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  • 1.  SEM model building question

    Posted 07-08-2014 12:52
    This message has been cross posted to the following eGroups: Social Statistics Section and Statistical Consulting Section .
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    I am attempting to build a SEM using 'risk' as a latent DV, and 'executive function' as one (of two) latent IV. My question is primarily a theoretical/specification question concerning having measurement variables whose parameter estimates have different signs as part of the same latent variable.
    We know that in our population a small negative relationship actually exists between hot and cold measures of EF, and that our 'hot' measure of executive functioning is negatively related to risk, but several 'cold' EF measures are positively related to risk. We would, however, like to still consider both types part of one overall 'executive function' latent IV, or include only a "cold EF" latent variable with the expectation that our single measure of 'hot EF' would load negatively onto it.
    My question concerns whether it would be generally acceptable (or justifiable) to include a single latent variable (EF) whose measurement variables contained different signs due to their opposite relationships with risk (and negative interrelationships). This would lead to a negative path coefficient from 'hot' measurement variables to EF, even though we are considering all variables part of that latent construct. Alternatively, would it be more appropriate to consider the latent IV 'cold EF' and include the one measure of 'hot' EF as a measurement variable with a negative loading?
    I realize that these (hot and cold) could certainly comprise two separate latent variable, but because of identification issues (other IVs are part of the model as well, and only one measure of 'hot' EF was used) it would be preferable to include them as part of the same latent variable if this did not constitute an egregious violation of SEM theory.
    Any thoughts are appreciated.
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    Dale Smith
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  • 2.  RE: SEM model building question

    Posted 07-08-2014 13:48
    Hi Dale,

    In the two decades I have been reading about and using SEM, I have seen a number of applications where the latent factors have observed indicators with different signs. I think it's fine to have observed variables with different signs loading onto the same latent factor. One just has to be clear what the interpretation of the factor is - if the cold EF observed variables are positively associated with the latent factor and the hot EF observed variables are negatively associated with the latent factor, then the latent factor could be thought of as "amount of cold EF". Conversely, if the hot EF observed variables were positively associated with the latent factor and the cold EF observed variables were negatively associated with the latent factor, then the factor could be thought of as "amount of hot EF".

    One trick that I learned fairly recently (I think it was from reading an article by Loeys on dyadic data analysis) is that you can change the scaling of the latent variable. For instance, the usual way to set the scale of a latent variable is to fix the loading of one of the items to positive 1. But you could just as easily set the scale of that variable (or of a different variable, if you prefer) to -1. For example, you could set the scale of the latent EF variable by fixing the factor loading of the lone hot EF observed variable to -1 and allowing the loadings for the multiple observed cold EF variables to be freely estimated. The resulting latent factor could be interpreted as "amount of cold EF".

    Another option which I've seen some investigators pursue is to reverse-score observed variables that would be negatively correlated with the latent factor. I've seen this done most frequently in factor analyses involving multiple survey items where some items are worded negatively whereas others are worded positively. Because one of the end goals of such analyses is computation of coefficient alpha to estimate internal consistency reliabilities for subscales and because programs to compute alpha typically require that the items have positive item-total correlations (and also because a factor analysis solution may simply look neater with all loadings being positive), investigators will often reverse-score the negatively-worded items before subjecting them to factor analysis and reliability analysis. You could do something similar with either the hot or the cold EF items in your study before analyzing them in the SEM.

    HTH,

    Tor Neilands

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    Torsten Neilands
    Professor of Medicine
    UCSF Center for AIDS Prevention Studies
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