On identifiability of parametric statistical models

Paulino, Carlos Daniel; Pereira, Carlos Alberto de Bragança

doi:10.1007/bf02589044

Cited by 42 publications

(35 citation statements)

References 17 publications

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“…As a consequence, parameters cannot be uniquely determined and estimated. In statistical terms, the models are said to be nonidentifiable, and thus nonestimable (Paulino and Pereira, 1994). In the cerebral malaria example, this problem was overcome by attributing complete allelic penetrance to the nonconferring alleles, because the susceptible parental strain exhibited reduced penetrance for susceptibility, while its resistant parental strain showed complete penetrance.…”

Section: Discussionmentioning

confidence: 99%

Allelic penetrance approach as a tool to model two-locus interaction in complex binary traits

et al. 2007

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Many binary phenotypes do not follow a classical Mendelian inheritance pattern. Interaction between genetic and environmental factors is thought to contribute to the incomplete penetrance phenomena often observed in these complex binary traits. Several two-locus models for penetrance have been proposed to aid the genetic dissection of binary traits. Such models assume linear genetic effects of both loci in different mathematical scales of penetrance, resembling the analytical framework of quantitative traits. However, changes in phenotypic scale are difficult to envisage in binary traits and limited genetic interpretation is extractable from current modeling of penetrance. To overcome this limitation, we derived an allelic penetrance approach that attributes incomplete penetrance to the stochastic expression of the alleles controlling the phenotype, the genetic background and environmental factors. We applied this approach to formulate dominance and recessiveness in a single diallelic locus and to model different genetic mechanisms for the joint action of two diallelic loci. We fit the models to data on the genetic susceptibility of mice following infections with Listeria monocytogenes and Plasmodium berghei. These models gain in genetic interpretation, because they specify the alleles that are responsible for the genetic (inter)action and their genetic nature (dominant or recessive), and predict genotypic combinations determining the phenotype. Further, we show via computer simulations that the proposed models produce penetrance patterns not captured by traditional two-locus models. This approach provides a new analysis framework for dissecting mechanisms of interlocus joint action in binary traits using genetic crosses.

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Section: Discussionmentioning

confidence: 99%

Allelic penetrance approach as a tool to model two-locus interaction in complex binary traits

et al. 2007

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“…This phenomenon is known as lack of parameters, statistical or distribution identifiability (Paulino and Pereira 1994). Woodbury et al (1994Woodbury et al ( , 1997 show that one can only expect statistical identifiability of the likelihood (9) if the parametric space is restricted to structural parameters λ k jl and moments up to order J of H (.).…”

Section: Assumptionmentioning

confidence: 98%

Ranking by competence using a fuzzy approach

Suleman

2010

Qual Quant

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“…A model is defined as identifiable in a situation where the model parameters are uniquely determined from the distribution of the observed random variables (Paulino and Pereira 1994). For estimation procedures based on maximization of a target function (e.g., the log-likelihood function), non-identifiability of parameters usually manifests itself as nonconvergence of the search algorithm or extreme sensitivity of the final estimates to initial values provided to the algorithm.…”

Section: Model Identifiabilitymentioning

confidence: 99%

Statistical Modelling of Neighbor Treatment Effects in Aquaculture Clinical Trials

Masaoud

Stryhn

Whyte

et al. 2010

JABES

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In the design of clinical trials involving fish observed over time in tanks, there may be advantages in housing several treatment groups within the same tank. In particular, such "within-tank" designs will be more efficient than designs with treatment groups in separate tanks when substantial between-tank variability is expected. One potential problem with within-tank designs is that it may not be possible to include all treatments in one tank; in statistical terms this means that the blocks (tanks) are incomplete. In incomplete block designs, there may be a concern that the treatments present in the same tank (denoted here as "neighbors") affect each other in their performance; thus the need for an assessment of neighbor effects. In this paper, we propose two statistical approaches to assess and account for neighbor effects. The first approach is based on a non-linear mixed model and the second involves cross-classified and multiple membership models. Both approaches are illustrated on simulated data as well as data from a clinical ISAV (Infectious Salmon Anaemia Virus) trial; corresponding computer code is available online.The simulation studies demonstrated that both models show promise in capturing neighbor treatment effects of the type assumed for the models, whenever such neighbor effects are of at least moderate magnitude. In the absence of or with low magnitudes of neighbor effects, the non-linear mixed model faced numerical challenges and produced noisy results. One version of the cross-classified and multiple membership model was shown to depend strongly on prior information about variance-covariance parameters for datasets similar to the ISAV data. Analyses of the ISAV trial data by both models did not provide any evidence of substantial neighbor effects.

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On identifiability of parametric statistical models

Cited by 42 publications

References 17 publications

Allelic penetrance approach as a tool to model two-locus interaction in complex binary traits

Allelic penetrance approach as a tool to model two-locus interaction in complex binary traits

Ranking by competence using a fuzzy approach

Statistical Modelling of Neighbor Treatment Effects in Aquaculture Clinical Trials

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