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</script>Finite mixture models have come to play a very prominent role in modelling data. The finite mixture model is predicated on the assumption that distinct latent groups exist in the population. The finite mixture model therefore is based on a categorical latent variable that distinguishes the different groups. Often in practice, distinct sub-populations do not actually exist. For example, disease severity (e.g., depression) may vary continuously and therefore, a distinction of diseased and non-diseased may not be based on the existence of distinct sub-populations. Thus, what is needed is a generalization of the finite mixture’s discrete latent predictor to a continuous latent predictor. We cast the finite mixture model as a regression model with a latent Bernoulli predictor. A latent regression model is proposed by replacing the discrete Bernoulli predictor by a continuous latent predictor with a beta distribution. Motivation for the latent regression model arises from applications where distinct latent classes do not exist, but instead individuals vary according to a continuous latent variable. The shapes of the beta density are very flexible and can approximate the discrete Bernoulli distribution. Examples and a simulation are provided to illustrate the latent regression model. In particular, the latent regression model is used to model placebo effect among drug-treated subjects in a depression study.
Statistics and Probability, Principal components, Applied Statistics, Applied Mathematics, k-means algorithm, quasi-Newton algorithms, Fourier basis, Beta distribution, skew normal distribution, Gaussian random functions, finite and infinite mixtures, Mathematics and Statistics, Physical Sciences and Mathematics, placebo effect, Mean squared error, Principal points, EM algorithm, Mathematics
Statistics and Probability, Principal components, Applied Statistics, Applied Mathematics, k-means algorithm, quasi-Newton algorithms, Fourier basis, Beta distribution, skew normal distribution, Gaussian random functions, finite and infinite mixtures, Mathematics and Statistics, Physical Sciences and Mathematics, placebo effect, Mean squared error, Principal points, EM algorithm, Mathematics
| citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | 15 | |
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| influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | Top 10% | |
| impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network. | Top 10% |
