factor anaylsis

Question 1

the main aim of factor analysis

Answer 1

to analyse patterns of correlation between variables (items) to a smaller set of underlying constructs /components/ factors

Question 2

the factors

Answer 2

are informative in their own right but are often used as IVs in multiple regression

Question 3

exploratory FA and Confirmatory FA

Answer 3

we only do exploratory

Question 4

a scale with 14 items would have

Answer 4

91 correlations to examine

Question 5

in a 14 is several of the correlation are >.30

Answer 5

there are a smaller number of constructs than 14

Question 6

EFA

Answer 6

used to identify a smaller number of underlying factors when analysing a large number of items within a scale

Question 7

principle components form of EFA

Answer 7

similar idea to regression in that it’s trying to explain variance
the aim is to construct a linear combination with the coeffiecents chosen to maximise the proportion of total variance accounted for by this factor

Question 8

factor loading

Answer 8

correlation between a variable/ item and a factor

loading squared= the proportion of variance explained by a given variable accounted for by a factor (x100 to get percentage)
.32 squared = .01 x 100= 10%

Question 9

eigenvalue

Answer 9

sum of squared loadings within a factor Σ L 2
down the whole item list
so the amount of variance across all items that a single factor can explain

Question 10

kaiser’s criterion

Answer 10

eigenvalue needs to be above 1 to be extracted because………

Question 11

communalities

Answer 11

how much variance do each of the factors explain in a single item

Question 12

absolute loadings

Answer 12

> .30/.32 are called salient and are interpreted because at least 10% of the variance is explained by the factor

Question 13

to how calculate the percentage of total variance accounted for by one (or more) factor

Answer 13

p= sum of selected eigenvalues x100/ no. of items

Question 14

communality

Answer 14

the item is unreliable and should be removed and run the factor analysis again
i.e. the item is explaining less than 30% of the variance

either

1) the item is different from the others in what its asking
2) or another factor is required to explain the variance in it

Question 15

what is cattell’s scree and kaiser’s criterion don’t match

Answer 15

e.g. one might suggest to extract more factors than the other… in which case run the factor analysis again but specify you want 3 factors extracted
then inspect the factor loadings again and see which items are loading on which factors and does this make sense as a psychologist.

Question 16

what do you plot on the axes

Answer 16

the item loadings

Question 17

all loadings in the centre of the axis

Answer 17

no structure

Question 18

all items high on one axis

Answer 18

one factor loading

Question 19

ideal structure

Answer 19

H=>.30

L=

Question 20

complex factor structure

Answer 20

where some items load highly on both factors ‘cross loading’

Question 21

solution to cross loading

Answer 21

rotation

Question 22

orthogonal rotations

Answer 22

right angles still

clearly two groupings but not loading neatly on axes

Question 23

explain orthogonal rotation

Answer 23

redistribute the variance amongst the factors instead of the first factor accounting for as much variance as possible
if shift the axes it will reveal that there are two seperate factors

Question 24

oblique rotation

Answer 24

still two groupings but not at right angles
so move each axis independently
if the correlations between factors in the matrix
if they exceed .32 there is a 10% overlap in the variance among factors just enough to justify oblique rotation

Question 25

bullet points of factor analysis write up

Answer 25

1) an EFA was conducted to examine ….
2) correlations computed
3) inspection of the correlations (want them to be modertte-strong)
4) number of items subjects to principle components factor analysis
5) which factors were extracted (above 1)
6) say how much variance each factor explained
7) inspection of scree plot- confirmed the extraction?
8) inspection of commonalities- do all the factors account for sufficient variance in all items (>.30)
9)factor loadings (strongly?) on both factors? - rotate
if loading strongly on separate factors then leave
10) say which items loaded on which factors
11) inspect the content of the items !