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Adekpedjou A, Dabo‐Niang S. Semiparametric estimation with spatially correlated recurrent events. Scand Stat Theory Appl 2020. [DOI: 10.1111/sjos.12480] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
Affiliation(s)
- Akim Adekpedjou
- Department of Mathematics and Statistics Missouri University of Science and Technology
| | - Sophie Dabo‐Niang
- Laboratoire Paul Painvelé UMR CNRS 8524, INRIA‐MODAL University of Lille
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2
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Castilla E, Martín N, Pardo L, Zografos K. Model Selection in a Composite Likelihood Framework Based on Density Power Divergence. ENTROPY (BASEL, SWITZERLAND) 2020; 22:e22030270. [PMID: 33286044 PMCID: PMC7516723 DOI: 10.3390/e22030270] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/22/2020] [Revised: 02/17/2020] [Accepted: 02/25/2020] [Indexed: 06/12/2023]
Abstract
This paper presents a model selection criterion in a composite likelihood framework based on density power divergence measures and in the composite minimum density power divergence estimators, which depends on an tuning parameter α . After introducing such a criterion, some asymptotic properties are established. We present a simulation study and two numerical examples in order to point out the robustness properties of the introduced model selection criterion.
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Affiliation(s)
- Elena Castilla
- Interdisciplinary Mathematics Institute and Department of Statistics and O.R. I, Complutense University of Madrid, 28040 Madrid, Spain;
| | - Nirian Martín
- Interdisciplinary Mathematics Institute and Department of Financial and Actuarial Economics & Statistics, Complutense University of Madrid, 28003 Madrid, Spain;
| | - Leandro Pardo
- Interdisciplinary Mathematics Institute and Department of Statistics and O.R. I, Complutense University of Madrid, 28040 Madrid, Spain;
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Hosseini F, Karimi O. Approximate likelihood inference in spatial generalized linear mixed models with closed skew normal latent variables. COMMUN STAT-SIMUL C 2020. [DOI: 10.1080/03610918.2018.1476700] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- Fatemeh Hosseini
- Department of Statistics, Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran
| | - Omid Karimi
- Department of Statistics, Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran
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Li F, Sang H. On approximating optimal weighted composite likelihood method for spatial models. Stat (Int Stat Inst) 2018. [DOI: 10.1002/sta4.194] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Affiliation(s)
- Furong Li
- School of Mathematical Sciences; Ocean University of China; 238 Songling Road Qingdao 266100 China
| | - Huiyan Sang
- Department of Statistics; Texas A&M University; 3143 TAMU, College Station TX 77843-3143 USA
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Hosseini F, Karimi O. Approximate composite marginal likelihood inference in spatial generalized linear mixed models. J Appl Stat 2018. [DOI: 10.1080/02664763.2018.1506020] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
Affiliation(s)
- Fatemeh Hosseini
- Department of Statistics, Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran
| | - Omid Karimi
- Department of Statistics, Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran
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6
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Cattelan M, Varin C. Marginal logistic regression for spatially clustered binary data. J R Stat Soc Ser C Appl Stat 2018. [DOI: 10.1111/rssc.12270] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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Hong C, Ning Y, Wang S, Wu H, Carroll RJ, Chen Y. PLMET: A Novel Pseudolikelihood-Based EM Test for Homogeneity in Generalilzed Exponential Tilt Mixture Models. J Am Stat Assoc 2017; 112:1393-1404. [PMID: 29416190 PMCID: PMC5798902 DOI: 10.1080/01621459.2017.1280405] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/01/2014] [Revised: 10/01/2016] [Indexed: 10/20/2022]
Abstract
Motivated by analyses of DNA methylation data, we propose a semiparametric mixture model, namely the generalized exponential tilt mixture model, to account for heterogeneity between differentially methylated and non-differentially methylated subjects in the cancer group, and capture the differences in higher order moments (e.g. mean and variance) between subjects in cancer and normal groups. A pairwise pseudolikelihood is constructed to eliminate the unknown nuisance function. To circumvent boundary and non-identifiability problems as in parametric mixture models, we modify the pseudolikelihood by adding a penalty function. In addition, the test with simple asymptotic distribution has computational advantages compared with permutation-based test for high-dimensional genetic or epigenetic data. We propose a pseudolikelihood based expectation-maximization test, and show the proposed test follows a simple chi-squared limiting distribution. Simulation studies show that the proposed test controls Type I errors well and has better power compared to several current tests. In particular, the proposed test outperforms the commonly used tests under all simulation settings considered, especially when there are variance differences between two groups. The proposed test is applied to a real data set to identify differentially methylated sites between ovarian cancer subjects and normal subjects.
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Affiliation(s)
- Chuan Hong
- Department of Biostatistics, Harvard University School of Public Health,
Boston, MA 02115, USA
| | - Yang Ning
- Department of Statistical Science, Cornell University, Ithaca, NY 14853,
USA
| | - Shuang Wang
- Department of Biostatistics, Mailman School of Public Health, Columbia
University, New York, NY 10027, USA
| | - Hao Wu
- Department of Biostatistics and Bioinformatics, Rollins School of Public
Health, Emory University, Atlanta, GA 30322, USA
| | - Raymond J. Carroll
- Department of Statistics, Texas A&M University, College Station, TX
77843-3143, USA
| | - Yong Chen
- Department of Biostatistics and Epidemiology, University of Pennsylvania,
Philadelphia, PA 19104, USA
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Katsikatsou M, Moustaki I. Pairwise Likelihood Ratio Tests and Model Selection Criteria for Structural Equation Models with Ordinal Variables. PSYCHOMETRIKA 2016; 81:1046-1068. [PMID: 27734296 DOI: 10.1007/s11336-016-9523-z] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/04/2014] [Revised: 06/29/2016] [Indexed: 06/06/2023]
Abstract
Correlated multivariate ordinal data can be analysed with structural equation models. Parameter estimation has been tackled in the literature using limited-information methods including three-stage least squares and pseudo-likelihood estimation methods such as pairwise maximum likelihood estimation. In this paper, two likelihood ratio test statistics and their asymptotic distributions are derived for testing overall goodness-of-fit and nested models, respectively, under the estimation framework of pairwise maximum likelihood estimation. Simulation results show a satisfactory performance of type I error and power for the proposed test statistics and also suggest that the performance of the proposed test statistics is similar to that of the test statistics derived under the three-stage diagonally weighted and unweighted least squares. Furthermore, the corresponding, under the pairwise framework, model selection criteria, AIC and BIC, show satisfactory results in selecting the right model in our simulation examples. The derivation of the likelihood ratio test statistics and model selection criteria under the pairwise framework together with pairwise estimation provide a flexible framework for fitting and testing structural equation models for ordinal as well as for other types of data. The test statistics derived and the model selection criteria are used on data on 'trust in the police' selected from the 2010 European Social Survey. The proposed test statistics and the model selection criteria have been implemented in the R package lavaan.
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Affiliation(s)
- Myrsini Katsikatsou
- Department of Statistics, London School of Economics, Houghton Street, London, WC2A 2AE , UK.
| | - Irini Moustaki
- Department of Statistics, London School of Economics, Houghton Street, London, WC2A 2AE , UK
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Bellio R, Varin C. A pairwise likelihood approach to generalized linear models with crossed random effects. STAT MODEL 2016. [DOI: 10.1191/1471082x05st095oa] [Citation(s) in RCA: 32] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
Abstract
Inference in generalized linear models with crossed effects is often made cumbersome by the high-dimensional intractable integrals involved in the likelihood function. We propose an inferential strategy based on the pairwise likelihood, which only requires the computation of bivariate distributions. The benefits of our approach are the simplicity of implementation and the potential to handle large data sets. The estimators based on the pairwise likelihood are generally consistent and asymptotically normally distributed. The pairwise likelihood makes it possible to improve on standard inferential procedures by means of bootstrap methods. The performance of the proposed methodology is illustrated by simulations and application to the well-known salamander mating data set.
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Ma TF, Yau CY. A pairwise likelihood-based approach for changepoint detection in multivariate time series models. Biometrika 2016; 103:409-421. [DOI: 10.1093/biomet/asw002] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/13/2022] Open
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Chen Y, Hong C, Ning Y, Su X. Meta-analysis of studies with bivariate binary outcomes: a marginal beta-binomial model approach. Stat Med 2015; 35:21-40. [PMID: 26303591 DOI: 10.1002/sim.6620] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/21/2013] [Revised: 05/01/2015] [Accepted: 07/23/2015] [Indexed: 11/11/2022]
Abstract
When conducting a meta-analysis of studies with bivariate binary outcomes, challenges arise when the within-study correlation and between-study heterogeneity should be taken into account. In this paper, we propose a marginal beta-binomial model for the meta-analysis of studies with binary outcomes. This model is based on the composite likelihood approach and has several attractive features compared with the existing models such as bivariate generalized linear mixed model (Chu and Cole, 2006) and Sarmanov beta-binomial model (Chen et al., 2012). The advantages of the proposed marginal model include modeling the probabilities in the original scale, not requiring any transformation of probabilities or any link function, having closed-form expression of likelihood function, and no constraints on the correlation parameter. More importantly, because the marginal beta-binomial model is only based on the marginal distributions, it does not suffer from potential misspecification of the joint distribution of bivariate study-specific probabilities. Such misspecification is difficult to detect and can lead to biased inference using currents methods. We compare the performance of the marginal beta-binomial model with the bivariate generalized linear mixed model and the Sarmanov beta-binomial model by simulation studies. Interestingly, the results show that the marginal beta-binomial model performs better than the Sarmanov beta-binomial model, whether or not the true model is Sarmanov beta-binomial, and the marginal beta-binomial model is more robust than the bivariate generalized linear mixed model under model misspecifications. Two meta-analyses of diagnostic accuracy studies and a meta-analysis of case-control studies are conducted for illustration.
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Affiliation(s)
- Yong Chen
- Department of Biostatistics and Epidemiology, University of Pennsylvania, Philadelphia, 19104, Pennsylvania, U.S.A
| | - Chuan Hong
- Division of Biostatistics, University of Texas School of Public Health, 1200 Pressler St, Houston, 77030, Texas, U.S.A
| | - Yang Ning
- Department of Operations Research and Financial Engineering, Princeton University, Princeton, 08544, New Jersey, U.S.A
| | - Xiao Su
- Division of Biostatistics, University of Texas School of Public Health, 1200 Pressler St, Houston, 77030, Texas, U.S.A
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Affiliation(s)
- Nicola Lunardon
- Department of Statistical Sciences; University of Padova; Padova Italy
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Lunardon N, Ronchetti E. Composite likelihood inference by nonparametric saddlepoint tests. Comput Stat Data Anal 2014. [DOI: 10.1016/j.csda.2014.05.014] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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Dasgupta P, Cramb SM, Aitken JF, Turrell G, Baade PD. Comparing multilevel and Bayesian spatial random effects survival models to assess geographical inequalities in colorectal cancer survival: a case study. Int J Health Geogr 2014; 13:36. [PMID: 25280499 PMCID: PMC4197252 DOI: 10.1186/1476-072x-13-36] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2014] [Accepted: 09/26/2014] [Indexed: 11/10/2022] Open
Abstract
BACKGROUND Multilevel and spatial models are being increasingly used to obtain substantive information on area-level inequalities in cancer survival. Multilevel models assume independent geographical areas, whereas spatial models explicitly incorporate geographical correlation, often via a conditional autoregressive prior. However the relative merits of these methods for large population-based studies have not been explored. Using a case-study approach, we report on the implications of using multilevel and spatial survival models to study geographical inequalities in all-cause survival. METHODS Multilevel discrete-time and Bayesian spatial survival models were used to study geographical inequalities in all-cause survival for a population-based colorectal cancer cohort of 22,727 cases aged 20-84 years diagnosed during 1997-2007 from Queensland, Australia. RESULTS Both approaches were viable on this large dataset, and produced similar estimates of the fixed effects. After adding area-level covariates, the between-area variability in survival using multilevel discrete-time models was no longer significant. Spatial inequalities in survival were also markedly reduced after adjusting for aggregated area-level covariates. Only the multilevel approach however, provided an estimation of the contribution of geographical variation to the total variation in survival between individual patients. CONCLUSIONS With little difference observed between the two approaches in the estimation of fixed effects, multilevel models should be favored if there is a clear hierarchical data structure and measuring the independent impact of individual- and area-level effects on survival differences is of primary interest. Bayesian spatial analyses may be preferred if spatial correlation between areas is important and if the priority is to assess small-area variations in survival and map spatial patterns. Both approaches can be readily fitted to geographically enabled survival data from international settings.
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Affiliation(s)
| | | | | | | | - Peter D Baade
- Cancer Council Queensland, PO Box 201, Spring Hill, QLD 4004, Australia.
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Abstract
The aim of this paper is to provide a composite likelihood approach to handle spatially correlated survival data using pairwise joint distributions. With e-commerce data, a recent question of interest in marketing research has been to describe spatially clustered purchasing behavior and to assess whether geographic distance is the appropriate metric to describe purchasing dependence. We present a model for the dependence structure of time-to-event data subject to spatial dependence to characterize purchasing behavior from the motivating example from e-commerce data. We assume the Farlie-Gumbel-Morgenstern (FGM) distribution and then model the dependence parameter as a function of geographic and demographic pairwise distances. For estimation of the dependence parameters, we present pairwise composite likelihood equations. We prove that the resulting estimators exhibit key properties of consistency and asymptotic normality under certain regularity conditions in the increasing-domain framework of spatial asymptotic theory.
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Affiliation(s)
- Jane Paik
- Department of Medicine, Stanford University, Stanford, CA 94305, United States
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Irincheeva I, Cantoni E, Genton MG. A Non-Gaussian Spatial Generalized Linear Latent Variable Model. JOURNAL OF AGRICULTURAL, BIOLOGICAL, AND ENVIRONMENTAL STATISTICS 2012. [DOI: 10.1007/s13253-012-0099-5] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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Bai Y, Song PXK, Raghunathan TE. Joint composite estimating functions in spatiotemporal models. J R Stat Soc Series B Stat Methodol 2012. [DOI: 10.1111/j.1467-9868.2012.01035.x] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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Eidsvik J, Finley AO, Banerjee S, Rue H. Approximate Bayesian inference for large spatial datasets using predictive process models. Comput Stat Data Anal 2012. [DOI: 10.1016/j.csda.2011.10.022] [Citation(s) in RCA: 28] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/15/2022]
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Abstract
Latent class analysis (LCA) and latent class regression (LCR) are widely used for modeling multivariate categorical outcomes in social science and biomedical studies. Standard analyses assume data of different respondents to be mutually independent, excluding application of the methods to familial and other designs in which participants are clustered. In this article, we consider multilevel latent class models, in which subpopulation mixing probabilities are treated as random effects that vary among clusters according to a common Dirichlet distribution. We apply the expectation-maximization (EM) algorithm for model fitting by maximum likelihood (ML). This approach works well, but is computationally intensive when either the number of classes or the cluster size is large. We propose a maximum pairwise likelihood (MPL) approach via a modified EM algorithm for this case. We also show that a simple latent class analysis, combined with robust standard errors, provides another consistent, robust, but less-efficient inferential procedure. Simulation studies suggest that the three methods work well in finite samples, and that the MPL estimates often enjoy comparable precision as the ML estimates. We apply our methods to the analysis of comorbid symptoms in the obsessive compulsive disorder study. Our models' random effects structure has more straightforward interpretation than those of competing methods, thus should usefully augment tools available for LCA of multilevel data.
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Affiliation(s)
- Chong-Zhi Di
- Division of Public Health Sciences, Fred Hutchinson Cancer Research Center, 1100 Fairview Avenue N, M2-B500, Seattle, Washington 98109, USA.
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A data cloning algorithm for computing maximum likelihood estimates in spatial generalized linear mixed models. Comput Stat Data Anal 2011. [DOI: 10.1016/j.csda.2010.11.004] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Zimmerman D. Likelihood-Based Methods. CHAPMAN & HALL/CRC HANDBOOKS OF MODERN STATISTICAL METHODS 2010. [DOI: 10.1201/9781420072884-c4] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
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Bhat CR, Varin C, Ferdous N. A comparison of the maximum simulated likelihood and composite marginal likelihood estimation approaches in the context of the multivariate ordered-response model. MAXIMUM SIMULATED LIKELIHOOD METHODS AND APPLICATIONS 2010. [DOI: 10.1108/s0731-9053(2010)0000026007] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
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Apanasovich TV, Ruppert D, Lupton JR, Popovic N, Turner ND, Chapkin RS, Carroll RJ. Aberrant crypt foci and semiparametric modeling of correlated binary data. Biometrics 2007; 64:490-500. [PMID: 17725810 PMCID: PMC2659549 DOI: 10.1111/j.1541-0420.2007.00892.x] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
Motivated by the spatial modeling of aberrant crypt foci (ACF) in colon carcinogenesis, we consider binary data with probabilities modeled as the sum of a nonparametric mean plus a latent Gaussian spatial process that accounts for short-range dependencies. The mean is modeled in a general way using regression splines. The mean function can be viewed as a fixed effect and is estimated with a penalty for regularization. With the latent process viewed as another random effect, the model becomes a generalized linear mixed model. In our motivating data set and other applications, the sample size is too large to easily accommodate maximum likelihood or restricted maximum likelihood estimation (REML), so pairwise likelihood, a special case of composite likelihood, is used instead. We develop an asymptotic theory for models that are sufficiently general to be used in a wide variety of applications, including, but not limited to, the problem that motivated this work. The splines have penalty parameters that must converge to zero asymptotically: we derive theory for this along with a data-driven method for selecting the penalty parameter, a method that is shown in simulations to improve greatly upon standard devices, such as likelihood crossvalidation. Finally, we apply the methods to the data from our experiment ACF. We discover an unexpected location for peak formation of ACF.
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Affiliation(s)
- Tatiyana V. Apanasovich
- School of Operations Research and Industrial Engineering, Cornell University, Ithaca, New York 14853, U.S.A
| | - David Ruppert
- School of Operations Research and Industrial Engineering, Cornell University, Ithaca, New York 14853, U.S.A
| | - Joanne R. Lupton
- Department of Nutrition and Food Science, Texas A&M University, College Station, Texas 77843-2253, U.S.A
| | - Natasa Popovic
- Department of Nutrition and Food Science, Texas A&M University, College Station, Texas 77843-2253, U.S.A
| | - Nancy D. Turner
- Department of Nutrition and Food Science, Texas A&M University, College Station, Texas 77843-2253, U.S.A
| | - Robert S. Chapkin
- Department of Nutrition and Food Science, Texas A&M University, College Station, Texas 77843-2253, U.S.A
| | - Raymond J. Carroll
- Department of Statistics, Texas A&M University, College Station, Texas 77843-3143, U.S.A
- email:
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Lee SY, Tang NS. Bayesian analysis of structural equation models with mixed exponential family and ordered categorical data. THE BRITISH JOURNAL OF MATHEMATICAL AND STATISTICAL PSYCHOLOGY 2006; 59:151-72. [PMID: 16709284 DOI: 10.1348/000711005x81403] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/09/2023]
Abstract
Structural equation models are very popular for studying relationships among observed and latent variables. However, the existing theory and computer packages are developed mainly under the assumption of normality, and hence cannot be satisfactorily applied to non-normal and ordered categorical data that are common in behavioural, social and psychological research. In this paper, we develop a Bayesian approach to the analysis of structural equation models in which the manifest variables are ordered categorical and/or from an exponential family. In this framework, models with a mixture of binomial, ordered categorical and normal variables can be analysed. Bayesian estimates of the unknown parameters are obtained by a computational procedure that combines the Gibbs sampler and the Metropolis-Hastings algorithm. Some goodness-of-fit statistics are proposed to evaluate the fit of the posited model. The methodology is illustrated by results obtained from a simulation study and analysis of a real data set about non-adherence of hypertension patients in a medical treatment scheme.
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Affiliation(s)
- Sik-Yum Lee
- Department of Statistics, The Chinese University of Hong Kong, Shatin.
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