Week 11 - Factor Analysis Flashcards

1
Q

What 2 aims of factor analysis used for ?

A

1) When looking for the underlying (predicted) structure of a set of related variables (You are specifically looking for an effect that you want to exist)
2) Trying to reduce set of variables to a single, composite variable that combine shared info in them (Variance) (More of an exploratory approach)

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2
Q

What does factor analysis seek to do?

A

Factor analysis seeks to form linear composites (sums of underlying variables)that represent the underlying structure of the correlation matrix
- Groups of highly intercorrelated items whose variance is well explained by the composite

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3
Q

What is main goal of factor analysis?

A

To start with a set of measured variables and find the smallest number of factors to account for most the variance in the measured variable and the correlations between them

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4
Q

Factor analysis allow to

A

Make statements about the patterns of intercorrelations

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5
Q

Typical factor analysis set up

A

Set of observed (questionnaire items) or conceptually related items (No Y variables)

  • Does underlying structure link a subset of items?
  • Subsets of variables that correlate highly with one another and low on other factors
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6
Q

Factor analysis is …

A

Geometric, based on correlations and the pattern of correlations that suggest linked items

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7
Q

Factors (Composites) in factor analysis should

A

Explain more than or two variables

Should explain systematic variance and exclude individual error as much as possible

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8
Q

History of factor analysis

A

Used in intelligence test (underlying g)

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9
Q

What can;t factor analysis do

A

Test for significance

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10
Q

2 reasons for doing factor analysis

A

1) data reduction to provide composites for further study
- empirical and technical reason
- after analysis is done we can obtain a factor as a new composite variable in our dataset
2) Investigate the underlying structure of a set of measured variables
- Give name to these variable using subjective judgement

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11
Q

Latent Variable

A

Not directly observed variable, Factor analysis uncover these

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12
Q

Observed Variables

A

Directly observed, exist in dataset already

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13
Q

Two Varieties of Factor Analysis

A

1) Principle Components factor analysis (PCA)

2) Factor analysis (Common factor model) (PAF)

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14
Q

Principle components factor analysis

A

Most basic form
Use mathematical properties of matrices (numbers)
Straight data reduction where error in original variables is not partialled out (all variance is used) (Does not ignore error in individual item)

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15
Q

Common factor model

A

First utilised for theory building - start with a set of variables and need to know how many dimensions (components) they contain
Known as exploratory factor analysis
Analyses common variance and leave out the unique variance to each individual variable

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16
Q

Differences Between PCA and PAF

A

PCA- Components PAF - Factors

PCA use R as is (diagonal)
PAF analyse covariance and modify R (estimated communalities on diagonal)

17
Q

Confirmatory factor analysis

A

Can test for significance, number of factors and and fit

18
Q

Subscale

A

Composite of constituent items

19
Q

Factor

A

Weighted linear composite

20
Q

In factor analysis we want to use data reduction to…

A

Reduce the number of measure variables (fewer = less error and more reliability)
Use a group of measured variables to indicate underlying construct that we can’t measure directly

21
Q

Correlation Matrix

A

Contain number of underlying factors and components (Implicit)

22
Q

Extraction

A

Extract factors, but only as few as needed to adequately summarise all the measured variables
Everytime we want to extract new factors we have to run another analysis
Each factor based on principle components of the correlation matrix

23
Q

Principle component of correlation matrix (4)

A

1) Ordered from first to last (As many principle components as they are variables)
2) Each account for as much variance as possible in the whole set of variables (first factor is always the largest as it is trying to account for all the variance in factors)
3) first the largest, then sequentially become smaller
4) Next principle component account for as much of the remaining variance and is uncorrelated with all the preceeding components.

24
Q

What is a factor/component

A

Each factor made up of sum of all measure variables (composite)

  • weighted to reflect the strength of the correlation (Relationship with the variables)
  • Higher weight = stronger relationship with the factor/component
25
Q

What are loadings

A

Tell us how much each variable link up with the factor/component
The correlation of each measured variable with each factor
Range from 0 - 1 (0 = no loading) (1 = high correlation/loading)
Help us to find out how much variance of the measured variable is shared with the factor/component
Loading sizes .3 = min .5/.6 = mod .7/.8 = high

26
Q

What are communalitites

A

How much each variable is explained by the factors/components
PCA = Communalities = 1
PAF = Communalities = Estimated squared multiple correlation (amount of variance accounted for by all the other variables)

After extraction Communialities become (h2) = sum of squared factor loadings

Use info from communalities to find how many factors and need to know number of factors to do communalities (indeterminacy problem)

27
Q

Rotation Types

A

Initially principle components are all uncorrelated (factors completely independant, no overlap)

Orthogonal (Varimax) = Not correlated

  • Maintains strict structure
  • Good for interpretation, may not match construct/ data

Oblique rotation (oblim) = Allow correlation

  • Relax constraint
  • distinct but related factors
  • when underlying constructs are seperate but related
28
Q

Rotation

A

Re-weight the loadings to achieve simple structure

29
Q

Simple structure

A

Is desirable - each variable only have high loading on 1 factor (Usually this does not occur)

30
Q

Eigenvector

A

Principle Component

31
Q

Eigenvalue

A

Variance explained by each component (total variance of all variables)
Each eigenvector has an associated eigenvalue

Negative eigenvalue mean there is measurement or statistical issue

32
Q

Steps of factor analysis (6)

A

1) Obtain data on a set of variables
2) Standardise and create correlation matrix
3) Check there is a point to doing the factor analysis (Screening Run)
4) Extract components/factors
5) Rotate the ones you have extracted
6) Interpret loadings of variables on the factors

33
Q

KMO

A

Measure sampling adequacy (.6 adequate)

Lower than .6 = more randomness than factors

34
Q

Bartletts Sphericity

A

How far from 0 is your actual data (Identify matrix)

If violated = Can;t do meaningful factor analysis

35
Q

Initial Communalities

A

Starting point

36
Q

After extraction communalitites

A

Update after specific factors have been removed/extracted

37
Q

Choosing factors to extract

A

Retain with egeinvalue >1 (Account for more variance than one single variable)
Catells scree test - as variance explained by factors decreases less rapidly (elbow in the plot) suggest the number of factors to extract (Subjective - inter-rator reliability can be low)