EFA Flashcards
Difference between EFA & PCA
EFA: Narrows it down - EFA is a technique we use in order to be able to create new constructs so we can use them in research as either DV or IV.
PCA: Only for data reduction
CFA - Testing the structure that you have found in the EFA
Both in a cyclus
Scree plot
eigenvalues plotted against factors, shows how much variance is explained in each factor, usually ordered in descending order, so we are looking for the turning point when the slope changes
Exploratory methods
Finds possible(simpler) underlying structures with less elements
Uses EFA & CPA
Confirmatory methods
Testing the “fit” of hypothesized underluying structures
EFA Workflow
1) Getting data
2) Assumptions
3) Extract factors
4) Rotations
5) Data inference
What are the benefits of rotation?
Tweek the model and increase the fit. Increase the interpretability of the data.
Principal components
Tries to explain all variance in data not separate what items have in common and what is unique and error
Principal axis factoring
Estimates communalities - squared multiple correlation of the items - tries to explain just this variance with factors
Kaiser criterion
We should keep all the factors that have eigenvalues higher than 1
Variance explained
the total factors that are retained should be explaining together about 60% of variance and more
Orthogonal
Varimix: simplify columns of loading matrix by maximizing variance and loadings on each factor, the spread of loadings within factor should be as wide as possible, high loadings after extraction become higher after rotation and vice versa
Oblique rotation
Oblimin: minimizes cross-products of loadings you can choose the level of correlation between the factors by choosing the level of Delta
What is a construct
To the extent that a variable is abstract and latent rather than concrete and observable (such as the rating itself), it is called a “construct.” Such a variable is literally something that scientists “construct” (put together from their own imaginations) and which does not exist as an observable dimension of behavior… Nearly all theories concern statements about constructs rather than about specific, observable variables because constructs are more general than specific behaviors by definition.
• A variable that is abstract and latent, which therefore is not concrete and something we can observe is a “construct”.
• We need to do something in order to capture/measure and analyze constructs EFA
Outline the different types of scales (Law & Wong)
Measurement - Types of scales:
Formative / aggregate (Factors er independent from each other, so we assume low correlation among the factors. We want to have as little overlap between the factos as possible. We add their total variance together to understand our construct = We can’t make an average like we can do in the latent model):
○ Key words:
■ The main construct is formed from its sub-dimensions
■ The main construct does not exist separately on a deeper level
■ Each dimension can weigh in on the entire construct differently or equally, but taking one away would severely impact the meaning of the overall construct (that is the totality of all the subdimensions)
■ We do not expect a person that scores high on the overall construct to score necessarily high on each sub-dimension
○ Example: friendship (construct) is an abstract thing but we look at things that can measure a friendship such as A) no. of cinema visits, B) no. of dinner dates and C) no. of phone calls. Together these items can help assess the friendship strength but it is not necessary for all three items to be high in order to have a high level of friendship.
○ We are looking at ‘what is causing a stronger friendship’ and different combinations of the items can give the same level of friendship.
○ Friendship = A + B + C. We will find the combination of items that explain a sufficient amount of construct variance.
○ Use varimax rotation Orthogonal rotation Fixed rotation where there is a constant 90 degrees ankle between the axis
■ Are you planning to make aggregate measure and you want to make sure the dimension overlap as little as possible? Then you should opt in for orthogonal rotation
Reflective / latent (Factors are related and have shared variance + We add them all together and can make a sum scale – Simply multiply all the factors and divide by number of factors = Average score (continuous variable)):
○ We are usually dealing with human opinions and perceptions, which are almost by definition latent/reflective
○ Factor analysis is serving us to create scales, so we want some theoretically meaningful structure to emerge from the analysis, especially when we are dealing with reflective scales (which we often do).
○ We know our questions are not going to be perfect, they are only reflecting (imperfectly) some underlying phenomenon that we are actually are trying to measure.
○ Key words:
■ The main construct exists at a deeper level than the sub-constructs=dimensions
■ Higher-order abstraction- commonality among the dimensions
■ The sub-dimensions are reflected in the items, the main construct is reflected in the subdimensions -
○ Example: we are not trying to assess the level of friendship from different indicators - we are looking at friendship as a deeper level construct that is not really observable → we look at the symptoms if a strengthen in friendship that gives a feeling of warmth and trust
○ Key difference from formative: the other way around compared to formative → a strong friendship would be reflected in some observable symptoms → feeling of warmth and trust. There is a change in unison as if friendship would increase the feeling of trust it would also increase the feeling of warmth → they have a common and shared variance with each other and are not independent.
■ Change of unison – In formative/aggregate you could have different combinations and still land at the same level of friendship
○ Use oblique rotation Pattern matric
■ Are all the items supposed to be part of the same reflective scale that has multiple dimensions? In that case, you expect the dimensions to be correlated and therefore shoulduse oblique rotations.
○ Our assignment: “Important to be successful and other recognize your achievements” Reflective scale if you score high in that overall construct Then it will be reflected in all the other factors/sub-behaviors So if a person score high on one dimension the most likely also score high on the others, as they have commonalities among them They move up and down together as they are related These factors could then be summarized in an overall construct as mentioned in the beginning Therefor we can create an average of them that then captures the overall construct
Profile: different from the two above
○ Key words:
■ Dimensions are at the same level as the construct but the constructs cannot be expressed as a function of these dimensions
■ Researchers therefore create profiles that have some specific levels of the dimensions
■ Theoretical reason for combinations
○ We cannot really say what better or worse but the profile scale can keep the dependent variable categories apart
○ Example: matrix of four different options: two independent variable (binary; ham and cheese) where each have binary options (yes/no). The dependent variables are four possible categories: 1) ham-n-cheese, 2) ham, 3) cheese, 4) bread
○ The profile scale has a function to predict the dependent variable based on the independent variables
○ Example: Big Five - personality traits. Together the 5 dimensions can help to sort an individual into one of multiple personality types (e.g. low on 1-3, high on 4-5 is one distinct DV category).
