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I was wondering if anybody could explain the core, philosophical/conceptual differences between Latent Class Analysis and Rasch Analysis.

I'm not necessarily referring to the exact mathematical calculations involved. I'm more interested in - why would one choose one over the other? Is there a core, fundamental difference or purpose between the two? Is one more suitable for certain types of data or research questions than others?

I'm primarily familiar with LCA but not Rasch, and most of the papers that I've read tend to go into slightly too much mathematical jargon that I simply can't focus on the arguments!

I was originally thinking about the two in the context of scale development but any other broader perspectives beyond scale development would be useful too.

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    $\begingroup$ en.wikipedia.org/wiki/Latent_variable_model might be to start with. "Latent trait" stands for IRT (and hence Rasch), most of the time. $\endgroup$ – ttnphns Oct 15 '14 at 15:25
  • $\begingroup$ Aha - thank you. I shall leave the question open for another day or two to see if there are any other contributions that can add more than the wikipedia article, and then mark it as answered. It highlights one distinction (categorical vs continuous) but I was unsure if there were other dimensions on which the two can be conceptually distinguished. $\endgroup$ – SimonsSchus Oct 15 '14 at 20:21
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Latent class analysis is a latent mixture modeling technique that is interested in finding latent subgroups in multivariate categorical data. It quite naturally is a way to classify individuals, which might be useful in understanding how patterns of symptoms are related to different typologies. The continuous version of latent class analysis is called latent profile analysis.

Rasch analysis is concerned with the development of a measure for a single latent trait. The interest in Rasch modeling is to have items that fit the model so that sufficient statistics are produced. That is to say a measure developed using Rasch techniques would allow you to use the total score to summarize a persons total standing on the latent trait. This can be useful for comparing people for classification purposes. However, I don't think of the two techniques you mentioned as closely related.

Please keep in mind I tried to keep this answer at a real surface level like you asked.

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While I am not well versed in Latent Profile Analysis, I am familiar with Rasch. In response to bfoste 01's answer, assuming latent class analysis is described correctly, I feel Rasch does provide similar information as LPA, because in the dimensionaality output table, there is information provided about the presence of other constructs (other than that being measured). Rasch is a 1-parameter IRT method, where the data must fit the parameter of the model (which is determined by what the developer sets within the code: what responses are considered indicative of the construct being measured and to what degree it is representative of the construct- from less to more); while LPA, if I understand correctly, is an IRT method that allows the data to inform the model, meaning the parameters of the model can be "massaged" to fit the responses according how the respondents reacted (thus the model is made to fit the respondents). Imagine a ruler: would you rather the ruler keep "inches" the same for everyone (1-parameter: height) or would you like the ruler to respond to the people in your sample (so that if your sample was from a taller group, "inches" would be further apart than if you sampled another group of slightly smaller people). The difficulty with Rasch is that you have to be VERY knowledgeable about what you are trying to measure (which is difficult, given the latent quality of the constructs trying to be measured) AND be willing to go through multiple iterations. Most likely,you will need to go back and rewrite items to better reflect the construct. Item writing is very difficult and to do it well (so it creates a scale) means using respondents authentic language (which means focus groups, cognitive interviewing, and maybe discourse analysis). So it takes a mixed-method approach- which most ppl won't take the time/effort to do.

More information on Rasch can be found at www.rasch.org/rasch.htm for good beginner information. Also,a good primer book on Rasch is by Fox and Bond. The software for using Rasch is Winsteps (the easiest one for scale creation using 1-P...if you're looking to create a measure for a known multi-dimensional construct, there is Facets software.

If LPA is different than that described, I would appreciate feedback on that as well.

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    $\begingroup$ I think a simple way to think about LCA is that it is similar to a kind of parametric cluster analysis, eg akin to finite Gaussian mixture modeling. $\endgroup$ – gung - Reinstate Monica Mar 11 '15 at 22:02
  • $\begingroup$ @Patti Lee: gung: nailed the difference in one sentence. $\endgroup$ – bfoste01 Mar 12 '15 at 13:16
  • $\begingroup$ It looks like finite Gaussian mixture modeling is a parametric test. I think if we are looking to model a latent variable from questionnaires w/ Likert-type responses, we are coding a ordinal categorical variable (NOT a true interval variable), so to go ahead and use ANY statistic method that is parametric (thus is meant for use with continuous variables: interval or ratio) isn't appropriate (too much error, as every person's "agree" is not equally the same, nor is the "distance"-interval- between each agreement category).Rasch analysis "fixes" that error by transformation through natural log $\endgroup$ – Patti Lee Mar 13 '15 at 16:25

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