Hypothetically, say I have I have three manifest variables measuring anxiety and three manifest variables (items) measuring stress. Then I want to use both to predict scores on depression, which I'm also assessing via three manifest variables.

I could simply add the scores on each of the manifest variables and create composite scores for Anxiety/Stress/Depress, then run a multiple regression. That approach is depicted in the following figure.

Multiple regression

Alternatively I could do latent variable modelling, as in the figure below.

Latent  variable modelling

Whenever I've done this the R Squared has increased.

Why does this happen? Are the reasons such that is it possible for the R Squared to instead stay the same, or reduce?


consider the two measurement model for Anxiety: in your first model you have given all three items equal weight, while in the second model you estimated the relative contribution of each of the items (in this case relative to item 3, so the loading for item 3 is 1). By fitting the relative contributions instead of constraining them all to be equal you are able to explain more of the variance, and thus R Squared should increase compared to your first model.

  • $\begingroup$ Do you believe it is impossible for R Squared to go down under the circumstances described? $\endgroup$ – user1205901 May 21 '13 at 13:12
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    $\begingroup$ I don't know enough to be comfortable with saying it is "impossible", but I would be surprised if I saw R Squared decrease and I would certainly investigate when that happend (e.g. are missing values treated in exactly the same way in both models). $\endgroup$ – Maarten Buis May 21 '13 at 13:18

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