Latent profile analysis is believed to offer a superior, model-based, cluster solution. Yet a combined hierarchical and non-hierarchical clustering approach (K means using Wards HC centroids as seeds) produces a solution in my dataset that is more theoretically consistent. Can anyone suggest a valid justification for switching from LPA to the older clustering algorithms? My sample consists of two distinct sub samples. Could this cause a problem with LPA but not with clustering? Any advice or tips would be gratefully received.
There are some algorithms that offer more flexibility than others, but in general it's not possible to state that one algorithm is always better than another.
In your specific case, K-means can be considered as a special case of Latent profile analysis. This does not mean that LPA will always be better, it just means that K-means does more assumptions than LPA. However, if those assumptions are correct, you can expect K-means to perform better. Also, if the number of datapoints that you have is relatively small, it is advisable to start with simple models instead of complex ones.
There is a lot of information out there comparing both methodologies, their advantages and disadvantages. You will find more information if you look for Gaussian Mixture Models instead of LPA. They are the same method, but the name LPA appears to be more common in social sciences, while Gaussian Mixture Models is the most common name in statistics and computer science. A good place to start is reading these answers in Quora, that compare both methodologies: https://www.quora.com/What-is-the-difference-between-K-means-and-the-mixture-model-of-Gaussian
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1- Latent profile analysis is not so "new" ... it goes back to
Lazarsfeld, P. F., & Henry, N. W. (1968). Latent structure analysis. Boston: Houghton Mifflin ...
admitedly, the idea of k-means is published in 1957
https://en.wikipedia.org/wiki/K-means_clustering#History
so clearly older than LPA ... but it's 2018 and both techniques could be qualified as "mature" !
2- a key assumption of LPA is that variables are independent conditional on class ; that is, the in-class covariance matrix is diagonal : if this is not true, LPA may perform quite poorly
you can check that once your LPA has converged ; remedy to violation of this assumption is more classes but there is a balance to be striken between many classes (leads to small classes) and the capacity to check the independence assumption (requires not too small classes)
3- k-means per se is just a quantifier and does not make distributional assumption
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Roberto, thanks so much for your answer. I followed your link and read about GMM but could not find an argument to use clustering. Like the LPA literature, it recommends use of GMM over Kmeans.
Hi Fabrice, thank you for your answer. Point taken regarding the relative modernity of the analyses. Would you please provide more info about checking for independence within classes?
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in theory you could apply statistical tests for independence under the multivariate gaussian hypothesis in each class to see if the hypothesis is rejected in some classes ...
... but i wouldn't do that since the risk of rejection is pretty high for the distribution in a class not being gaussian (whereas you'd rather test the independence ... and care less about gaussianity as long as the deviation is not too terrible)
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non parametric tests for multivariate independence exist but they require quite a lot of data
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i would just go the modest pragmatic way : for each class, compute the covariance matrix and hunt for particularly shocking deviations of the independence hypothesis (that is, particularly large non diagonal elements, as compared to diagonal elements) ; this would be a first step and a pretty cheap one
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