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Latent Variable Models in Reliability
Published in Mangey Ram, Reliability Engineering, 2019
A latent variable is a variable that is not directly observable and is assumed to affect the response variables. There are many statistical models that involve latent variables. Such models are called latent variable models. Surprisingly, there are few monographs specifically dedicated to latent variable models (see, e.g., [1–4]). Latent variables typically are encountered in econometric, reliability, and survival statistical model with different aims. A latent variable may represent the effect of unobservable covariates or factors and then it allows accounting for the unobserved heterogeneity between subjects, it may also account for measurement errors assuming that the latent variables represent the “true” outcomes and the manifest variables represent their “disturbed” versions, it may also summarize different measurements of the same (directly) unobservable characteristics (e.g., quality of life), so that sample units may be easily ordered or classified based on these traits (represented by the latent variables). Hence, latent variable models now have a wide range of applications, especially in the presence of repeated observations, longitudinal/panel data, and multilevel data.
Probabilistic nonlinear dimensionality reduction through gaussian process latent variable models: An overview
Published in Arun Kumar Sinha, John Pradeep Darsy, Computer-Aided Developments: Electronics and Communication, 2019
Tipping and Bishop introduced a probabilistic framework for principal component analysis by constraining the noise distribution of a LVM [26]. A LVM transforms a set of n d-dimensional observed variables encoded as a design matrix, =[y1,…yn]T, to a set of n q-dimensional latent (unobserved) variables, X =[x1,…xn]T. Latent variables are parsimonious, it is generally the case that q ≪ d, explaining the original data with fewer variables. A notable latent variable model is that of factor analysis, one that assumes linearity in relation of the observed data set. For each observed data point, yi ∊ Y,1≤i≤n, there is an associated latent variable xi. The original data can be represented in terms of the corresponding latent variable as () yi=Wxi+μi+∈i
A deep variational auto-encoder based dimensionality reduction for fault diagnosis in ball bearings
Published in Stein Haugen, Anne Barros, Coen van Gulijk, Trond Kongsvik, Jan Erik Vinnem, Safety and Reliability – Safe Societies in a Changing World, 2018
G.A. San Martín, V. Meruane, E. López Droguett, M.C. Moura
The definition of the latent variables of a certain model is usually a complex problem. The nature of those variables or the relationship between them are very difficult to express beforehand without deep knowledge about the situation that we want to model. VAEs takes an easy approach to this, assuming that the latent variables are distributed according the following distribution: () p(z)~N(z|0,I)
Adopting cross-laminated timber in architectural design to reduce embodied carbon emission in China based on the diffusion of innovation theory
Published in Building Research & Information, 2023
The multivariate statistical analysis technique, structural equation modelling (SEM) was used to test the hypothesis. SEM is a technique used to specify and estimate a model of linear relationships among variables. Each variable in the model consists of observable variables and latent variables. A latent variable is a hypothetical construct that cannot be measured directly and is typically represented by multiple observable variables that serve as indicators of the construct (MacCallum & Austin, 2000). SEM is the integration of multiple multivariate techniques, such as regression analysis, path analysis and confirmatory factor analysis (Cheung, 2015), which allows for the simultaneous analysis of the observed variables and the latent constructs, their relationships and their impact on the corresponding outcomes (Cudeck et al., 2001).
The impact of economic and political imperatives on the successful use of public-private partnership (PPP) in projects
Published in Production Planning & Control, 2022
Ahmad Meile Almeile, Maxwell Chipulu, Udechukwu Ojiako, Ramesh Vahidi, Alasdair Marshall
Structural Equation Modelling (SEM) has two types of variables (i) measured items and (ii) latent variables. Whereas the measured items can be observed and directly measured, the latent variables are theoretical and/or hypothetical constructs, which are deducible from the measured items. Since a Structural Equation Model can hold a very complicated series of structural (regression) equations between different elements, path diagrams are generally prepared to illustrate these relationships, thus providing a clearer visualisation of the theory under study. In the path diagrams, the measured items are represented in rectangles, while the latent variables are represented in ovals. One-direction and two-direction arrows are usually used to connect the elements and represent the causal flows of relationships. The one-direction arrow indicates the regressive relationships, with the direction of the arrow implying the direction of influence. The two-direction arrow indicates the inter-correlation between variables. Structural Equation Modelling (SEM) combines: (i) a measurement model and (ii) a structural model in a single statistical test (Schumacker and Lomax 2010; Byrne 2016). The measurement model (confirmatory factor analysis CFA) is concerned with: (i) how the set of items will measure the latent constructs and (ii) addressing the model’s validity and reliability.
A comprehensive analysis of the trip frequency behavior in COVID scenario
Published in Transportation Letters, 2021
Latent variables are the variables which can’t be observed or measured directly (Jolliffe and Bartholomew 1989). But their impact on the observable variables such as choice, can be measured by using indicators, which conditionally reflect the effect of the latent variable. Factor analysis is used as a tool to include the impact of the latent variables into the ordered logit model. For this purpose, the factor scores and factor loadings of the indicators are evaluated using an exploratory factor analysis approach with a varimax rotation. The mean values of latent variables are then calculated by multiplying the factor scores of each indicator to the responses of the individuals, as explained in Equation (2) (Guttman 1955; Steiger 1979; Train, McFadden, and Goett 1987).