Measurement scale

[ghozali]

Hi,
I read an article published in Information Systems Research, Vol 16 No.1 march 2005. In this article the authour using three different measurement scale for their indicators such as Nominal (dummy), ordinal and continoues. I was wondering, could smartPLS handled to run the model with three different measurement scale simultanouesly? and How to justify this matter methodologically.

Thanks

[cringle]

Hi,

I actually have no idea how ordinal or dummy variables can possibly be used for the basic PLS-algorithm by Wold. This does not look to good to me...

However, any suggestions for modifications of the algorithm are welcome and my be discussed here.

Best
Christian

[cgrimpe]

Hi,

PLS can be used to analyze many different types of data such as binary coded data, categorical data or - of course - continuously coded data. For details see Falk, R.F. and Miller, N.B. (1992): A Primer for Soft Modeling, p. 32.

Best regards,

Christoph

[cringle]

Hi, I will check on that article. Lohmoeller (viewtopic.php?t=16) gives suggestions on the use of dummy variables, as well. However, this topic is on my "to-do-list". If anybody has suggestions or additional information on the use of distinctive scales (dummy, ordinal and continoues) for PLS path modeling, please join this discussion.

This might be an issue for future developments of the methodology.

Best
Christian

[jjsailors]

That's actually one of the key points about PLS--it does not make any distributional requirements on the data.

[rpelz]

I faced the same problem after a prestest of my initial questionnaire when I discovered that some of my items were binary coded. According to Prof. Rigdon, PLS does not care about scales:

Richard--
Wold was explicit that PLS doesn't care about the scale
of the observed variables. You just dump them in and PLS
produces a result. Remember, PLS does not do factor
analysis or structural equation modeling, but rather a
structured form of principal components. To PLS, the scale of
your observed variables, from ratio scale to dummy variables,
does not matter.
--Ed Rigdon

Edward E. Rigdon, Professor and Chair,
Department of Marketing
Georgia State University
P.O. Box 3991
Atlanta, GA 30302-3991

[nkraemer]

Hi,

I do not agree with the opinion that the scale of the data does not matter. In my opinion, two completely different aspects are mixed up in the above discussion.

1) From a technical point of view, the PLS algorithms are able to handle variables at all kind of scales: If you plug in categorical variables (e.g. encoded as 1,2,3,..), the algorithm will produce a solution. This is the case for basically all algorithms and does not depend on any assumptions on the data.

2) The important question is of course: Does this solution make any sense? I am sure that PLS can produce odd solutions if you do not take the scale of the data into account. Let me give you an example from linear regression: Suppose you want to predict the color ("red","blue" and "green") of an object from a continuous variable x. Of course you can simply assign numbers 1,2 and 3 to the colors "red", "blue" and "green" respectively and use ordinary least squares to estimate the relationship between x and the color. If you do it this way, you punish misclassifications differently:

If you predict "blue" instead of "red", the error is 2-1=1
If you predict "green" instead of "red", the error is 3-1=2


This is of course purely artificial, so we can expect our method to perform suboptimal on new data sets. This is the reason why we should encode categorical variables as dummy variables.

The same thing can of course happen in PLS. The difference to the above mentioned example is that in PLS, hardly no one ever evaluates the quality of his model (e.g. on a test set)! If you do not compare your model to other models, you will never find out if it is suboptimal or not.

It would definitely be worthwile to compare the solutions of PLS with not-transformed categorical variables to PLS with dummy-transformed categorical variables. Just so see if there is a difference in practice.

Best regards,

Nicole

[viswadatta]

We have to go back to regression for an answer. Dummy variables are used only as independant variables. If the dependant variable is nominal, then we use discriminant analysis. Dummy variable regression is doen for OLS regression itself, and so must be applicable for PLS regression as well. But in models we have interdependant variables making some dependant variables as dummies as well, this is a troublesome point to be resolved.

Regards
Vivek

[byun80]

Hi,
I find this paper:
http://www.sciencedirect.com/science?_o ... 62328e1581Jakobowicz E., Derquenne C. A modified PLS path modeling algorithm handling reflective categorical variables and a new model building strategy (2007) Computational Statistics and Data Analysis, 51 (8), pp. 3666-3678.
and
http://epp.eurostat.ec.europa.eu/portal ... LES_TR.pdf
Trinchera L., Russolillo G. Role and treatment of categorical variables in PLS Path Models for Composite Indicators. (2006) Eurostat.

Anyone can give comment on these papers? Because I have some categorical data to be performed

Regards,

Budi