| 1. |
- Felleki, Majbritt, et al.
(author)
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Estimation of breeding values for mean and dispersion, their variance and correlation using double hierarchical generalized linear models
- 2012
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In: Genetics Research. - : Cambridge University Press. - 0016-6723 .- 1469-5073. ; 94:6, s. 307-317
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Journal article (peer-reviewed)abstract
- The possibility of breeding for uniform individuals by selecting animals expressing a small response to environment has been studied extensively in animal breeding. Bayesian methods for fitting models with genetic components in the residual variance have been developed for this purpose, but have limitations due to the computational demands. We use the hierarchical (h)-likelihood from the theory of double hierarchical generalized linear models (DHGLM) to derive an estimation algorithm that is computationally feasible for large datasets. Random effects for both the mean and residual variance parts of the model are estimated together with their variance/covariance components. An important feature of the algorithm is that it can fit a correlation between the random effects for mean and variance. An h-likelihood estimator is implemented in the R software and an iterative reweighted least square (IRWLS) approximation of the h-likelihood is implemented using ASReml. The difference in variance component estimates between the two implementations is investigated, as well as the potential bias of the methods, using simulations. IRWLS gives the same results as h-likelihood in simple cases with no severe indication of bias. For more complex cases, only IRWLS could be used, and bias did appear. The IRWLS is applied on the pig litter size data previously analysed by Sorensen & Waagepetersen (2003) using Bayesian methodology. The estimates we obtained by using IRWLS are similar to theirs, with the estimated correlation between the random genetic effects being −0·52 for IRWLS and −0·62 in Sorensen & Waagepetersen (2003).
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| 2. |
- Lee, Sangin, et al.
(author)
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Sparse estimation of gene-gene interactions in prediction models
- 2017
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In: Statistical Methods in Medical Research. - : SAGE Publications. - 0962-2802 .- 1477-0334. ; 26:5, s. 2319-2332
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Journal article (peer-reviewed)abstract
- Current assessment of gene-gene interactions is typically based on separate parallel analysis, where each interaction term is tested separately, while less attention has been paid on simultaneous estimation of interaction terms in a prediction model. As the number of interaction terms grows fast, sparse estimation is desirable from statistical and interpretability reasons. There is a large literature on sparse estimation, but there is a natural hierarchy between the interaction and its corresponding main effects that requires special considerations. We describe random-effect models that impose sparse estimation of interactions under both strong and weak-hierarchy constraints. We develop an estimation procedure based on the hierarchical-likelihood argument and show that the modelling approach is equivalent to a penalty-based method, with the advantage of the models being more transparent and flexible. We compare the procedure with some standard methods in a simulation study and illustrate its application in an analysis of gene-gene interaction model to predict body-mass index.
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| 3. |
- Alam, Moudud, et al.
(author)
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Likelihood estimate of treatment effects under selection bias
- 2012
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Reports (other academic/artistic)abstract
- We consider methods for estimating causal effects of treatment in the situation where the individuals in the treatment and the control group are self selected, i.e., the selection mechanism is not randomized. In this case, simple comparison of treated and control outcomes will not generally yield valid estimates of casual effects. The propensity score method is frequently used for the evaluation of treatment effect. However, this method is based onsome strong assumptions, which are not directly testable. In this paper, we present an alternative modeling approachto draw causal inference by using share random-effect model and the computational algorithm to draw likelihood based inference with such a model. With small numerical studies and a real data analysis, we show that our approach gives not only more efficient estimates but it is also less sensitive to model misspecifications, which we consider, than the existing methods.
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| 4. |
- Alam, Moudud, et al.
(author)
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Likelihood estimate of treatment effects under selection bias
- 2013
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In: Statistics and its Interface. - 1938-7989 .- 1938-7997. ; 6:3, s. 349-359
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Journal article (peer-reviewed)abstract
- We consider methods for estimating the causal effects of treatment in the situation where the individuals in the treatment and the control group are self selected, i.e., the selection mechanism is not randomized. In this case, a simple comparison of treated and control outcomes will not generally yield valid estimates of casual effect. The propensity score method is frequently used for the evaluation of treatment effect. However, this method is based on some strong assumptions, which are not directly testable. In this paper, we present an alternative modelling approach to draw causal inferences by using a shared random-effect model and the computational algorithm to draw likelihood based inference with such a model. With small numerical studies and a real data analysis, we show that our approach gives not only more efficient estimates but also is less sensitive to model misspecifications, which we consider, than existing methods.
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| 5. |
- Jin, Shaobo, 1987-, et al.
(author)
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A review of h-likelihood and hierarchical generalized linear model
- 2021
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In: Wiley Interdisciplinary Reviews. - : John Wiley & Sons. - 1939-5108 .- 1939-0068. ; 13:5
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Research review (peer-reviewed)abstract
- Fisher's classical likelihood has become the standard procedure to make inference for fixed unknown parameters. Recently, inferences of unobservable random variables, such as random effects, factors, missing values, etc., have become important in statistical analysis. Because Fisher's likelihood cannot have such unobservable random variables, the full Bayesian method is only available for inference. An alternative likelihood approach is proposed by Lee and Nelder. In the context of Fisher likelihood, the likelihood principle means that the likelihood function carries all relevant information regarding the fixed unknown parameters. Bjørnstad extended the likelihood principle to extended likelihood principle; all information in the observed data for fixed unknown parameters and unobservables are in the extended likelihood, such as the h-likelihood. However, it turns out that the use of extended likelihood for inferences is not as straightforward as the Fisher likelihood. In this paper, we describe how to extract information of the data from the h-likelihood. This provides a new way of statistical inferences in entire fields of statistical science.
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| 6. |
- Jin, Shaobo, 1987-, et al.
(author)
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H-Likelihood Approach to Factor Analysis for Ordinal Data
- 2018
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In: Structural Equation Modeling. - : Informa UK Limited. - 1070-5511 .- 1532-8007. ; 25:4, s. 530-540
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Journal article (peer-reviewed)abstract
- Marginal likelihood-based methods are commonly used in factor analysis for ordinal data. To obtain the maximum marginal likelihood estimator, the full information maximum likelihood (FIML) estimator uses the (adaptive) Gauss-Hermite quadrature or stochastic approximation. However, the computational burden increases rapidly as the number of factors increases, which renders FIML impractical for large factor models. Another limitation of the marginal likelihood-based approach is that it does not allow inference on the factors. In this study, we propose a hierarchical likelihood approach using the Laplace approximation that remains computationally efficient in large models. We also proposed confidence intervals for factors, which maintains the level of confidence as the sample size increases. The simulation study shows that the proposed approach generally works well.
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| 7. |
- Jin, Shaobo, 1987-, et al.
(author)
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Robust nonlinear structural equation modeling with interaction between exogenous and endogenous latent variables
- 2021
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In: Structural Equation Modeling. - : Taylor & Francis Group. - 1070-5511 .- 1532-8007. ; 28:4, s. 547-556
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Journal article (peer-reviewed)abstract
- A handful of studies have been devoted to nonlinear structural equation modeling (SEM) in the literature. However, they generally overlooked the interactions among exogenous and endogenous latent variables and the interactions among endogenous latent variables. In this study, we propose a maximum likelihood approach for a nonlinear SEM model that incorporates such overlooked interactions. We also propose a two-stage pseudo maximum likelihood approach under the assumption of a normal mixture, being computationally efficient and robust against distributional misspecification. The simulation study shows that both approaches accurately estimate the unknown parameters if the distribution is correctly specified. However, only the pseudo maximum likelihood approach is robust against distributional misspecification.
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| 8. |
- Jin, Shaobo, 1987-, et al.
(author)
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Standard error estimates in hierarchical generalized linear models
- 2024
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In: Computational Statistics & Data Analysis. - : Elsevier. - 0167-9473 .- 1872-7352. ; 189
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Journal article (peer-reviewed)abstract
- Hierarchical generalized linear models are often used to fit random effects models. However, attention is mostly paid to the estimation of fixed unknown parameters and inference for latent random effects. In contrast, standard error estimators receive less attention than they should be. Currently, the standard error estimators are based on various approximations, even when the mean parameters may be estimated from a higher-order approximation of the likelihood and the dispersion parameters are estimated by restricted maximum likelihood. Existing standard error estimation procedures are reviewed. A numerical illustration shows that the current standard errors are not necessarily accurate. Alternative standard errors are also proposed. In particular, a sandwich estimator that accounts for the dependence between the mean parameters and the dispersion parameters greatly improve the current standard errors.
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