L9 - Scales creation and exploratory factor analysis Flashcards
Latens models
Law, K. S., Wong, C., Mobley W. (1998).
Multidimensional constructs that exist at deeper levels than their dimensions
- A higher-level construct that underlies its dimensions.
- The constructs lead to the dimensions.
Aggregate model
Law, K. S., Wong, C., Mobley W. (1998).
Constructs formed as algebraic functions of their dimensions.
Example: Motivating potential of a job.
Dimensions: the degree of skill variety, task autonomy, task significance, task identity, and the amount of feedback.
Construct: Job motivation
Profile model
Law, K. S., Wong, C., Mobley W. (1998).
Constructs formed as different profiles of dimensional characteristics
There are some multidimensional constructs scholars theorize at the same level as their dimensions but do not define as algebraic functions of their dimensions. The levels are being profiled.
From items to scales
Law, K. S., Wong, C., Mobley W. (1998).
Their will bee three models for constructing items to scales
- Reflective model
The researcher would on the basis of the theory suggested that an underlying latent construct causes people to answer the items in a similar way. - Latent construct means that it is a construction that we can not directly measure, but we expected based on the theory that it must exist. (e.g. personality) –> So because they have this personality we expect they will answer this way on the items. - Formative Model
Will use this model for more objective construct, not for this latent construct
Ask question like, do you work late often
Open questions - Profile model (combine item in to scale)
Should be informed by a theory
If you answer this way our theory would place you as X.
you can combine respondents to individual items in meaningful ways to make them into profiles.
Structural Model
What are the variables of interest and how do that relate to each other?
How do you think your variable a related to each other on the background of the theory
–> Based on Theory
Tested with statistical tools (E.g. regression)
Measurement Model
The dots are items, and the color represent the variable that the items should belong to
→ Dots that are close together correlate strongly, otherwise if they are long from each other they correlate loosely or maybe not at all.
Exploratory factor Analysis (EFA)
Tabachnick, BG & Fidell, LS (2013)
EFA takese the correlation matrix of all items and reduces them into less underlying factors.
Factor loadings (the strength of association between observed variable and the factor) help define the factor- give it meaning- help to name the pattern we have uncovered.
Fra opgaven til EFA
- The purpose of the EFA was to search for possible correlation between the
items and if there was seen correlation, then reduce the complexity to smaller
numbers of factors
Correlation matrix
Tabachnick, BG & Fidell, LS (2013)
A correlation matrix.
- To calculate the factors loading.
- is used to determine the relationships between variables.
- Factor loadings connect invisibile questions (=items)
EFA vs. CFA
Brown, T. (2006)
In the EFA we don’t tell SPSS which items belong to which construct. We let SPSS find out. In CFA we tell SPSS how we expected the items should connect with the constructs.
- So they are both telling the quality of our data, but with different strategies.
Do I even need EFA?
EFA is a technique to explore data structure when you are not sure about your data structure. If you have a clear idea about your structure beforehand, CFA is preferable (or both).
The procedure for EFA
Get data and check assumptions - checking assumptions and the correlation matrix of the items we have selected
Extract Factors –> the core task is to repackage the correlation matrix and find the factors and its association with each variable - factor loadings.
Rotate - Rotation of factors to increase interpretability:
- We want to find which items belong to which factor - where is the highest
factor loadings, we then delete variables that had low association with the
retained factors
Interpretation - Interpret the results, save factors for future analysis
- Ending up with clear structur (no overlap between factors) we interpret the
factors (name the underlying pattern) and save the factor scores for future
analysis
5 decisions you have to make with EFA
(A practical approach)
Fabrigar, L. R., Wegener, D. T., MacCallum, R. C., Strahan, E. J. (1999)
- Study design (Sample size)
- EFA, PCA and CFA
- Model Fitting procedure: what type of EFA (Principal axis vs. ML)
- Determining number of factors (Scree plot, kaiser criterium)
- Rotation
- Study design: Sample size
Rules of thumb
- 3-5 items per construct/factor
- sample size of 10 / construct (subscale), (aim for) minimum 100 participants in
total
- If you know your sample size will be restricted, plan your survey accordingly
EFA or PCA
Fabrigar, L. R., Wegener, D. T.,
EFA, if
- you are measuring a latent construct - reflective scale
- Expect that items may have unique and shared variance
PCA, if
- Do not have any indication that there will be unique items variance (e.g., very
objective questions with different wording) - Formative scale
- Determining number of factors
Fabrigar, L. R., Wegener, D. T., MacCallum, R. C., Strahan, E. J. (1999)
Rules of thumb
- All with eigenvalue of 1 or more
- inspect scree plot
- Total variance explained 60+%
There are three ways to decide how many of the factors we wanna retain (Fabrigar et al., 1999)
- Scree plot
- Kaiser criterion
- the variance explained
