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I have to create a survey that will measure customers' attitude to home products. Imagine:

  • I have concept A (it could be consumer ethnocentrism, for example). I am going to measure it using 10 items (Likert scale).
  • I have concept B (it could be some behavioral intentions of the consumer). I am going to measure it using 5 items (Likert scale).

How can I determine:

  1. if concept B is part of concept A (like, that kind of behavior is part of ethnocentrism)

    or maybe

  2. concept B is separate concept, but A somehow is correlated with B (like, ethnocentric consumers more likely will do that and that)

What do we call this in statistics? What should I look for (e.g., in Google)?

Community
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renathy
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  • You could search for Scale development; Correlated factors; Simple structure; Internal consistency; and Cronbach's alpha. @Conjugateprior's concepts and terms may well be very productive but they are more specialized and advanced and less mainstream than these. – rolando2 Sep 25 '14 at 23:24

1 Answers1

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Try googling "Guttman scaling" and "Mokken scaling" to get an idea of how Likert items might be scaled. Then look at "Mokken’s AISP" for an automated method of partitioning (and if necessary discarding) Likert items into groups that scale together on the basis of 'Guttman errors'.

(This is all implemented in the R package mokken, though you'll want to read the vignette / JSS article carefully before applying.)

If you find that your A and your B items partition nicely when AISP is applied to them all at once then you have some evidence that your intuitions about what they measure and what they actually measure might be aligned. If you find AISP groupings take items from A and B, then you have some evidence that there might be overlap. Finally, if you find that AISP finds multiple groups within A and/or B then you have some evidence that more than one thing is being measured within your intuitive categories.

These conclusions make strong but often reasonable assumptions about how your concepts relate to your items - principally that it is a dominance relationship rather than e.g. a class or an unfolding structure. For these, different models are appropriate.

If you are happy to make the dominance assumption but would prefer to use factor analysis (for some reason) then you can do exploratory factor analysis and rotate to identify items that form coherent scales. You'll want to use the matrix of polychoric correlations among your items, not the usual correlation coefficients. Probably for actual analysis you'd want to use some form of ordinal IRT model on the data directly.

conjugateprior
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  • Can you, please, explain a bit the following statement - If you are happy to make the dominance assumption but would prefer to use factor analysis. Thank you. – renathy Sep 25 '14 at 14:07
  • I have read for using factor analysis and not Mokken scaling. Why factor analysis is wider used than Mokken scaling? – renathy Sep 25 '14 at 14:09
  • Can we say that Mokken scale analysis can be compared with factor analysis results? Can results be different? – renathy Sep 25 '14 at 14:25
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    1/3 Dominance is the relationship where as the latent variable gets larger(smaller) each indicator gets larger(smaller). It's an assumption of factor analysis too. The alternative is an ideal point structure where the indicator has its own 'position' and the indicator is largest when the latent variable is closest to it and smallest when it is further away. Compare how people feel about money (more is always better = dominance) and sugar in tea (they can have too little or too much = ideal point structure) – conjugateprior Sep 25 '14 at 16:56
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    2/3 If you haven't heard about Mokken scaling that's probably because a) you're not Dutch, b) the maths for factor analysis is all linear and normal, whereas it isn't for ordinal analyses. Note that the proper parametric model (ie factor analysis equivalent) for multiple Likert items is something like a graded response IRT model - something you are more likely to have heard of - but it doesn't tell you 'where' the scales might be among your items. Ordinal IRT is a (very) complementary tool. – conjugateprior Sep 25 '14 at 17:01
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    3/3 Basically yes, you should get the same scale decisions from a factor analysis provided you use the right correlations to get it. Here's a useful paper – conjugateprior Sep 25 '14 at 17:04