Estimation of Parameters in Heteroscedastic Linear Models

Mak, T. K.

doi:10.1111/j.2517-6161.1992.tb01903.x

Cited by 17 publications

(13 citation statements)

References 13 publications

(10 reference statements)

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“…Several studies, particularly in the health care cost research field, indicate that estimates of mean responses may be quite sensitive to how estimators treat skewness and correlation of the outcome [34][35][36]. Some of the solutions used in the literature rely on transformations (usually logarithmic) to deal with skewness, on Gamma multi-level approaches [37], on the decomposition of the response into a series of models that deal with specific parts of the distribution [38], or on various combinations of these.…”

Section: Discussionmentioning

confidence: 99%

Flexibility of Bayesian generalized linear mixed models for oral health research

Berchialla¹,

Baldi

Notaro

et al. 2009

Statistics in Medicine

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Many outcome variables in oral research are characterized by positive values and heavy skewness in the right tail. Examples are provided by many distributions of dental variables such as DMF (decayed, missing, filled teeth) scores, oral health impact profile score, gingival index scores, and microbiologic counts. Moreover, heterogeneity in data arises when more than one tooth is studied for each patient, due to the clusterization.Over the past decade, linear mixed models (LMEs) have become a common statistical tool to account for within-subject correlation in data with repeated measures. When a normal error is reasonably assumed, estimates of LMEs are supported by many statistical packages. Such is not the case for skewed data, where generalized linear mixed models (GLMMs) are required. However, the current software available supports only special cases of GLMMs or relies on crude Laplace-type approximation of integrals. In this study, a Bayesian approach is taken to estimate GLMMs for clustered skewed dental data. A Gamma GLMM and a log-normal model are employed to allow for heterogeneity across clusters, deriving from the patient-operator-tooth susceptibility typical of this clinical context. A comparison to the frequentist framework is also provided. In our case, Gamma GLMM fits data better than the log-normal distribution, while providing more precise estimates compared with the likelihood approach. A key advantage of the Bayesian framework is its ability to readily provide a flexible approach for implementation while simultaneously providing a formal procedure for solving inference problems.

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Section: Discussionmentioning

confidence: 99%

Flexibility of Bayesian generalized linear mixed models for oral health research

Berchialla¹,

Baldi

Notaro

et al. 2009

Statistics in Medicine

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“…We also noted that the tested cell lines in the RNA-seq data sets are genetically independent of each other. Accordingly, the weighted linear mixed model [50], one of the variants of the traditional mixed model [51], [52], [53] under heteroscedasticity [54], for assessing the effects of fixed and random factors on an expression trait can be generally formulated as follows.…”

Section: Methodsmentioning

confidence: 99%

“…When the correlations between samples are ignored, (2) can be simplified as the following heteroscedastic linear model (HLM) [54]. …”

Section: Methodsmentioning

confidence: 99%

Inferring Polymorphism-Induced Regulatory Gene Networks Active in Human Lymphocyte Cell Lines by Weighted Linear Mixed Model Analysis of Multiple RNA-Seq Datasets

et al. 2013

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Single-nucleotide polymorphisms (SNPs) contribute to the between-individual expression variation of many genes. A regulatory (trait-associated) SNP is usually located near or within a (host) gene, possibly influencing the gene’s transcription or/and post-transcriptional modification. But its targets may also include genes that are physically farther away from it. A heuristic explanation of such multiple-target interferences is that the host gene transfers the SNP genotypic effects to the distant gene(s) by a transcriptional or signaling cascade. These connections between the host genes (regulators) and the distant genes (targets) make the genetic analysis of gene expression traits a promising approach for identifying unknown regulatory relationships. In this study, through a mixed model analysis of multi-source digital expression profiling for 140 human lymphocyte cell lines (LCLs) and the genotypes distributed by the international HapMap project, we identified 45 thousands of potential SNP-induced regulatory relationships among genes (the significance level for the underlying associations between expression traits and SNP genotypes was set at FDR < 0.01). We grouped the identified relationships into four classes (paradigms) according to the two different mechanisms by which the regulatory SNPs affect their cis- and trans- regulated genes, modifying mRNA level or altering transcript splicing patterns. We further organized the relationships in each class into a set of network modules with the cis- regulated genes as hubs. We found that the target genes in a network module were often characterized by significant functional similarity, and the distributions of the target genes in three out of the four networks roughly resemble a power-law, a typical pattern of gene networks obtained from mutation experiments. By two case studies, we also demonstrated that significant biological insights can be inferred from the identified network modules.

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“…, Carroll & Ruppert (1988) and Mak (1992). In particular, the maximum likelihood approach has been criticised for its sensitivity to misspecification of the error density and the assumed model for the dispersion.…”

Section: Techniques For Analyzing Data With Nonconstant Variability Hmentioning

confidence: 99%

A Note on Nonregular Likelihood Functions in Heteroscedastic Regression Models

Crisp

Burridge

1994

Biometrika

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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.. Biometrika Trust is collaborating with JSTOR to digitize, preserve and extend access to Biometrika. SUMMARYThe existence of maximum likelihood estimates for a class of heteroscedastic regression models is considered. For a given dispersion function we show that, under a weak condition, the likelihood is singular at points corresponding to nonreplicated observations, causing unrestricted maximum likelihood estimation to break down, whilst for an alternative class of dispersion functions we obtain a much stronger linear independence condition for the likelihood to be unbounded.Some key words: Mean-variance relationship; Multimodality; Normal-mixture; Singularity.

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Estimation of Parameters in Heteroscedastic Linear Models

Cited by 17 publications

References 13 publications

Flexibility of Bayesian generalized linear mixed models for oral health research

Flexibility of Bayesian generalized linear mixed models for oral health research

Inferring Polymorphism-Induced Regulatory Gene Networks Active in Human Lymphocyte Cell Lines by Weighted Linear Mixed Model Analysis of Multiple RNA-Seq Datasets

A Note on Nonregular Likelihood Functions in Heteroscedastic Regression Models

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