WK 10 Flashcards
What is the key feature that distinguishes factor analysis and principal component analysis?
Latent variables
What do latent variables do?
Explains correlations between measured variables
In PCA what are the observed measures?
The observed measures are independent variables
In PCA what is the component (z)?
The component is the dependent variable
What does PCA explain?
It explains as much variance in the measures as possible
- goal of PCA is to explain/ account for all possible variance by this reduced set
In PCA what are the components?
The components are determinate
In EFA, what are the observed measures?
They are the dependent variables?
In EFA, what is the factor?
It is the independent variable
What does EFA model?
EFA models the relationship between variables
- In factor analysis, we are not concerned by all variance but rather common variance
In EFA, what are indeterminate?
Factors
What are correlations?
standardized covariates
What does EFA try to explain?
Tries to explain patterns of correlations
What does factor analysis have to distinguish?
Factor analysis has to distinguish between the true and unique variance
What is true variance?
True variance is variance common to an item and at least one other item as well as variance specific to an item that is not shared with any other items
What is unique variance?
Variance specific to an item that is not shared with any other items and error variance
What is the issue with unique variance?
We cannot distinguish between unique variance and error variance in the model -> all we know is that it is not shared
What is the error term?
when we see the error term in factor analysis it comprises of var(specific) + var(error) -> It is both legitimate error and the bit of variance in the item that is not shared
What are the assumptions in EFA?
- the residual/ error terms should be uncorrelated
- the residual/errors should not correlate with factor
- relationships between items and factors should be linear
What is the estimation method in EFA?
We need to estimate the model parameters -> primarily here the factor loading’s
When we run a FA, what is the main element of our output?
Factor loading’s and factor correlations
What do factor loadings show?
They show the relationship between the measured variable and factor
How do we interpret out factor models?
Interpret our factor models by the pattern and size of these loading’s
What are primary loadings?
They refer to the factor on which a measured variable has it’s highest loading
What are cross-loadings?
They refer to all other factor loadings for a given measured variable
What is the range of factor loadings?
they range between 1 and -1
If we have a good factor solution, what will the sizes of the loadings be?
primary loadings should be big and all other loadings are small
What is the most efficient way to factor analyze data?
To start by estimating communalities
What are communalities?
Communalities are estimates of how much true variance any variable has
Why is estimating communalities hard?
It is hard because population communalities are unknown
What is the range of communalities?
They range from 0 (no shared variance) to 1 (all variance is shared)
What is a heywood case?
A communality estimate larger or equal to 1
What are the issues with MLE?
non-convergence issues
What is the assumption with constructs we seek to measure by questionnaire?
They are assumed to be continuously distributed
In factor analysis, how do we decide on the number of factors?
- visualise eigenvalues with scree plot
-treat MAP as a minimum and power analysis as maximum - explore all solutions in this range and select the one that yields the best numerically and theoretically
What is factor rotation?
It is an approach to clarifying the relationships between items and factors
What is the aim of rotation?
Rotation aims to maximise the relationship of a measured item with a factor
(Make the primary loafing big and cross loadings small)
What does orthogonal rotation include?
Includes varimax and quartimax rotations
What are the criteria of orthogonal rotations?
Orthogonal rotation factors are not allowed to correlate with each other (correlations are zero) , and their axes are at right angles
What does oblique rotations include?
Includes promax and oblimin rotations
What are the criteria of oblique rotations?
They are allowed to have correlations between factors (correlations are not zero), and their axes are not at right angles
How do I choose which rotation?
Always choose oblique
Why should you always choose oblique rotation?
It is very unlikely factors have correlations of 0, if they are close to 0, they are allowed within oblique rotation
When we have an obliquely rotated solution, what do we need to draw a distinction between?
We need to draw a distinction between the pattern and structure matrix
What is a pattern matrix?
Pattern matrix : matrix of regression weights (loadings’) from factors to variables
What is a structure matrix?
the structure matrix is the pattern matrix multiplied by the factor correlations
