Factor analysis Flashcards
Why use factor analysis?
- effective for investigating relationships for complex concepts
- investigate concepts not easily measured
Test dimensionality
how many dimensions does the test have?
are the dimensions correlated?
Unidimensional
reflect only one psychological dimension
dimensionally has implications for scoring, evaluation and use
Multidimensional tests with correlated dimensions
- tests with higher order factors
- items reflect more than one psychological attribute
- correlated dimensions
Two types of factor analysis
- exploratory factor analysis (EFA)
- confirmatory factor analysis (CFA)
Steps of EFA
- choose extraction method
- identify number of factors
- factor rotation
- examine factor loadings
- examine inter-factor loadings (where approriate)
PAF
principal axis factoring
PCA
principle components analysis
Elgenvalues
examine elgenvalue sizes, location has implications for number of dimensions
- egenvalue > 1.0
Factor rotation
- Used with multidimensional scales
- to clarify psychological meaning of factors
Two general types of factor analysis
- orthogonal rotation (uncorrelated)
- oblique rotation (either correlated or uncorrelated)
“Factor loading”
- range between -1 and +1
- influenced by type of rotation
orthogonal
loadings can be seen as correlations
oblique
several kinds of loadings
pattern coefficients
unique associations - unique association between item and factor
structure coefficients
correlations between responses and total
size of loadings
> .30 or .40 = strong
>.70 or .80 = very strong
positive loading
high score on item can have high level of factor
negative loading
high score on item have low level of factor
Examining associations among factors
- oblique rotations
- correlation for each pair of factors
- higher-order associations
primary objectives of EFA
determine number of common factors and strength of relationships
Confirmatory factor analysis (CFA)
- confirmatory procedure
- used when there are clear indication of test dimensionality
- testing specific hypotheses about underlying dimensions
Primary objective of CFA
determine the ability of a predefined factor model to fit an observed set of data
Factors affecting responses to test items
- respondent trait level
- item difficulty
- item discrimination
IRT measurement models
- one parameter logistic model
- two parameter logistic model
- three parameter model
One parameter logistic model (Rasch model)
- simplest IRT model
- responses to binary items = determined by item difficulty
- trade off between trait level and item difficulty
- applies only to binary items
Two parameter logistic model
- more complex
- includes two item parameters
- responses to binary items (trait level, item difficulty, and item discrimination)
Three parameter model
- incorporates respondent guessing
- as trait increases as does chance of guessing correct
Graded response model
Many tests include more than two response options.
- specific order, or ranking of responses
- allows us to estimate how well test questions measure latent trait
Initial parameter estimates obtained through two-step process
- determine proportion of items each respondent answered correctly
- compare response probabilities to actual responses
Model fit
- ‘fit includes’ - reflect model compatibility with actual responses
- suggest incompatibility - exercise caution
- suggest good fit - proceed with interpretation
Item and test information
- IRT provides information about items and tests
- item characteristics are used to evaluate items and maximise test quality
Item characteristic curves
- reflects relationship between latent ability and performance on test items
- each item has a curve
Applications of IRT
- test development and improvement
- differential item functioning
- person fit
- computerised adaptive testing
