| 1. |
- Andersson, Björn, et al.
(författare)
-
Fast estimation of multiple group generalized linear latent variable models for categorical observed variables
- 2023
-
Ingår i: Computational Statistics & Data Analysis. - : Elsevier. - 0167-9473 .- 1872-7352. ; 182
-
Tidskriftsartikel (refereegranskat)abstract
- A computationally efficient method for marginal maximum likelihood estimation of multiple group generalized linear latent variable models for categorical data is introduced. The approach utilizes second-order Laplace approximations of the integrals in the likelihood function. It is demonstrated how second-order Laplace approximations can be utilized highly efficiently for generalized linear latent variable models by considering symmetries that exist for many types of model structures. In a simulation with binary observed variables and four correlated latent variables in four groups, the method has similar bias and mean squared error compared to adaptive Gauss-Hermite quadrature with five quadrature points while substantially improving computational efficiency. An empirical example from a large-scale educational assessment illustrates the accuracy and computational efficiency of the method when compared against adaptive Gauss-Hermite quadrature with three, five, and 13 quadrature points.
|
|
| 2. |
- Ankargren, Sebastian, et al.
(författare)
-
On the least-squares model averaging interval estimator
- 2018
-
Ingår i: Communications in Statistics - Theory and Methods. - : Informa UK Limited. - 0361-0926 .- 1532-415X. ; 47:1, s. 118-132
-
Tidskriftsartikel (refereegranskat)abstract
- In many applications of linear regression models, randomness due to model selection is commonly ignored in post-model selection inference. In order to account for the model selection uncertainty, least-squares frequentist model averaging has been proposed recently. We show that the confidence interval from model averaging is asymptotically equivalent to the confidence interval from the full model. The finite-sample confidence intervals based on approximations to the asymptotic distributions are also equivalent if the parameter of interest is a linear function of the regression coefficients. Furthermore, we demonstrate that this equivalence also holds for prediction intervals constructed in the same fashion.
|
|
| 3. |
- Cao, Chunzheng, et al.
(författare)
-
Bayesian inference in a heteroscedastic replicated measurement error model using heavy-tailed distributions
- 2017
-
Ingår i: Journal of Statistical Computation and Simulation. - : Informa UK Limited. - 0094-9655 .- 1563-5163. ; 87:15, s. 2915-2928
-
Tidskriftsartikel (refereegranskat)abstract
- We introduce a multivariate heteroscedastic measurement error model for replications under scale mixtures of normal distribution. The model can provide a robust analysis and can be viewed as a generalization of multiple linear regression from both model structure and distribution assumption. An efficient method based on Markov Chain Monte Carlo is developed for parameter estimation. The deviance information criterion and the conditional predictive ordinates are used as model selection criteria. Simulation studies show robust inference behaviours of the model against both misspecification of distributions and outliers. We work out an illustrative example with a real data set on measurements of plant root decomposition.
|
|
| 4. |
- Cao, Chunzheng, et al.
(författare)
-
Improved likelihood ratio tests in a measurement error model for multivariate replicated data
- 2020
-
Ingår i: Communications in Statistics - Theory and Methods. - : TAYLOR & FRANCIS INC. - 0361-0926 .- 1532-415X. ; 49:5, s. 1025-1042
-
Tidskriftsartikel (refereegranskat)abstract
- We present a measurement error model for multivariate replicated data and focus on the improved likelihood ratio tests for parameters of interest. By assuming that the random terms follow the scale mixtures of normal distributions, the model can bring robust inference and can target on both error-prone and error-free covariates. We derive modified versions from the original likelihood ratio statistics to achieve better asymptotic properties with high degree of accuracy. Simulation studies are conducted to display finite sample behavior as compared to the unmodified counterpart. The practical utility is illustrated through a root decomposition data.
|
|
| 5. |
- Giordano, Michael L., et al.
(författare)
-
Estimating and Testing Random Intercept Multilevel Structural Equation Models with Model Implied Instrumental Variables
- 2022
-
Ingår i: Structural Equation Modeling. - : Taylor & Francis Group. - 1070-5511 .- 1532-8007. ; 29:4, s. 584-599
-
Tidskriftsartikel (refereegranskat)abstract
- This study develops a new limited information estimator for random intercept Multilevel Structural Equation Models (MSEM). It is based on the Model Implied Instrumental Variable Two-Stage Least Squares (MIIV-2SLS) estimator, which has been shown to be an excellent alternative or supplement to maximum likelihood (ML) in SEMs (Bollen, 1996). We also develop a multilevel overidentification test statistic that applies to equations at the within or between levels. Our Monte Carlo simulation analysis suggests that MIIV-2SLS is more robust than ML to misspecification at within or between levels, performs well given fewer than 100 clusters, and shows that our multilevel overidentification test for equations performs well at both levels of the model.
|
|
| 6. |
- Jin, Shaobo, 1987-, et al.
(författare)
-
A note on the accuracy of adaptive Gauss-Hermite quadrature
- 2020
-
Ingår i: Biometrika. - : Oxford Academic. - 0006-3444 .- 1464-3510. ; 107:3, s. 737-744
-
Tidskriftsartikel (refereegranskat)abstract
- 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.
|
|
| 7. |
- Jin, Shaobo, 1987-, et al.
(författare)
-
A review of h-likelihood and hierarchical generalized linear model
- 2021
-
Ingår i: Wiley Interdisciplinary Reviews. - : John Wiley & Sons. - 1939-5108 .- 1939-0068. ; 13:5
-
Forskningsöversikt (refereegranskat)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.
|
|
| 8. |
- Jin, Shaobo, 1987-, et al.
(författare)
-
A unified model-implied instrumental variable approach for structural equation modeling with mixed variables
- 2021
-
Ingår i: Psychometrika. - : Springer Nature. - 0033-3123 .- 1860-0980. ; 86:2, s. 564-594
-
Tidskriftsartikel (refereegranskat)abstract
- The model-implied instrumental variable (MIIV) estimator is an equation-by-equation estimator of structural equation models that is more robust to structural misspecifications than full information estimators. Previous studies have concentrated on endogenous variables that are all continuous (MIIV-2SLS) or all ordinal . We develop a unified MIIV approach that applies to a mixture of binary, ordinal, censored, or continuous endogenous observed variables. We include estimates of factor loadings, regression coefficients, variances, and covariances along with their asymptotic standard errors. In addition, we create new goodness of fit tests of the model and overidentification tests of single equations. Our simulation study shows that the proposed MIIV approach is more robust to structural misspecifications than diagonally weighted least squares (DWLS) and that both the goodness of fit model tests and the overidentification equations tests can detect structural misspecifications. We also find that the bias in asymptotic standard errors for the MIIV estimators of factor loadings and regression coefficients are often lower than the DWLS ones, though the differences are small in large samples. Our analysis shows that scaling indicators with low reliability can adversely affect the MIIV estimators. Also, using a small subset of MIIVs reduces small sample bias of coefficient estimates, but can lower the power of overidentification tests of equations.
|
|
| 9. |
- Jin, Shaobo, 1987-, et al.
(författare)
-
Approximate Bayesianity of frequentist confidence intervals for a binomial proportion
- 2017
-
Ingår i: American Statistician. - : Informa UK Limited. - 0003-1305 .- 1537-2731. ; 71, s. 106-111
-
Tidskriftsartikel (refereegranskat)abstract
- The well-known Wilson and Agresti–Coull confidence intervals for a binomial proportion p are centered around a Bayesian estimator. Using this as a starting point, similarities between frequentist confidence intervals for proportions and Bayesian credible intervals based on low-informative priors are studied using asymptotic expansions. A Bayesian motivation for a large class of frequentist confidence intervals is provided. It is shown that the likelihood ratio interval for p approximates a Bayesian credible interval based on Kerman’s neutral noninformative conjugate prior up to O(n− 1) in the confidence bounds. For the significance level α ≲ 0.317, the Bayesian interval based on the Jeffreys’ prior is then shown to be a compromise between the likelihood ratio and Wilson intervals. Supplementary materials for this article are available online.
|
|
| 10. |
- Jin, Shaobo, 1987-, et al.
(författare)
-
Approximated penalized maximum likelihood for exploratory factor analysis : An orthogonal case
- 2018
-
Ingår i: Psychometrika. - : Springer Science and Business Media LLC. - 0033-3123 .- 1860-0980. ; 83:3, s. 628-649
-
Tidskriftsartikel (refereegranskat)abstract
- The problem of penalized maximum likelihood (PML) for an exploratory factor analysis (EFA) model is studied in this paper. An EFA model is typically estimated using maximum likelihood and then the estimated loading matrix is rotated to obtain a sparse representation. Penalized maximum likelihood simultaneously fits the EFA model and produces a sparse loading matrix. To overcome some of the computational drawbacks of PML, an approximation to PML is proposed in this paper. It is further applied to an empirical dataset for illustration. A simulation study shows that the approximation naturally produces a sparse loading matrix and more accurately estimates the factor loadings and the covariance matrix, in the sense of having a lower mean squared error than factor rotations, under various conditions.
|
|
