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The [[Rasch model]] represents the simplest form of item response theory. [[Mixture models]] are central to latent profile analysis.
In [[factor analysis]] and [[latent trait analysis]] the latent variables are treated as continuous [[normal distribution|normally distributed]] variables, and in latent profile analysis and latent class analysis as from a [[multinomial distribution]].<ref>{{cite book |last=Everitt |first=BS |title=An Introduction to Latent Variables Models |year=1984 |publisher=Chapman & Hall |isbn=978-9401089548 }}</ref> The manifest variables in factor analysis and latent profile analysis are continuous and in most cases, their conditional distribution given the latent variables is assumed to be normal. In latent trait analysis and latent class analysis, the manifest variables are discrete. These variables could be [[dichotomy|dichotomous]], ordinal or nominal variables. Their conditional distributions are assumed to be binomial or multinomial.
Because the distribution of a continuous latent variable can be approximated by a discrete distribution, the distinction between continuous and discrete variables turns out not to be fundamental at all. Therefore, there may be a psychometrical latent variable, but not a [[psychology|psychological]] psychometric variable.
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