FA; Lec 1 & 2; Lab 1 & 2 Flashcards
What is a very widely used form of data reduction?
Factor analysis
Questions addressing similar issues are thought to address the same [X]?
Underlying construct
Items/variables consistently responded to in similar manner by different respondents supposedly address the same [X]?
Underlying construct/Latent variable/Common factor (or just plain ‘factor’)
What is a latent variable/underlying construct?
A hidden variable. For example, ‘health’ - there isn’t a single measurement of ‘health’ - it is an abstract concept. Instead we measure physical properties from our boy e.g. blood pressure, weight etc. These separate measurements can then be used by a trained person to judge your health. If we had a sensor for health we could measure and use that variable, but since we don’t we use other measurements which all contribute in some way to assessing health.
When do you need FA?
- To understand the structure of a set of variables (e.g. ‘intelligence’)
- To formulate a questionnaire to measure a latent variable
- To reduce a data set to a more manageable size while retaining as much of the original information as possible
What is a common criticism of FA?
That it produces facile results. This is because it can always be used, resulting in erroneous application.
What is a correlation matrix?
A grid organised such that the value of any cell represents the correlation between the variable assigned to the row and the variable assigned to the column, It is usual that the order of variables in the rows is the same as the columns so that the diagonal values of this grid represent the correlation of a given variable with itself.. This means that the diagonal values are all 1.
What does a correlation matrix tell you?
It gives you a complete view of the bi-variate correlations that exist in whatever dataset you’re looking at.
What is the symbol for Pearson’s Product-Moment Correlation Coefficient?
r
What does Pearson’s correlation give an indication of?
It gives an indication of the extent to which a criterion variable (Y) varies in conjunction with the predictor variable (X)
What is the 1. the verbal, and 2. the mathematical formula for Pearson’s Product-Moment Correlation Coefficient?
- r= covariability of X and Y/Variability of X and Y separately
- r= Sxy/√Sx².Sy²
If you are eyeballing a correlation matrix how high must the correlation be to considered a correlation?
.3=<
If you are asked to complete the cosine values for an anti-clockwise degree value, how do you work that out?
360-anticlockwise degree
e.g. 360-70=290
If an item were at an angle of 360degrees to F1, what would be the correlation between the two of them?
Perfectly positive
If an item were at an angle of 180degrees to F1, what would be the correlation between the two of them?
Perfectly negative
Looking at correlation values, how would you determine if an item loaded onto a factor?
We usually require the correlation between an item and a factor to be equal to or greater than a magnitude of .3 before agreeing that it loads onto a factor.
- How would do you calculate communality for an item?
- What does calculating the communality tell you?
- When you have the communality, how do you determine how much of the variance of that item remains unexplained by the proposed factors?
- The sum of the square of the correlations of that item across all the factors. E.g. (0.53)²+(0.14)²+(0.27)²= 0.37
- This tells you how much of the variance for that item is explained by the three factors. In this example = 37%
- 1 - (communality of item)
e. g. 1 - 0.37 = 0.63 = 63% of variance for that item is unexplained by the three factors.
How is FA represented through geometry?
Items of factors can be represented by straight lines of equal length. Lines are positioned such that the correlation between the items = cosine of the angle
How do you calculate the cosine of the angle?
cosine of angle is = adjacent/hypotenuse
If F1 is represented through geometry, and Item 1 is at a right angle to it - what is the correlation?
Item 1 has a zero correlation to F1
What is an orthogonal solution?
When two common factors are extracted which are not themselves correlated (i.e. they are at right angles to each other). If the common factors are not correlated then they truly represent independent factors.
What is an oblique solution?
When the common factors extracted may themselves be correlated. (more plausible for psychology)
What is a ‘factor loading’?
The correlation between an item and a factor.
What is a factor/structure matrix?
A table showing the correlations between all the items and the factors.
what does b =?
factor loading
Factor loading is determined by the coordinate of that variable on the graph with respect to that factor.
What 3 things does a factor matrix show?
- Which items make up which common factor
- The amount of overlap between an item/items and the potential factors - calculated through communality
- The relative importance of each common factor (e.g. a factor that explains 40% of the overlap between the items will be more important than one that only explains 25%) - this is calculated through the eigenvalue.
What is the communality of an item?
How much of the variability of an item is explained by the common factors.
What is the most common way of calculating the communality of an item?
Squared multiple correlation
Give 3 reasons why the communality for an item may be low?
- Because it measures something conceptually different from all the other items
- Because it has excessive measurement error
- Because there are few individual differences in the way the item is responded to - it may be very easy or very difficult.
How do you calculate the eigenvalue for a factor?
Square the factor loadings (items loading onto that factor) for a single factor, add them up = eigenvalue
How do you calculate the proportion of variance explained by a factor?
2 steps
- Square the factor loadings (all items) for a single factor, add them up = eigenvalue
- Divide the eigenvalue by the number of items
What are the two branches of FA?
- Exploratory factor analysis - no prior assumptions about relationships among factors
- Confirmatory factor analysis - tests a hypothesis that specific items are associated with specific factors (structural equation modelling)
What are two types of exploratory factor analysis?
- Principal components analysis
2. Factor analysis (principal axis factoring)
What are two types of confirmatory factor analysis?
- Path analysis
2. Latent variable analysis
What does the sum of the square of all loadings, irrespective of magnitute, onto a particular factor give you?
The eigenvalue
How do you calculate the percentage of variance explained by each factor?
The eigenvalue divided by the number of items
