Factor Analysis
Typically ignore factor loadings below
.40
Orthogonal (uncorrelated)
Assumes factors are completely independent, easy to interpret
Oblique (correlated)
Assumes underlying factors are correlated - can be harder to interpret
SPSS Factor extraction % of variance column
Can see the % of variance each factor explains the data
To reduce a data set to a manageable size EG
Collect 20 measures of intelligence, realise there are only 2 main factors - Verbal and Performance , so collapse scores over 20 measures down to 2 measures
Exploratory Factor Analysis
No past research, first time; looking for inter correlations amongst variable to identify underlying factors - no past research so not testing hypothesis.
Eigenvalue rule =
Kaiser (1960) rule
KMO stands for
Kaiser Meyer-Olkin Measure of sampling adequacy
PCA examines the correlation matrix and :-
Looks for variables that are strongly correlated; Identifies them as a potential factor; summarises (in one value) the magnitude of the variance the factor accounts for; Value is called the Eingenvalue
PCA and strongly correlated variables
likely to reflect an underlying factor that can explain a lot of variance in the data
Factor Analysis has
lots of measures, lots of DV's, groups of tests
Factors themselves are not
measured directly
To understand the structure of a construct EG
might want to understand the structure of IQ or personality
The larger the eigenvalue the
more variance in the data the factor can explain
If a large number of variables are measured and small clusters are strongly correlated...
with each other but not other variables they may represent important underlying factors
Factor Extraction ways
1. Principle Component Analysis (PCA); 2. Principal Axis Factoring (principle factors); 3. Image Factoring; 4. Maximun Liklihood Factoring; 5. Alpha Factoring; 6. Unweighted least Squares 7. Generalised Least Squares
Variables can be 1 and/OR 2 - 1
1. scores on a test (eg digit span scores) if looking for correlations between different test AND OR
Variables can be 2
2. Can be answers to individual questionnaire items if looking for correlations between different questions
PCA technical name for factors is
Component
Assumptions
Continuous data (interval or ratio); NO CATEGORICAL ; large sample size around 300, Normality - kolgorov smirnoff p>.05 QQ plots not s; no outliers (windsor data- replace with highest score not an outlier); Linerarity
PCA examines the
Correlation matrix
Factorability of the correlation matrix
Correlation matrix should show some correlations of r=.3 or greater, if only a few then factor analysis make not be appropriate
To design a new test measuring a construct EG
Designing a new personality test, so ask P's 100s of Q's about self see which strongly correlate to produce factors such as extroversion and introversion and discard others not associated with theses factors
SPSS oblique
Direct Oblimin; Promax
PCA looking for consistancy accross variables EG
Does everyone answer high to one question or another which identifies a common theme? Or high on same Q's
% of variance calculation
Eigenvalue/TOTAL # of potential factors ID x 100
Factor Analysis Definition
Generic name for a group of multivariate stats techniques that look for correlations amongst variables
Eigenvalue tells us
How good a factor is and how well it explains what is going on with the data
Kaiser (1960) rule
Only factors with an eigenvalue of 1 or more should be extracted
Two types of factor rotation
Orthogonal and Oblique
Confirmatory Factor Analysis
Testing whether previously identified factors are associated with previously identified variables - Test hypothesis
Factor plot points come from
The Component matrix
Principal Components Analysis (PCA) explores
The extent to which P's behaviour on each variable varies ( variation)
Factor Extraction is
The process of identifying factors within a large number of variables
Why we use Factor Analysis
To Understand a construct; design a new test that measures a construct; to reduce a data set to a manageable size
SPSS output Eigenvalue is in the
Total Variance Explained table
Factor Rotation
Transforms data to maximise the variance of factor loadings, making factors easier to interpret
SPSS - orthogonal
Varimax; Quartimax;Equamax
PCA looks for
consistancy in P's behaviour accross variables
Oblique rotation done first.. if there is a
correlation then switch to orthoganal
Variables are the
dependent measures being analysed in the Factor anlaysis
Catell's Scree Test (1966) -
plots Eigenvalue's on a graph, where we would extract anything above the point of inflection
Factor plot shows us
which variables are strongly associated with one factor
KMO
tests factorability - 0.6 good min value;
Bartletts test
tests factorability: Bartletts must be p<.05 sig;
Point of inflection - Scree
the point where the plot becomes near horizontal as these show the most variation in the data
Kaiser rule over 1 then
use Scree test as well
Latent variables are
variables associated with factors
PCA looks for communal
variance between variables
