Hello,
I am conducting a SEM analysis and when I checked latent correlations, I noticed that the correlation between IV and two DVs are between .85 and .90 (and the regression paths are .93 and .98). However the correlations between indicators range between .45 and .60. Why do I observe such huge difference between observed and latent variables? Any explanation and help would be much appreciated.
Hi Serap,
the answer is simple: Because latent variables are stripped from the measurement error with which observed variables are contaminated.
But to make sense, the measurement models habe to be correctly specified that is, the indicators must really share the latent variable as their underlying cause. Otherwise the latent variable simply means not much (with the extreme that it is completely nonsense) and the factor loadings will be low leading to an overcorrection of the latent correlations.
With such high correlations as in your case, I would however have some doubts about the validity of the IV and DV. As aforementioned these could signal misspecification and overcorrection or lack of discriminant validity. But of course this depends on the context. As always in SEM: Test the model in a rigid way (i.e., by the chisquare test) and use (also) the parameter values (e.g., your correlation) as a basis whether the model is correct and meaningful.
Best,
Holger
Hi Serap,
the answer is simple: Because latent variables are stripped from the measurement error with which observed variables are contaminated.
But to make sense, the measurement models habe to be correctly specified that is, the indicators must really share the latent variable as their underlying cause. Otherwise the latent variable simply means not much (with the extreme that it is completely nonsense) and the factor loadings will be low leading to an overcorrection of the latent correlations.
With such high correlations as in your case, I would however have some doubts about the validity of the IV and DV. As aforementioned these could signal misspecification and overcorrection or lack of discriminant validity. But of course this depends on the context. As always in SEM: Test the model in a rigid way (i.e., by the chisquare test) and use (also) the parameter values (e.g., your correlation) as a basis whether the model is correct and meaningful.
Best,
Holger
Hi Serap
I agree 100% with Holger, but would like to add some comments. As Holger noted the effect of ignoring measurement errors will result in an estimate of a correlation/regression coefficient that is lower than the true value. Fleiss and Shrout demonstrated this very elegantly many years ago (see Article Effects of measurement errors on some multivariate procedures
). If this was always the case then things would be fine, we'd just have to note that our estimates are likely to be 'conservative'. However, this will not always be the case.Once we move from a bivariate (1 IV, 1 DV) model to a multivariate model (multiple IVs) then the effects of measurement error are much less predictable, indeed they are unpredictable. Estimates from such models can be attenuated, over-estimated, or close to the true value. The problem is we don't know which are too high or too low. Cole and Preacher do a fantastic job at describing the many problems that measurement error causes in their 2014 paper (http://quantpsy.org/pubs/cole_preacher_2014.pdf).
There have been different approaches to dealing with measurement error and latent variable modelling is probably the most widely used approach, by explicitly incorporating a measurement model that 'firewalls' the measurement error. This has been used for decades, but it not without its critics. Rhemtulla and colleagues have shown that misspecified measurement models can cause serious problems with model estimates (see doi: 10.1037/met0000220).
Best wishes
Mark
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