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