Factor Analysis Lecture 2.

Question 1

What is the relationship between FA and Geometry?

Answer 1

You can represent Correlations and items by drawing straight lines.

Question 2

What can the lines help help us determine?

Answer 2

The correlation between lines can be determined from the angle between lines

Question 3

What does the cosine of the angle tell us?

Answer 3

The correlation value is the same as cosine of angle. It tells us the correlation between variable 1 and 2. T

Question 4

What does it mean if lines are closer together?

Answer 4

They are highly correlated. They will have a smaller angle between them.

Question 5

What does the cosine number mean?

Answer 5

It tells us the correlation between the variables. A cosine of 0.867 means there is a correlation of 0.87 between 1 and 2.

Question 6

What does it mean to get a high cosine?

Answer 6

A high cosine means a high correlation.

Question 7

What does an angle that is horizontal to Factor 1 mean?

Answer 7

It means Factors/items above the horizontal line are positively correlated to factor 1.

Question 8

What does an angle that is at a right angle/90 degrees to factor 1 mean?

Answer 8

Factors/items at right angles to F1 have zero correlation to it

Question 9

What does an angle at 180 degrees mean?

Answer 9

Factors/items at 180°have a perfect negative correlation.

Question 10

What does Orthogonal mean? What angle is it at?

Answer 10

1: Your score on variable 1 tells us nothing about how you score on variable 2.

2: It means you got 0 correlation between variable 1 and
2.

3: It is a 90 degrees angle. No relationship=Orthogonal.
4: It means you have independent factors. There is two distinct, separate things going on.

Question 11

How do you get a correlation of 0?

Answer 11

You have to get an Orthogonal rotation?

Question 12

What does Oblique mean?

Answer 12

The common factors may be or are correlated. They can or kinda correlate with each other. It is much more plausible for Psychology.

Question 13

What does a small oblique angle mean?

Answer 13

It suggests that our factors are correlated with each other.

Question 14

How does the way we plot our variables using geometry impact our interpretation?

Answer 14

It will impact how we interpret our FA and how we make it meaningful. It can impact how we interpret the relationship between items and factors.

Question 15

What is a Factor Matrix? What do we use it for?

Answer 15

A table showing the correlations between all the items/variables and the factors.

We use it to work out correlations between the angles of each items and factor.

Question 16

What is Factor Loading?

Answer 16

A correlation between an item and a factor.
This means for example item one loads onto factor one. Items “load” onto factors.

The co-ordinate of a variable along a classification axis is known as factor loading. Can be thought of as the pearson correlation between a factor and variable.

Question 17

What does b mean in factor loading?

Answer 17

b=factor loading

b=coordinate of that variable on the graph with respect to that factor

Question 18

How do we get factor score?

Answer 18

We add all the variables. b1+b2+b3+b4+b5+b6

Question 19

What is another name for factor matrix?

Answer 19

Component matrix

Question 20

What does Factor Matrix show us?( 3 things)

Answer 20

1: Which items make up which common factor (By looking at the nature of the items you can speculate on the nature of the common factor)
2: Reveals amount of overlap between item and the potential factors.

The square of correlation indicates the common variance between item and factor –Communality of item –how much of the variability in an item is explained by the common factors.

Squared multiple correlation is the most common method •For I1= .9(squared)+ .1(squared) = .82

3: Indicates relative importance of each common factor –a factor that for example explains 40% of the overlap between the items will be more important than one that only explains 25%

An Eigenvalue tells you the importance/explanatory power of your factor. Calculated through eigenvalue –Square the factor loadings for a single factor, add them up = the eigenvalue –Divide the eigenvalue by the number of items = proportion of variance explained by that factor

eigenvalue = .9(squared)+ .98(squared)+ .9(squared)+ .1(squared)+ 0(squared)+ -.1 (squared)=2.6

6=number of items.

Variance explained by factor 1= 2.6/6= 43%.

Question 21

What number does an item have to have to contribute to a factor?

Answer 21

Convention dictates that an item only contributes to a factor if the correlation is greater than ±.3.

Question 22

What is communality?

Answer 22

Communality of item –how much of the variability in an item is explained by the common factors

•squared multiple correlation is the most common method. Eg you square item 1 score for factor one and 2 and add them together eg 0.90(squared) + 0.10(squared) = 0.82(communality).

0.82 multiplied by 100 = 82%. Factor 1 and 2 account for 82% of the variance in factor 1.

It tells us how much of the variance is shared between 2 things. Correlation value is amount of variance shared.

Question 23

Why would Communality be low? (5 answers)

Answer 23

Communality for an item may be low because it:

Low communality of a variability means either the measurement error is high or the variable is measuring something different to rest of variables.

Items not well explained by factors. Measuring something else.

1: measures something conceptually different from all the other items.
2: has excessive measurement error
3: are few individual differences in the way the item is responded to -may be very easy or very difficult.

4: Factors are an approximation -some of the original information is sacrificed during this process
5: Different methods of FA make different assumptions about the possibility of unexplained variance

Question 24

What is an Eigenvalue?

Answer 24

Eigenvalue score tells you the importance/explanatory power of your factor.

An Eigenvalue is an indication of the amount of variance explained by any one factor.

Question 25

How do you get an Eigenvalue?

Answer 25

You square each factor loading in the table and then add up each factor.

9(squared)+ .98(squared)+ .9(squared)+ .1(squared)+ 0(squared)+ -.1 (squared)=2.6

Variance explained by factor 1= 2.6/6= 43%.