Factor analysis

Question 1

Why use factor analysis?

Answer 1

• effective for investigating relationships for complex concepts
• investigate concepts not easily measured

Question 2

Test dimensionality

Answer 2

how many dimensions does the test have?

are the dimensions correlated?

Question 3

Unidimensional

Answer 3

reflect only one psychological dimension

dimensionally has implications for scoring, evaluation and use

Question 4

Multidimensional tests with correlated dimensions

Answer 4

• tests with higher order factors
• items reflect more than one psychological attribute
• correlated dimensions

Question 5

Two types of factor analysis

Answer 5

• exploratory factor analysis (EFA)

- confirmatory factor analysis (CFA)

Question 6

Steps of EFA

Answer 6

• choose extraction method
• identify number of factors
• factor rotation
• examine factor loadings
• examine inter-factor loadings (where approriate)

Question 7

PAF

Answer 7

principal axis factoring

Question 8

PCA

Answer 8

principle components analysis

Question 9

Elgenvalues

Answer 9

examine elgenvalue sizes, location has implications for number of dimensions
- egenvalue > 1.0

Question 10

Factor rotation

Answer 10

• Used with multidimensional scales

- to clarify psychological meaning of factors

Question 11

Two general types of factor analysis

Answer 11

• orthogonal rotation (uncorrelated)

- oblique rotation (either correlated or uncorrelated)

Question 12

“Factor loading”

Answer 12

• range between -1 and +1

- influenced by type of rotation

Question 13

orthogonal

Answer 13

loadings can be seen as correlations

Question 14

oblique

Answer 14

several kinds of loadings

Question 15

pattern coefficients

Answer 15

unique associations - unique association between item and factor

Question 16

structure coefficients

Answer 16

correlations between responses and total

Question 17

size of loadings

Answer 17

> .30 or .40 = strong

>.70 or .80 = very strong

Question 18

positive loading

Answer 18

high score on item can have high level of factor

Question 19

negative loading

Answer 19

high score on item have low level of factor

Question 20

Examining associations among factors

Answer 20

• oblique rotations
• correlation for each pair of factors
• higher-order associations

Question 21

primary objectives of EFA

Answer 21

determine number of common factors and strength of relationships

Question 22

Confirmatory factor analysis (CFA)

Answer 22

• confirmatory procedure
• used when there are clear indication of test dimensionality
• testing specific hypotheses about underlying dimensions

Question 23

Primary objective of CFA

Answer 23

determine the ability of a predefined factor model to fit an observed set of data

Question 24

Factors affecting responses to test items

Answer 24

• respondent trait level
• item difficulty
• item discrimination

Question 25

IRT measurement models

Answer 25

- one parameter logistic model - two parameter logistic model - three parameter model

Question 26

One parameter logistic model (Rasch model)

Answer 26

- simplest IRT model - responses to binary items = determined by item difficulty - trade off between trait level and item difficulty - applies only to binary items

Question 27

Two parameter logistic model

Answer 27

- more complex - includes two item parameters - responses to binary items (trait level, item difficulty, and item discrimination)

Question 28

Three parameter model

Answer 28

- incorporates respondent guessing | - as trait increases as does chance of guessing correct

Question 29

Graded response model

Answer 29

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

Question 30

Initial parameter estimates obtained through two-step process

Answer 30

- determine proportion of items each respondent answered correctly - compare response probabilities to actual responses

Question 31

Model fit

Answer 31

- 'fit includes' - reflect model compatibility with actual responses - suggest incompatibility - exercise caution - suggest good fit - proceed with interpretation

Question 32

Item and test information

Answer 32

- IRT provides information about items and tests | - item characteristics are used to evaluate items and maximise test quality

Question 33

Item characteristic curves

Answer 33

- reflects relationship between latent ability and performance on test items - each item has a curve

Question 34

Applications of IRT

Answer 34

- test development and improvement - differential item functioning - person fit - computerised adaptive testing