I have a set of likert items all of which are constructed with scales of 7 categories, except for one likert item, which is constructed with a scale of 11 categories.
These likert items are to be used in a Structural Equation Model and analysed using Partial Least Squares.
My question is now:
- How, if at all, will this discrepancy influence the analysis?
Hey Lars,
there exists a variety of ways to address the issue of categorical indicators in PLS-PM, e.g. Canatkuppi and Boari (2012) or Russolillo (2012). In a joint paper (under review), we developed a new consistent approach to deal with ordinal categorical indicators. In this context, we also run some simulations and we find out that for 7 and more categories the difference between PLSc and our approach is small. Hence, the scale of the indicators can be negected for more than 7 categories. For covariance-based estimators,similar studies exist, e.g. Rhemtulla et al. (2012).
I hope this helps. Best regards,
Florian
Rhemtulla, Mijke, Patricia É. Brosseau-Liard, and Victoria Savalei. "When can categorical variables be treated as continuous? A comparison of robust continuous and categorical SEM estimation methods under suboptimal conditions." Psychological methods 17.3 (2012): 354.
Boari, Giuseppe, and Gabriele Cantaluppi. "A PLS algorithm version working with ordinal variables." XLVI Riunione Scientifica della Società Italiana di Statistica. cleup, 2012.
Russolillo, Giorgio. "Non-metric partial least squares." Electronic Journal of Statistics 6 (2012): 1641-1669.
Hi Florian,
Thank you for your answer. I'm in the process of reading the material you linked, but I have this clarifying question:
In my research, I am trying to utilize a variant of the ECSI (European Customer Satisfaction Index) model. Different latent variables are measured by indicators (likert items) with 7 categories, but in one of the latent variables, one of the three indicators consists of 11 categories. All latent variables are reflective.
From what I understand, your answer leads me to the conclusion that having multiple latent variables, the scale length (number of categories) does not affect results too much as long as each indicator is of 7 or more categories. As such, having one indicator with 11 categories as a part of a 3-indicator latent variable (of which the two other indicators are constructed using 7 categories), would not disturb the possible results gravely.
Am I completely off here?
Kind regards,
Lars
Hey Lars,
here we have two issues. You said that all latent variables are reflective, I assume that the constructs are modeled as common factors. Traditional PLS doesn't produce consistent estimates for common factor models, instead consistent PLS should be used (Henseler & Dijkstra, 2015). The second issue is the scale of the indicators. There are several approaches for PLS (which is inconsistent for common factor models) but to my knowledge there is no approach for PLSc (We proposed one in the paper under review). To answer your question, the bias induced by ignoring the scale of the indicator should be small in your case with two indicators having 7 categories and one indicator having 11 categories. I don't know which software you use, but to my knowledge in the most popular software SmartPLS and ADANCO none of these approaches is supported.
Best regards,
Florian
Dijkstra, Theo K., and Jörg Henseler. "Consistent and asymptotically normal PLS estimators for linear structural equations." Computational statistics & data analysis 81 (2015): 10-23.
Hi again Florian,
Thank you for your answer.
I'm planning to use Consistent PLS in SmartPLS , so I believe I'm covered.
I'm going to read on and keep a note on the potential bias.
Once again, thank you very much for your time. You've helped a great deal.
Kind regards,
Lars
http://www.smartpls.de/documentation/pls-c-algorithm
Hey Lars,
yes SmartPLS has an implementation of PLSc. One disadvantage of SmartPLS compared to ADANCO is e.g. the test for overall-fit (there is no possibility to perform a overall test of fit for a model which contains common factors and composites) and the circumstance that the mode used for outer estimation in PLS is not disentangled from the way how the construct is modeled (comopsite or common factor). If you send me your email address I can also send you a preversion of our paper about categorical indicators in PLS.
Best regards,
Florian
Check this out:
https://www.smartpls.com/resources/ebook_on_pls-sem.pdf
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