kaiser-Meyer-Olkin Measure of Sampling Adequacy (KMO)
    ○ .750
    ○ >.50 is adequate
  • Bartlett’s Test of Sphericity
    ○ Tests that there is a level of correlations between our variables (item scores)
    ○ Needs to be significant
56
Q

Table of Eigenvalues

A
  • We have set 1 eigenvalue as the lowest level of extraction
    ○ We have said we are not interested in anything lower than I (Kaiser’s cut off point)
  • In our criterion (and Kaiser’s) we have 5 factors left
    ○ Which explain 59.28% of the variance
    ○ The components (factors) are ranked in order of importance
    Scree Plot
  • To check on the number of factors (components in the graph) we can look at the Scree plot
    ○ There are 5 factors above the inflection point
  • So Cattel and Kaiser criterion agree.
  • Which is good evidence for extracting 5 factors
    …and not uncommon.
57
Q

Factor Loading [in rotated component matrix table]

A
  • How much each item correlates with the factor
  • The higher the absolute value the stronger the relationship
  • Negative factors scores mean the relation with the factor is inverted
  • For clarity we can strip out the factors below .4
58
Q

what happens if a correlation is negative?

A

negative loading -> can reverse code these as well as change the scale
* means there tends to be a negative correlation between general response and statement

59
Q

what is reliability?

A
  • internal consistency of a measure
  • how much can you rely on a score from a test, sub scale etc.
  • how good your measure is at measuring something
60
Q

what is Cronbach’s Alpha (α)

A
  • reliable if α > .7 (greater than)
  • depends on the number of items -> more questions tend to produce a bigger α
  • treat sub scale separately
  • all scores should be in the same direction
  • reverse code, reverse questions
  • is a property of a set of test scores so α can change across different populations
  • you should do your own reliability measure even for established tests
61
Q

Factor scores for individuals

A
  • You can use factor analysis to get individual scores for each participant (and this is called factor scores)
  • You can get scores for each factor for each participant
  • Calculated by a combination of the factor loadings and the actual scores
  • You can have an extroversion score, an agreeableness score, etc. for each participant (based on factor scores)
  • You can use these in your analysis as variables
  • If we had a wellbeing measure
  • We could see what of our new measures can predict wellbeing
  • This is useful because we can use that to predict wellbeing (i.e. from personality)
  • We can use factor loading with score and then use that of analysis of individual factors - we will look at this in the lab

research methods 2 (8 decks)

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