Sparse Inverse of Covariance Matrix of QTL Effects with Incomplete Marker Data

2004 ◽  
Vol 3 (1) ◽  
pp. 1-21 ◽  
Author(s):  
R. Mark Thallman ◽  
Kathryn J Hanford ◽  
Stephen D Kachman ◽  
L. Dale Van Vleck
Keyword(s):  
Covariance Matrix ◽  
Random Effects ◽  
Mixed Model ◽  
Simple Algorithm ◽  
Equivalent Model ◽  
Breeding Values ◽  
Marker Data ◽  
Proposed Model ◽  
Model Equations ◽  
Outbred Populations

Gametic models for fitting breeding values at QTL as random effects in outbred populations have become popular because they require few assumptions about the number and distribution of QTL alleles segregating. The covariance matrix of the gametic effects has an inverse that is sparse and can be constructed rapidly by a simple algorithm, provided that all individuals have marker data, but not otherwise. An equivalent model, in which the joint distribution of QTL breeding values and marker genotypes is considered, was shown to generate a covariance matrix with a sparse inverse that can be constructed rapidly with a simple algorithm. This result makes more feasible including QTL as random effects in analyses of large pedigrees for QTL detection and marker assisted selection. Such analyses often use algorithms that rely upon sparseness of the mixed model equations and require the inverse of the covariance matrix, but not the covariance matrix itself. With the proposed model, each individual has two random effects for each possible unordered marker genotype for that individual. Therefore, individuals with marker data have two random effects, just as with the gametic model. To keep the notation and the derivation simple, the method is derived under the assumptions of a single linked marker and that the pedigree does not contain loops. The algorithm could be applied, as an approximate method, to pedigrees that contain loops.

scholarly journals Reduced Animal Models Fitting Only Equations for Phenotyped Animals

2021 ◽  
Vol 12 ◽  
Author(s):  
Mohammad Ali Nilforooshan ◽  
Dorian Garrick
Keyword(s):  
Animal Model ◽  
Animal Models ◽  
Mixed Model ◽  
Reduced Model ◽  
Relationship Matrix ◽  
Full Model ◽  
Breeding Values ◽  
Reduced Animal Model ◽  
Numerator Relationship Matrix ◽  
Model Equations

Reduced models are equivalent models to the full model that enable reduction in the computational demand for solving the problem, here, mixed model equations for estimating breeding values of selection candidates. Since phenotyped animals provide data to the model, the aim of this study was to reduce animal models to those equations corresponding to phenotyped animals. Non-phenotyped ancestral animals have normally been included in analyses as they facilitate formation of the inverse numerator relationship matrix. However, a reduced model can exclude those animals and obtain identical solutions for the breeding values of the animals of interest. Solutions corresponding to non-phenotyped animals can be back-solved from the solutions of phenotyped animals and specific blocks of the inverted relationship matrix. This idea was extended to other forms of animal model and the results from each reduced model (and back-solving) were identical to the results from the corresponding full model. Previous studies have been mainly focused on reduced animal models that absorb equations corresponding to non-parents and solve equations only for parents of phenotyped animals. These two types of reduced animal model can be combined to formulate only equations corresponding to phenotyped parents of phenotyped progeny.

scholarly journals Sporthorse performance testing in eventing by own and progeny performance

2012 ◽  
pp. 49-56
Author(s):  
Anita Mezei ◽  
János Posta ◽  
Sándor Mihók
Keyword(s):  
Random Effects ◽  
Fixed Effects ◽  
Mixed Model ◽  
Linear Mixed Model ◽  
Performance Testing ◽  
Population Based ◽  
Descriptive Statistics ◽  
European Countries ◽  
Breeding Values ◽  
Progeny Performance

The aim of the study was to evaluate the Hungarian Sporthorse population based on eventing competition performance. The database contained the results of 792 horses and 449 riders between 2000 and 2006. The eventing results were gathered from Hungary and other European countries. Blom transformed ranks were used to evaluate the sport performance.Three models were fitted to the Blom scores. Evaluating all the competition categories at the same time weighted Blom scores were used according to the difficulty of the category. The linear mixed model included fixed effects for age, sex, breeder, owner, location, year; and random effects for animal and rider. Horses from the database were judged by their own performance, and stallions were investigated by performance of their progenies on the basis of descriptive statistics of Blom scores and weighted Blom scores. Breeding values of eventing performance were predicted. To improve the reliability of breeding values, more progenies should beused in eventing competitions. 

Simple explicit model of liquid mean flow in region above axial impeller

1985 ◽  
Vol 50 (11) ◽  
pp. 2396-2410
Author(s):  
Miloslav Hošťálek ◽  
Ivan Fořt
Keyword(s):  
Vortex Flow ◽  
Flow Model ◽  
Quantitative Agreement ◽  
Mean Flow ◽  
Flat Bottom ◽  
Proposed Model ◽  
Minimum Number ◽  
The Mean ◽  
Model Equations ◽  
Radial Circulation

The study describes a method of modelling axial-radial circulation in a tank with an axial impeller and radial baffles. The proposed model is based on the analytical solution of the equation for vortex transport in the mean flow of turbulent liquid. The obtained vortex flow model is tested by the results of experiments carried out in a tank of diameter 1 m and with the bottom in the shape of truncated cone as well as by the data published for the vessel of diameter 0.29 m with flat bottom. Though the model equations are expressed in a simple form, good qualitative and even quantitative agreement of the model with reality is stated. Apart from its simplicity, the model has other advantages: minimum number of experimental data necessary for the completion of boundary conditions and integral nature of these data.

scholarly journals The generalizability crisis

2020 ◽  
pp. 1-37
Author(s):  
Tal Yarkoni
Keyword(s):  
Quantitative Analysis ◽  
Statistical Inference ◽  
Random Effects ◽  
False Positive ◽  
Mixed Model ◽  
Linear Mixed Model ◽  
Random Effect ◽  
Statistical Procedures ◽  
Subject Variability ◽  
Replication Crisis

Abstract Most theories and hypotheses in psychology are verbal in nature, yet their evaluation overwhelmingly relies on inferential statistical procedures. The validity of the move from qualitative to quantitative analysis depends on the verbal and statistical expressions of a hypothesis being closely aligned—that is, that the two must refer to roughly the same set of hypothetical observations. Here I argue that many applications of statistical inference in psychology fail to meet this basic condition. Focusing on the most widely used class of model in psychology—the linear mixed model—I explore the consequences of failing to statistically operationalize verbal hypotheses in a way that respects researchers' actual generalization intentions. I demonstrate that whereas the "random effect" formalism is used pervasively in psychology to model inter-subject variability, few researchers accord the same treatment to other variables they clearly intend to generalize over (e.g., stimuli, tasks, or research sites). The under-specification of random effects imposes far stronger constraints on the generalizability of results than most researchers appreciate. Ignoring these constraints can dramatically inflate false positive rates, and often leads researchers to draw sweeping verbal generalizations that lack a meaningful connection to the statistical quantities they are putatively based on. I argue that failure to take the alignment between verbal and statistical expressions seriously lies at the heart of many of psychology's ongoing problems (e.g., the replication crisis), and conclude with a discussion of several potential avenues for improvement.

scholarly journals Response transformations for random effect and variance component models

2020 ◽  
pp. 1471082X2096691
Author(s):  
Amani Almohaimeed ◽  
Jochen Einbeck
Keyword(s):  
Maximum Likelihood ◽  
Random Effects ◽  
Mixed Model ◽  
Linear Mixed Model ◽  
Random Effect ◽  
Statistical Technique ◽  
Response Distribution ◽  
Level Data ◽  
Variance Component Models ◽  
Response Transformation

Random effect models have been popularly used as a mainstream statistical technique over several decades; and the same can be said for response transformation models such as the Box–Cox transformation. The latter aims at ensuring that the assumptions of normality and of homoscedasticity of the response distribution are fulfilled, which are essential conditions for inference based on a linear model or a linear mixed model. However, methodology for response transformation and simultaneous inclusion of random effects has been developed and implemented only scarcely, and is so far restricted to Gaussian random effects. We develop such methodology, thereby not requiring parametric assumptions on the distribution of the random effects. This is achieved by extending the ‘Nonparametric Maximum Likelihood’ towards a ‘Nonparametric profile maximum likelihood’ technique, allowing to deal with overdispersion as well as two-level data scenarios.

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