One indicator construct
Message/Author
 Antonis Ventouris posted on Sunday, August 01, 2010 - 8:32 am
Hello!As someone extremely new to SEM, I am faced with this situation: one of the scales I used presented issues with the factors' loadings, since the scale was not measuring one thing only. A professor of mine suggested that I should use it as formative, by adding the scores in each question and dividing it by the number of question. Therefore, what I have now is a construct that has only one indicator (the sum of the scores divided by the number of questions). I have read in different books that in such cases you usually set the variance of the error to some level, according to the reliability of the other constructs (i.e 0.5). The questions are:
1)Is this approach right, and what else could I do?
2) If I do something like this, do I include it both in the measurement and the structural model? If yes, do I include it as a latent factor with one indicator, whose error's variance is set to a number, or as an observed variable?
Thank you very much!
 Linda K. Muthen posted on Sunday, August 01, 2010 - 10:11 am
When you sum a set of items, you make an implicit assumption of unidimensionality. I would not recommend summing items when you know they are not unidimensional.

It is true that single indicators can be corrected for unreliability. I think this should be done only when the reliability estimate is extremely good. If it is not, it will introduce other problems.

I would suggest using EFA to examine your data and perhaps use only the items that measure the scale of interest well.
 Antonis Ventouris posted on Sunday, August 01, 2010 - 10:40 am
Thank you for your answer. The reliability for this scale was indeed below .7 (actually it was .682), but I know which item is creating the problem. So, after deleting this item, I will proceed to do an EFA, with Eigenvalues of 1, and see which items belong to the scale, right?
 Antonis Ventouris posted on Sunday, August 01, 2010 - 10:46 am
To update this, I removed the item, and the scale reached an alpha of .725. Then I did an EFA, with Eigenvalues greater than 1 and supressing coefficients less than .35, and the remaining items load fine in the scale (.5 and above). Furthermore, the scale mean if item deleted column suggests that the means are close. Do you think that this is enough evidence to support unidimensionality and proceed with my CFA?
 Linda K. Muthen posted on Sunday, August 01, 2010 - 11:14 am
Eigenvalues greater than one has been shown to be inadequate for deciding on the number of factors, for an overview, see Fabrigar et al. in Psych Methods. I would recommend looking at chi-square and the scree of the Eigenvalues along with substantive interpretation. The Topic 1 course video goes over EFA in detail. You may find that useful.
 Antonis Ventouris posted on Sunday, August 01, 2010 - 11:34 am
Thank you once again. Since I am new to this forum, can you please indicate where I can find this video?
 Linda K. Muthen posted on Sunday, August 01, 2010 - 11:43 am
See the left column of the website www.statmodel.com under Training.