Robustness of the Restricted Maximum Likelihood Estimator Derived Under Normality as Applied to Data with Skewed Distributions

Banks, Buck; Mao, I.L.; Walter, John P.

doi:10.3168/jds.s0022-0302(85)81028-6

Cited by 37 publications

(26 citation statements)

References 6 publications

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“…Boldman and Freeman (1990) showed that log transformation of milk yield records did not affect heritability estimates. Although REML is expected to be robust to deviations from normality (Banks et al 1985), the difference in heritability estimates obtained in the present study after transformation suggest that one of the assumptions for applying the REML approach, i.e. random classes and samples within each class to be normally distributed, was violated.…”

Section: Parameter Estimates For Milk Yieldmentioning

confidence: 67%

“…The REML approach, however, assumes that random classes and samples within each class are normally distributed. Deviations from a normal distribution increase the error variance estimates and in consequence the functions of variance components are biased (Banks et al 1985). Logarithmic or BC transformation are usually employed when dealing with unbalanced data to overcome non-normal fitting of the data (Strabel and Szwaczkowski 1997) and heterogeneity of variances between groups (Everett and Keown 1984;Boldman and Freeman 1990;Vissher et al 1991).…”

mentioning

confidence: 99%

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Genetic parameters for milk yield and litter size in Boutsico dairy sheep

Kominakis¹,

Rogdakis²,

Koutsotolis³

1998

Can. J. Anim. Sci.

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Kominakis, A., Rogdakis, E. and Koutsotolis, K. 1998. Genetic parameters for milk yield and litter size in Boutsico dairy sheep. Can. J. Anim. Sci. 78: 525-532. Lactation and litter size records (n = 2553) of Boutsico dairy sheep were used to estimate direct additive, maternal genetic, maternal and animal's permanent environmental variance components for milk yield and litter size by restricted maximum likelihood under a repeated records animal model. Raw milk yield data were transformed by log and Box-Cox (BC) transformations. Heritability estimates of direct additive effects were between 0.21 and 0.30, 0.18 and 0.24 and 0.21 and 0.27 for untransformed, log transformed and BC transformed data, respectively. Only maternal and animal's environmental effects were important for milk yield. Direct-maternal genetic covariance did not significantly (P > 0.05) influence milk yield. Repeatability for milk yield ranged from 0.32 to 0.38. Only additive genetic effects were important for litter size. Heritability and repeatability for litter size were 0.07 and 0.11, respectively. Genetic and phenotypic correlations between yield and litter size were 0.13 and 0.19, respectively.

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Section: Parameter Estimates For Milk Yieldmentioning

confidence: 67%

mentioning

confidence: 99%

Genetic parameters for milk yield and litter size in Boutsico dairy sheep

Kominakis¹,

Rogdakis²,

Koutsotolis³

1998

Can. J. Anim. Sci.

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“…In the model, total rust incidence (RUST), stem rust incidence (STEM), and height-dbh ratio (HDR) were analyzed without transformation, because evidence shows that REML estimates are robust to violations of normality (BANKS et al, 1985;WESTFALL, 1987).…”

Section: Discussionmentioning

confidence: 99%

Realized Genetic Gains of Rust Resistant Selections of Slash Pine (Pinus elliottii var. elliottii) Planted in High Rust Hazard Sites

et al. 2007

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SummaryRealized gains from selection for resistance to the fungal disease fusiform rust caused by Cronartium quercuum f. sp. fusiforme were estimated using data from five field trials planted on large rectangular plots in high rust-hazard sites. These five realized gain trials, planted as a Best Management Practices study (BMP), compared resistant and susceptible mixtures of families from the first-generation breeding population of slash pine (Pinus elliottii var. elliottii Engelm.) in southeastern North America.Analyses of variance (Proc Mixed using REML in SAS), conducted to test the significance of realized gains and interactions contrasting resistant with susceptible seedlots, detected important and highly significant realized gains in both rust resistance and mid-rotation yield. Significant gains were obtained for rust resistance at age 5 and stand yield at age 16 with high stability across sites and across silvicultural treatments, indicating that gains in rust resistance and the associated influence on gains in stand yield were consistent under many environmental conditions. Additionally, the values of realized gains in stand yield steadily increased with age, primarily due to increased rust associated mortality with age in the susceptible material. The 25 % realized gain for rust resistant material compared to rust susceptible material obtained at age 16 was conservatively extrapolated to a 25-year-old rotation-age gain of 51.4 m 3 ha -1 (735 feet 3 acre -1 ) in inside-bark volume.

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“…The optimal transformation parameter t, to fulfill the same normality condition, was not a constant over time. Nevertheless, Banks et al [3] reported that REML is robust and they verified this robustness even for slight skewness. Therefore, in the present analysis, in order to avoid the scale diversity due to different transformation parameters, we used the same …”

Section: Data Distribution and Transformationmentioning

confidence: 99%

Estimation of genetic variability and selection response for clutch length in dwarf brown-egg layers carrying or not the naked neck gene

Chen

Tixier‐Boichard

2003

Genet. Sel. Evol.

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-In order to investigate the possibility of using the dwarf gene for egg production, two dwarf brown-egg laying lines were selected for 16 generations on average clutch length; one line (L1) was normally feathered and the other (L2) was homozygous for the naked neck gene NA. A control line from the same base population, dwarf and segregating for the NA gene, was maintained during the selection experiment under random mating. The average clutch length was normalized using a Box-Cox transformation. Genetic variability and selection response were estimated either with the mixed model methodology, or with the classical methods for calculating genetic gain, as the deviation from the control line, and the realized heritability, as the ratio of the selection response on cumulative selection differentials. Heritability of average clutch length was estimated to be 0.42 ± 0.02, with a multiple trait animal model, whereas the estimates of the realized heritability were lower, being 0.28 and 0.22 in lines L1 and L2, respectively. REML estimates of heritability were found to decline with generations of selection, suggesting a departure from the infinitesimal model, either because a limited number of genes was involved, or their frequencies were changed. The yearly genetic gains in average clutch length, after normalization, were estimated to be 0.37 ± 0.02 and 0.33 ± 0.04 with the classical methods, 0.46 ± 0.02 and 0.43 ± 0.01 with animal model methodology, for lines L1 and L2 respectively, which represented about 30% of the genetic standard deviation on the transformed scale. Selection response appeared to be faster in line L2, homozygous for the NA gene, but the final cumulated selection response for clutch length was not different between the L1 and L2 lines at generation 16. dwarf chicken / naked neck gene / clutch length / genetic variability / selection response

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Robustness of the Restricted Maximum Likelihood Estimator Derived Under Normality as Applied to Data with Skewed Distributions

Cited by 37 publications

References 6 publications

Genetic parameters for milk yield and litter size in Boutsico dairy sheep

Genetic parameters for milk yield and litter size in Boutsico dairy sheep

Realized Genetic Gains of Rust Resistant Selections of Slash Pine (Pinus elliottii var. elliottii) Planted in High Rust Hazard Sites

Estimation of genetic variability and selection response for clutch length in dwarf brown-egg layers carrying or not the naked neck gene

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