Can you elaborate on how we can calculate - the latent variable (DV) from independent variables found after PCA? Since I already found the factors, how can I combine these factors to measure the construct- latent variable? Thank you.
If you are asking how to calculate factor scores after a PCA or PAA, there are various different methods. Two common ones are what I call differential and unit weighting schemes.
- In the differential weighting scheme, you standardize the scores and multiply by the standardized lambdas. Aggregate all items for each factor.
So, if you have three items with lambdas of .4, .5. and .6, your LVestimate would be:
LVest = .4*z(V1) + .5*z(V2) + .6*z(V3)
- In the unit weighting scheme, you simply take the average of the standardized scores belonging to that factor.
So, if you have three items with lambdas of .4, .5. and .6, your LVestimate would be:
LVest = z(V1) + z(V2) + z(V3)
The differential method will better fit the data in your sample, but results found with the unit-weighting scheme generalize better across samples/research contexts. Further, simulation studies show that the factor scores created using both methods highly correlate (estimates put the average between .9 and .95).
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