Dear community,
I would like to combine two subscales of a questionnaire to form one predictor: It is an instrument on intrinsic vs. extrinsic goals which assesses for several goals their attainment and importance by two separated questions. Since using the attainment and the importance as two distinct predictors won't work I was thinking of using the difference as a variable by subtracting the importance from the attainment. For example a positive or zero value for the scale "personal growth" would mean that the attainment is large/as large as it's attributed importance, while a negative value indicates the lack of attainment of an important value.
Has anybody modelled something similar before, e.g. using lavaan or MPLUS? It seems to work nicely as manifest varibale in a MLR but I would like to try it as SEM.
Thank you very much in advance,
Kind regards
Matteo
Hello Matteo,
this remembers me a bit on the discussion of value congruence or person-environment fit theory and the procedure of using difference scores to model "fit" or "congruence". On this procedure there was a long heating debate and as I remember, the conclusion was not to do it.
Perhaps this is helpful (as remedies are straightforward):
Edwards, J. R. (2001). Ten difference score myths. Organizational Research Methods, 4(3), 265-287.
Edwards, J. R., & Parry, M. E. (1993). On the use of polynomial regression equations as an alternative to difference scores in organizational research. Academy of Management Journal, 36(6), 1577-1613.
Edwards, J. R. (1995). Alternatives to difference scores as dependent variables in the study of congruence in organizational research. Organizational Behavior and Human Decision Processes, 64(3), 307-324.
Edwards, J. R. (1994). The study of congruence in organizational behavior research: Critique and a proposed alternative. Organizational Behavior and Human Decision Processes, 58, 51-100.
Cheung, G. W. (2009). Introducing the latent congruence model for improving the assessment of similarity, agreement, and fit in organizational research. Organizational Research Methods, 12(1), 6-33. doi:10.1177/1094428107308
Best,
--Holger
Hello Matteo,
It wasn't clear why you would be unable to use both an attainment and an importance rating in your model. Maybe you could explain why that restriction exists for your research.
However, it is important to note that difference scores are always less reliable than either of the two constituent scores unless: (a) both measures are perfectly reliable (highly unlikely in your scenario); or (b) the correlation between the measures is zero (probably unlikely as well). If both measures have comparable variance, then the formula for reliability of a difference score is: (mean reliability - rxy) / (1 - rxy), where: mean reliability is the average reliability of the two measures, and rxy is the correlation between measure "x" and measure "y".
One final thought: Imagine two respondents, one with maximum rating on attainment and maximum rating on importance (yielding a zero difference, following your proposed approach); the other with a minimum rating on attainment and minimum rating on importance (again, zero difference). Numerically, these are "identical" cases. However, I'd be hard pressed to argue that they're comparable with respect to the goal in question.
Good luck with your work.
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