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Fast estimation of multiple group generalized linear latent variable models for categorical observed variables. Comput Stat Data Anal 2023. [DOI: 10.1016/j.csda.2023.107710] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
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Hui FK. GEE-assisted Forward Regression for Spatial Latent Variable Models. J Comput Graph Stat 2022. [DOI: 10.1080/10618600.2022.2058002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Affiliation(s)
- Francis K.C. Hui
- Research School of Finance, Actuarial Studies and Statistics, The Australian National University, Canberra, Australia
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Abstract
Summary
Numerical quadrature methods are needed for many models in order to approximate integrals in the likelihood function. In this note, we correct the error rate given by Liu & Pierce (1994) for integrals approximated with adaptive Gauss–Hermite quadrature and show that the approximation is less accurate than previously thought. We discuss the relationship between the error rates of adaptive Gauss–Hermite quadrature and Laplace approximation, and provide a theoretical explanation of simulation results obtained in previous studies regarding the accuracy of adaptive Gauss–Hermite quadrature.
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Affiliation(s)
- Shaobo Jin
- Department of Statistics, Uppsala University, Box 513, 75120 Uppsala, Sweden
| | - Björn Andersson
- Centre for Educational Measurement, University of Oslo, Box 1161, 0373 Oslo, Norway
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Niku J, Warton DI, Hui FKC, Taskinen S. Generalized Linear Latent Variable Models for Multivariate Count and Biomass Data in Ecology. JOURNAL OF AGRICULTURAL BIOLOGICAL AND ENVIRONMENTAL STATISTICS 2017. [DOI: 10.1007/s13253-017-0304-7] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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Hui FKC, Warton DI, Ormerod JT, Haapaniemi V, Taskinen S. Variational Approximations for Generalized Linear Latent Variable Models. J Comput Graph Stat 2017. [DOI: 10.1080/10618600.2016.1164708] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- Francis K. C. Hui
- Mathematical Sciences Institute, The Australian National University, Canberra, ACT, Australia
| | - David I. Warton
- School of Mathematics and Statistics and Evolution & Ecology Research Centre, The University of New South Wales, Sydney, NSW, Australia
| | - John T. Ormerod
- School of Mathematics and Statistics, The University of Sydney, Sydney, NSW, Australia and ARC Centre of Excellence for Mathematical & Statistical Frontiers, The University of Melbourne, Parkville, VIC, Australia
| | - Viivi Haapaniemi
- Department of Mathematics and Statistics, University of Jyväskylä, Jyväskylän, Finland
| | - Sara Taskinen
- Department of Mathematics and Statistics, University of Jyväskylä, Jyväskylän, Finland
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Bianconcini S, Cagnone S, Rizopoulos D. Approximate likelihood inference in generalized linear latent variable models based on the dimension-wise quadrature. Electron J Stat 2017. [DOI: 10.1214/17-ejs1360] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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8
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Bianconcini S. Asymptotic properties of adaptive maximum likelihood estimators in latent variable models. BERNOULLI 2014. [DOI: 10.3150/13-bej531] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Bianconcini S, Cagnone S. The Role of Posterior Densities in Latent Variable Models for Ordinal Data. COMMUN STAT-THEOR M 2014. [DOI: 10.1080/03610926.2013.810266] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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Karimi H, McAuley KB. An Approximate Expectation Maximization Algorithm for Estimating Parameters, Noise Variances, and Stochastic Disturbance Intensities in Nonlinear Dynamic Models. Ind Eng Chem Res 2013. [DOI: 10.1021/ie4023989] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Hadiseh Karimi
- Department of Chemical Engineering, Queen’s University, Kingston, K7L3N6, Canada
| | - Kimberley B. McAuley
- Department of Chemical Engineering, Queen’s University, Kingston, K7L3N6, Canada
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