A combined overdispersed and marginalized multilevel model
01 Jun 2012-Computational Statistics & Data Analysis (Elsevier Science Publishers B. V.)-Vol. 56, Iss: 6, pp 1944-1951
TL;DR: It turns out that by explicitly allowing for overdispersion random effect, the model significantly improves and is applied to two clinical studies and compared to the existing approach.
About: This article is published in Computational Statistics & Data Analysis.The article was published on 2012-06-01 and is currently open access. It has received 26 citations till now. The article focuses on the topics: Quasi-likelihood & Overdispersion.
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Summary
- Overdispersion and correlation are two features often encountered when modeling non-Gaussian dependent data, usually as a function of known covariates.
- Methods that ignore the presence of these phenomena are often in jeopardy of leading to biased assessment of covariate effects.
- The beta-binomial and negative binomial models are well known in dealing with overdispersed data for binary and count data, respectively.
- Similarly, generalized estimating equations (GEE) and the generalized linear mixed models (GLMM) are popular choices when analyzing correlated data.
- A so-called combined model simultaneously acknowledges the presence of dependency and overdispersion by way of two separate sets of random effects.
- A marginally specified logistic-normal model for longitudinal binary data which combines the strength of the marginal and hierarchical models has been previously proposed.
- These two are brought together to produce a marginalized longitudinal model which brings together the comfort of marginally meaningful parameters and the ease of allowing for overdispersion and correlation.
- Apart from model formulation, estimation methods are discussed.
- The proposed model is applied to two clinical studies and compared to the existing approach.
- It turns out that by explicitly allowing for overdispersion random effect, the model significantly improves.
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Citations
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TL;DR: In this article, a modelo Bayesiano for estimating parâmetros genéticos for a postura diária de ovos de codornas, by meio of Modelos de Regressão Aleatória (MRA), was presented.
Abstract: Este trabalho teve por objetivo apresentar um modelo Bayesiano que permita estimar parâmetros genéticos para a postura diária de ovos de codornas, por meio de Modelos de Regressão Aleatória (MRA). Foram considerados como efeitos fixos época de nascimento e dieta, em um modelo animal com efeito linear, quadrático e cúbico que apresentaram Critério de Informação da Deviance (DIC), respectivamente, 17.212, 13.374 e 2.596, culminando na escolha do modelo cúbico o mais indicado para ajustar os dados de postura em codornas, por meio de MRA. Para tal modelo não se observou efeito de dieta (p=0,456), entretanto, foram significativos os efeitos de época de nascimento (p=0,003) e da covariável ocasião de postura (p<0,01), tendência cúbica heterogênea decrescente, variando aproximadamente 50% em média, para os valores genéticos preditos, ao longo do tempo. Observou-se variância genética aditiva inicialmente decrescente, atingindo seu ponto de mínimo, com variação inferior a 1%, aproximadamente aos 100 dias de idade e crescente daí por diante. Tal comportamento foi observado de forma análoga para a herdadilidades, cujos valores, em média, foram aproximadamente de 23%. A heterogeneidade genética é observada ao longo do tempo, oque sinaliza uma maior influencia de fatores ambientais sobre a produção de ovos após o pico de produção.
1 citations
01 Jan 2013
TL;DR: A marginalized, zero-inflated, overdispersed model for correlated count data is proposed and using an empirical dataset, it is shown that the proposed model leads to important improvements in model fit.
Abstract: Iddi and Molenberghs (2012) merged the attractive features of the socalled combined model of Molenberghs et al (2010) and the marginalized model of Heagerty (1999) for hierarchical non-Gaussian data with overdispersion. In this model, the fixed-effect parameters retain their marginal interpretation. Lee et al (2011) also developed an extension of Heagerty (1999) to handle zero-inflation from count data, using the hurdle model. To bring together all of these features, a marginalized, zero-inflated, overdispersed model for correlated count data is proposed. Using an empirical dataset, it is shown that the proposed model leads to important improvements in model fit.
TL;DR: In this paper, the marginal mean response is modeled in terms of covariates and random effects, and a Bayesian approach is employed to make the statistical inference by implementing the Markov chain Monte Carlo scheme.
Abstract: Random-effects models are frequently used to analyze clustered binomial data. The direct computation of the marginal mean response, when integrated over the distribution of random effects, is challenging due to taking nonclosed-form expressions of the marginal link function. This paper extends the marginalized modeling methodology using innovative link functions, where the marginal mean response is modeled in terms of covariates and random effects. To derive the explicit closed-form representation of both marginal and conditional means, the regression structure is designed through an original strategy to introduce particular random-effects distributions. It will consequently allow for a reasonable interpretation of covariate effects. A Bayesian approach is employed to make the statistical inference by implementing the Markov chain Monte Carlo scheme. We conducted simulation studies to show the usefulness of our methodology. Two real-life data sets, taken from the teratology and respiratory studies, have been analyzed for illustration. The findings confirm that our new modeling methodology offers convenient settings for analyzing binomial responses in practice.
29 Sep 2014
TL;DR: Three families of models for repeated categorical data are introduced: marginal models, conditional models, and random-effects models, which are presented for binary and for ordinal data.
Abstract: We briefly review two building blocks (generalized linear models and linear mixed models) for models for repeated categorical data. Three families of models for repeated categorical data are introduced: marginal models, conditional models, and random-effects models. A number of marginal models are presented for binary and for ordinal data in turn. Major differences between marginal models and conditional models (such as loglinear models) are discussed.
Keywords:
binary data;
conditional model;
generalized linear mixed model;
linear mixed model;
logistic regression;
marginal model;
odds ratio;
ordinal data
TL;DR: Investigation in Ethiopia found that the incidence rate of modern contraceptive users increased by one due to an additional nurse in the delivery point, and the Government of Ethiopia would take immediate steps to address causes of the number ofmodern contraceptive users.
Abstract: Ethiopia is among countries with low contraceptive usage prevalence rate and resulted in high total fertility rate and unwanted pregnancy which intern affects the maternal and child health status. This study aimed to investigate the major factors that affect the number of modern contraceptive users at service delivery point in Ethiopia. The Performance Monitoring and Accountability2020/Ethiopia data collected between March and April 2016 at round-4 from 461 eligible service delivery points were in this study. The weighted log-linear negative binomial model applied to analyze the service delivery point’s data. Fifty percent of service delivery points in Ethiopia given service for 61 modern contraceptive users with the interquartile range of 0.62. The expected log number of modern contraceptive users at rural was 1.05 (95% Wald CI: − 1.42 to − 0.68) lower than the expected log number of modern contraceptive users at urban. In addition, the expected log count of modern contraceptive users at others facility type was 0.58 lower than the expected log count of modern contraceptive users at the health center. The numbers of nurses/midwives were affecting the number of modern contraceptive users. Since, the incidence rate of modern contraceptive users increased by one due to an additional nurse in the delivery point. Among different factors considered in this study, residence, region, facility type, the number of days per week family planning offered, the number of nurses/midwives and number of medical assistants were to be associated with the number of modern contraceptive users. Thus, the Government of Ethiopia would take immediate steps to address causes of the number of modern contraceptive users in Ethiopia.
References
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01 Jan 1983TL;DR: In this paper, a generalization of the analysis of variance is given for these models using log- likelihoods, illustrated by examples relating to four distributions; the Normal, Binomial (probit analysis, etc.), Poisson (contingency tables), and gamma (variance components).
Abstract: The technique of iterative weighted linear regression can be used to obtain maximum likelihood estimates of the parameters with observations distributed according to some exponential family and systematic effects that can be made linear by a suitable transformation. A generalization of the analysis of variance is given for these models using log- likelihoods. These generalized linear models are illustrated by examples relating to four distributions; the Normal, Binomial (probit analysis, etc.), Poisson (contingency tables) and gamma (variance components).
23,215 citations
TL;DR: In this article, an extension of generalized linear models to the analysis of longitudinal data is proposed, which gives consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence.
Abstract: SUMMARY This paper proposes an extension of generalized linear models to the analysis of longitudinal data. We introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence. The estimating equations are derived without specifying the joint distribution of a subject's observations yet they reduce to the score equations for multivariate Gaussian outcomes. Asymptotic theory is presented for the general class of estimators. Specific cases in which we assume independence, m-dependence and exchangeable correlation structures from each subject are discussed. Efficiency of the proposed estimators in two simple situations is considered. The approach is closely related to quasi-likelih ood. Some key ironh: Estimating equation; Generalized linear model; Longitudinal data; Quasi-likelihood; Repeated measures.
17,111 citations
TL;DR: In this article, categorical data analysis was used for categorical classification of categorical categorical datasets.Categorical Data Analysis, categorical Data analysis, CDA, CPDA, CDSA
Abstract: categorical data analysis , categorical data analysis , کتابخانه مرکزی دانشگاه علوم پزشکی تهران
10,964 citations
01 May 1972
TL;DR: In this paper, the authors used iterative weighted linear regression to obtain maximum likelihood estimates of the parameters with observations distributed according to some exponential family and systematic effects that can be made linear by a suitable transformation.
Abstract: JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. Blackwell Publishing and Royal Statistical Society are collaborating with JSTOR to digitize, preserve and extend access to Journal of the Royal Statistical Society. Series A (General). SUMMARY The technique of iterative weighted linear regression can be used to obtain maximum likelihood estimates of the parameters with observations distributed according to some exponential family and systematic effects that can be made linear by a suitable transformation. A generalization of the analysis of variance is given for these models using log-likelihoods. These generalized linear models are illustrated by examples relating to four distributions; the Normal, Binomial (probit analysis, etc.), Poisson (contingency tables) and gamma (variance components). The implications of the approach in designing statistics courses are discussed.
8,793 citations