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I'm a psychology student/researcher and looking to model a phenomenun in which there are 3 variables. The relation of these variables are exactly unclear but I assume these variables are non-linear in nature, which means I shouldn't use linear regression or correlation analsis (let's say, the motivation for studying, the results of tests, and the sense of accomplishment, for people with dyslexia). However, since I don't have data at my hands the nature of the data distribution is unclear.

I have asked my colleagues about this and they have recommended me to use GLM (generalized linear model) but I'm not sure if it's a good fit since it says linear. Besides, even if it is applicable to non-linear models, I assume the nature of regression line needs to be specified (e.g. binominal), but how do you even do that? Is it going to be by hand and exploratory? It seems information critria like AIC are utilized but I assume the nature still needs to be somehow specified.

The other option I've been thinking about is to ditch the idea of creating a regression model altogether and using cluster analysis to identify the trends of the data. However, it obviously does not "predict" the data, it just classifies them so I fear the granularity of the data would be lost, by "arbitrarily" throwing them into chunks.

I'm relatively familiar with R and know a little bit about statistics, but obviously statistics and math are not my forte. If there's anyone who can help me, I would appreciate it wholeheartedly.

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You will need to know something about the metadata. Bear in mind that traditional k-means cluster analysis will work only for continuous variables. There are also other clustering models such as hierarchical cluster, where a knowledge of the metadata is very important.

I would also strongly suggest that you look into GLM models, which do handle non-linear model such as normal, exponential, gamma, Poisson, Bernoulli, binomial, multinomial, and negative binomial. So if you know a little bit about the data types, you can at least learn something about the design, without having access to the data.

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