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Mixture Modelling of Discrete Data
Published in Sylvia Frühwirth-Schnatter, Gilles Celeux, Christian P. Robert, Handbook of Mixture Analysis, 2019
Suppose that the data refer to a binary multivariate random variable Y = (Y1, …, Yd)⊺, that is, the Yi take values 0 and 1. In a latent class model (also known as a latent structure model) the correlation between the elements Y1, …, Yd of Y is assumed to be caused by a discrete latent variables zi, also called the latent class. It is then assumed that the variables Y1, …, Yd, which are also called manifest variables, are stochastically independent conditional on the latent variable zi. Latent structure analysis is closely related to multivariate mixture modelling, as marginally the distribution of Y is a multivariate discrete mixture given by p(yi|θ)=∑g=1Gηg∏m=1dθg,myim(1−θg,m)1−yim,
Making sense of smart features in the smart office: a stated choice experiment of office user preferences
Published in Building Research & Information, 2023
Alex Donkers, Dujuan Yang, Sara Guendouz, Bei Wang
The Latent Class model (LCM) is a statistical method that aims to identify unobserved subgroups within a population that share similar characteristics. It is commonly used to reveal different preference structures among individuals and identify heterogeneity in their preferences. The LCM assumes each class has a unique set of preferences that may vary in terms of the importance of different attributes or the direction and magnitude of the effects of those attributes on choice. To estimate the parameters, the LCM analyses individual response patterns on explicit indicators and assigns each individual to a class based on their probability of belong to that class. The model is estimated by maximizing the likelihood of the observed data given the underlying latent structure, and each class has a different vector of parameters (Heckman & Singer, 1984; Greene & Hensher, 2003). The probability of an individual choosing alternative j from a choice set J, conditional on belonging to class s, is expressed as Equation (3).
Investigating college students’ choice of train trips for homecoming during the Spring Festival travel rush in China: results from a stated preference approach
Published in Transportation Letters, 2021
In a latent class model, it is assumed that there exist a certain number of latent classes among individuals. Individuals’ heterogeneous preferences could be observed across different classes. In other words, individuals’ preferences are homogeneous within each class. According to the rule of random utility maximization, the random utility of an alternative for a certain class could be specified as follows: