Saturday, April 01, 2017

latent variable variance

  • It is necessary to make a constraint to have a metric for the latent variable variance. Typically this is done by setting a loading equal to 1 or setting the factor variance equal to 1. 
unstandardized models, Estimated Factor Variance (marker item)
  • one of the loadings is set to one (called the marker variable), the others are free, and the latent variable variance is free
  • Set one item’s factor loading to 1, Set the factor mean to 0
  • Mplus, Amos Default
  • Estimated factor variance, estimated factor mean
  • One item factor loading fixed to 1, one item intercept fixed to 0
  • Marker item: Fix that item’s factor loading to 1 and its intercept to 0
  • Factor variance is based on part of that item that relates to factor (as opposed to part that is measurement error)
  • Will cause problems when marker item is unrelated to factor -- thus, u need to change to use another item as the marker item, especially the one that seems to be related to the factor
  • if you choose an item which is unrelated to the factor as the marker item, you are very likely to end up an unidentified model 
standardized models, Standardized Factor Variance (fixed variance)
  • the latent variable's variance is set equal to one and all the loadings are free to vary
  • Set the factor variance to 1, Set the factor mean to 0
  • Standardized factor variance, estimated factor mean
  • All loadings estimated – one item intercept fixed to 0
  • Put factor on scale of mean=0 and variance=1
  • All item factor loadings and all item intercepts are estimated

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