An Overview of Normal Theory Structural Measurement Error Models

Thompson, Jeffrey R.; Carter, Randy L.

doi:10.1111/j.1751-5823.2007.00014.x

Cited by 11 publications

(3 citation statements)

References 27 publications

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“…All these methods assume that predictors are measured without error. When this assumption is violated, downwardly biased estimates are obtained (for a review on problems and proposed models to deal with measurement error see Thompson & Carter, ). Measurements of most traits, including size, will virtually always be made with nontrivial error, for two reasons.…”

Section: Developmentmentioning

confidence: 99%

Towards robust evolutionary inference with integral projection models

Janeiro

Coltman

Festa‐Bianchet

et al. 2016

J of Evolutionary Biology

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1Integral projection models (IPMs) are extremely flexible tools for ecological and evolutionary infer-2 ence. IPMs track the distribution of phenotype in populations through time, using functions describing 3 phenotype-dependent development, inheritance, survival and fecundity. For evolutionary inference, two 4 important features of any model are the ability to (i) characterize relationships among traits (including 5 values of the same traits across ages) within individuals, and (ii) characterize similarity between indi-6 viduals and their descendants. In IPM analyses, the former depends on regressions of observed trait 7 values at each age on values at the previous age (development functions), and the latter on regressions 8of o↵spring values at birth on parent values as adults (inheritance functions). We show analytically that 9 development functions, characterized this way, will typically underestimate covariances of trait values 10 across ages, due to compounding of regression to the mean across projection steps. Similarly, we show 11 that inheritance, characterized this way, is inconsistent with a modern understanding of inheritance, and 12 underestimates the degree to which relatives are phenotypically similar. Additionally, we show that the 13 use of a constant biometric inheritance function, particularly with a constant intercept, is incompati-14 ble with evolution. Consequently, current implementations of IPMs will predict little or no phenotypic 15 evolution, purely as artifacts of their construction. We present alternative approaches to constructing 16 development and inheritance functions, based on a quantitative genetic approach, and show analytically 17 and through an empirical example on a population of bighorn sheep how they can potentially recover 18 patterns that are critical to evolutionary inference. 19 20 Keywords: integral projection models, regression to the mean, inheritance, development, body size, 21 evolutionary responses, bighorn sheep 22

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Section: Developmentmentioning

confidence: 99%

Towards robust evolutionary inference with integral projection models

Janeiro

Coltman

Festa‐Bianchet

et al. 2016

J of Evolutionary Biology

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“…Parameter estimates of MEMs can basically be obtained either through the ordinary least squares, estimating equations, method‐of‐moments, likelihood, or Bayesian approaches (Dellaportas & Stephens, 1995; Yi, 2017). It is well known that the ordinary least squares estimators are biased and inconsistent (Thompson & Carter, 2007). Due to the complexity of method‐of‐moments, we consider methods for statistical inference based on the likelihood function.…”

Section: Introductionmentioning

confidence: 99%

Multivariate measurement error models with normal mean‐variance mixture distributions

Mirfarah

Naderi

Lin

et al. 2022

Stat

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The class of normal mean‐variance mixture (NMVM) distributions is a rich family of asymmetric and heavy‐tailed distributions and has been widely considered in parametric modeling of the data for robust statistical inference. This paper proposes an extension of measurement error models by assuming the NMVM distributions for the unobserved covariates and error terms in the model, referred to as the NMVM‐MEM. An expectation conditional maximization either (ECME) algorithm is developed to compute the maximum likelihood (ML) estimates of model parameters. Furthermore, an information‐based approach is performed to derive the asymptotic covariance matrix of ML estimators. The analysis of a blood pressure dataset illustrates the superiority of NMVM‐MEM to accommodate asymmetry and outliers over the normal counterpart. Two simulation studies are undertaken to validate our proposed techniques.

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“…There are several studies available that addressed for parameter estimation of the model in (2.2) for each identifiability case, where the common methods are: maximum likelihood, weighted least square, orthogonal regression and moment methods, see, e.g., Fuller (1987, Section 1.2-1.3), Hood, Nix and Iles (1999), Thompson and Carter (2007) and Gillard (2010). Some classical references considering the maximum likelihood method are, for instance, for Cases 1 and 2, see Birch (1964); for Case 3, see Madansky (1959); for Case 4, see Cheng and Ness (1999, p. 17) and for Case 5, see Chan and Mak (1979).…”

Section: Modelmentioning

confidence: 99%

Some extensions in measurement error models

Tomaya¹,

Yanet²

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In this dissertation, we approach three different contributions in measurement error model (MEM). Initially, we carry out maximum penalized likelihood inference in MEM's under the normality assumption. The methodology is based on the method proposed by Firth (1993), which can be used to improve some asymptotic properties of the maximum likelihood estimators. In the second contribution, we develop two new estimation methods based on generalized fiducial inference for the precision parameters and the variability product under the Grubbs model considering the two-instrument case. One method is based on a fiducial generalized pivotal quantity and the other one is built on the method of the generalized fiducial distribution. Comparisons with two existing approaches are reported. Finally, we propose to study inference in a heteroscedastic MEM with known error variances. Instead of the normal distribution for the random components, we develop a model that assumes a skew-t distribution for the true covariate and a centered Student's t distribution for the error terms. The proposed model enables to accommodate skewness and heavy-tailedness in the data, while the degrees of freedom of the distributions can be different. We use the maximum likelihood method to estimate the model parameters and compute them via an EM-type algorithm. All proposed methodologies are assessed numerically through simulation studies and illustrated with real datasets extracted from the literature.

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An Overview of Normal Theory Structural Measurement Error Models

Cited by 11 publications

References 27 publications

Towards robust evolutionary inference with integral projection models

Towards robust evolutionary inference with integral projection models

Multivariate measurement error models with normal mean‐variance mixture distributions

Some extensions in measurement error models

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