Random Variance Components Research Articles

Evaluating the genetic components of growth in ostriches with multi-trait and random regression models

ABSTRACT 1. The heritability (h2) of liveweight (LW) in ostriches can be highly variable, depending on age at recording. The objective of this study was to consider random regression (RR) as an alternative to the multi-trait (MT) structure for the analysis of repeated measures of LW. 2. The data included 74 683 LW phenotypes recorded from 10 052 birds aged between 20 and 410 days (d) of age. Statistical analysis included single trait (ST), MT and RR analysis in a linear mixed model framework using the ASREML V4.2 software. 3. For ST and MT, six traits were defined to represent LW at 28, 77, 150, 230, 300 and 365 d of age. Random variance components included direct genetic and maternal permanent environment (PE) effects. A MT analysis including all six traits converged. 4. For RR, the data was transformed (LW + 10)−0.5 due to difficulty in dealing with large scale effects. The final RR model fitted direct genetic and animal PE components as third degree Legendre polynomials and heterogeneous residuals. 5. The h2 estimates was in agreement across analysis, ranging from moderate (0.16-0.20) for W28 to high (0.41-0.51) for W230 to W365. Importantly, the genetic relationship between LW recorded as a chick and juvenile was only moderate (~0.35 to 0.55). The correlations between RR and MT EBVs for the six traits were 0.85, 0.54, 0.65, 0.75, 0.83 and 0.91, showing a considerable level of re-ranking. 6. This study reaffirmed age dependent genetic variation when determining LW in ostriches. The RR structure was useful for overcoming the dimension problem of MT analysis, but was susceptible to scale effects present in the data, despite transformation. It remains unknown whether the need for cubic terms reflected scale or animal effects.

Optimizing the Expected Maximum of Two Linear Functions Defined on a Multivariate Gaussian Distribution

We study stochastic optimization problems with objective function given by the expectation of the maximum of two linear functions defined on the component random variables of a multivariate Gaussian distribution. We consider random variables that are arbitrarily correlated, and we show that the problem is NP-hard even if the space of feasible solutions is unconstrained. We exploit a closed-form expression for the objective function from the literature to construct a cutting-plane algorithm for a highly nonlinear function, which includes the evaluation of the cumulative distribution function and probability density function of a standard normal random variable with decision variables as part of the arguments. To exhibit the model’s applicability, we consider two featured applications. The first is daily fantasy sports, where the algorithm identifies entries with positive returns during the 2018–2019 National Football League season. The second is a special case of makespan minimization for two parallel machines and jobs with uncertain processing times; for the special case where the jobs are uncorrelated, we prove the equivalence between its deterministic and stochastic versions and show that our algorithm can deliver a constant-factor approximation guarantee for the problem. The results of our computational evaluation involving synthetic and real-world data suggest that our discretization and upper bounding techniques lead to significant computational improvements and that the proposed algorithm outperforms suboptimal solutions approaches. History: Andrea Lodi, Area Editor for Design & Analysis of Algorithms–Discrete. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ijoc.2022.1259 .

Overall and repeated measures agreement between brachial-femoral and carotid-femoral measures of pulse wave velocity in young and healthy individuals.

Carotid-femoral pulse-wave velocity (cfPWV) is the gold standard measure of arterial stiffness and independently predicts cardiovascular disease. However, obtaining cfPWV requires technical precision and can be difficult in some populations. Brachial-femoral PWV (bfPWV) is a simpler alternative, but there is limited research comparing the two measures. For physiological studies, it is important to know how well the measures agree at rest, and to what extent changes in the measures correspond after perturbation. To assess the overall and repeated measures agreement between cfPWV and bfPWV. cfPWV and bfPWV were measured in the supine and seated positions, both before and after a 3-h bout of prolonged sitting. The intraclass correlation coefficient (ICC) for overall agreement was calculated using the random variance components from linear mixed-model regression. Repeated measures agreement (change in cfPWV vs. change in bfPWV) was calculated using repeated measures correlation. Complete data from 18 subjects (22.6 ± 3.1 years old, 33% female) were included in the analysis. There was strong (ICC ≥ 0.70) overall agreement (ICC, 0.75; 95% CI, 0.60-0.85) and very strong (ICC ≥ 0.90) repeated measures agreement (ICC, 0.90; 95% CI, 0.84-0.94) between cfPWV and bfPWV. The current findings indicate strong overall agreement and very strong repeated measures agreement between bfPWV and cfPWV. bfPWV is a user-friendly alternative method that agrees with cfPWV-based assessments of central arterial stiffness.

Multilevel multinomial logit regression model with random effects: application to flash EuroBarometer euro survey data

A multilevel model for nominal data in the framework of generalized linear mixed models (GLMM) is developed to account for the inherent dependencies among observations within clusters. Motivated by a dataset from the Flash EuroBarometer survey (FEBS), the random region and country effects are incorporated into the linear predictor of a GLMM to accommodate the nested clusterings. The fixed effects are estimated by maximizing the penalized likelihood function, whereas the random variance component parameters are predicted via the restricted maximum likelihood (REML) estimation method. The model is employed to analyse the FEBS data. A Monte Carlo simulation study is conducted to evaluate the performance of estimators.

Reliability-Based Criterion for Evaluating Explicit Approximations of Colebrook Equation

Numerous explicit approximations of the Colebrook equation have been developed and evaluated based on two criteria: prediction accuracy and computational efficiency. This paper introduces a new evaluation criterion based on the reliability of each equation. The reliability is defined by the coefficient of variation (CV) of the explicit friction factor that is a function of the variabilities of component random variables (roughness height of the internal pipe surface and kinematic viscosity of the fluid). The coefficient of variation of the friction factor depends on its first derivative for roughness height of the inner pipe surface and kinematic viscosity of the fluid and their correlation. Seven explicit approximations were evaluated using the new reliability-based criterion. The results show that all explicit approximations are very reliable, but variations exist regarding the reliability level. The reliabilities of the seven approximations is very close for the rough-flow regime and when the CV of the viscosity is minimal. However, for the smooth-flow regime, and when the CV of the roughness is minimal, various approximations showed substantially different reliabilities. The novelty of the proposed criterion is that it addresses an evaluation dimension that complements the accuracy and efficiency criteria.

Agreement Of Seated And Supine Pulse Wave Velocity Measurements With Prolonged Sitting

During prolonged sitting research, measuring pulse wave velocity (PWV) in the seated posture would minimize participant burden and preserve the detrimental vascular effects of inactivity. However, PWV is validated in the supine position and it is unknown how supine and seated PWV measures compare. PURPOSE: This study evaluated agreement between the following seated and supine measures of PWV: carotid-femoral (cf), brachial-femoral (bf), and femoral-ankle (fa). We evaluated: (i) the overall agreement between seated and supine measures and (ii) the repeated measures agreement. METHODS: cfPWV, bfPWV, and faPWV were recorded while supine and then seated, and then following a three-hour period of uninterrupted sitting, all measurements were repeated. Mixed model regression was used to calculate agreement between the supine and seated measures. For each PWV outcome, the supine measures were regressed against the seated measures and nested within subject and time (pre vs. post sitting), with subject and time specified as random. The random variance components were used to calculate intraclass correlation coefficients (ICC) with 95% confidence intervals. Overall agreement and repeated-measures ICCs were calculated. An ICC ≥ 0.70 represented strong agreement, and ICC ≥ 0.90 represented a very strong agreement. RESULTS: A total of 18 subjects were included in the final analysis (age: 22.6 ± 3.1 years, female: 6, cfPWV: 6.1 ± 0.9 m/s). The overall agreement between seated and supine measures was strong for cfPWV (ICC: 0.77, 95%CI: 0.63-0.86), weak but significant for bfPWV (ICC: 0.37, 95%CI: 0.11-0.58), and non-significant and weak for faPWV (ICC: 0.26, 95%CI: -0.02-0.49). The cfPWV measurement had strong repeated-measure (i.e., change in pre-sit vs change in post-sit) agreement (ICC: 0.87, 95%CI: 0.78-0.92). There was a very strong repeated measures agreement in bfPWV (ICC: 0.96, 95%CI: 0.93-0.98) and faPWV (ICC: 0.93, 95%CI: 0.88-0.96). CONCLUSIONS: There was strong overall seated and supine agreement for cfPWV but weak overall agreement for bfPWV and faPWV, which indicated that seated and supine measurements are only comparable for cfPWV. Strong to very-strong repeated-measures agreement for all measures suggest that change in PWV is comparable regardless of posture.

Hidden truncation in multivariate Pareto (II) data: properties and inference

In this follow up article of Arnold and Ghosh, we re-visit and study in details one of the two special cases of multivariate hidden truncation -(a) single variable truncation from above in a trivariate scenario where the component random variables follow an appropriate Pareto (type II) distribution. The case with single variable truncation was not discussed in details earlier in Arnold and Ghosh, in particular the estimation under both the classical and the Bayesian paradigm. It is well known that the Pareto distribution is a simple model for nonnegative data with a power law probability tail. Accumulating experience rapidly pointed out the fact that it is only in the upper tail of the income distributions that Pareto-like behavior can be expected. In practice, it has been observed that in income modeling and in other medical studies, quite often the observed data has been truncated with respect to several other unobserved co-variable(s) attaining certain critical levels. In this paper, we consider both the classical and the Bayesian inference (under the non-informative priors set up) of the resulting hidden truncated model. For illustrative purposes, a real data set on abalone is considered to show the flexibility of a single variable truncated Pareto (type II) distribution in a trivariate setting. Finally, the large sample behavior of the smallest order statistic in the case of a single co-variable truncation from above is provided in the appendix.

Limb occlusion pressure for blood flow restricted exercise: Variability and relations with participant characteristics

ObjectiveAssess lower-extremity blood flow restricted exercise (BFR) limb occlusion pressure (LOP) variability and identify related intrinsic characteristics using a portable Delphi BFR system. DesignRepeated measures. SettingLaboratory. ParticipantsForty-two healthy males (n = 25) and females (n = 17) (25.8 ± 5.2 y, 1.76 ±0 .09 m, 78.9 ± 14.9 kg) completed two visits. Brachial artery blood pressure, thigh circumferences (TC), and LOP were measured supine. Main outcome measuresLinear mixed-effects models (LMM) and generalizability theory were used to evaluate LOP between legs and days, determine intrinsic characteristic relations, and assess random variance components. ResultsLOP was not different between legs (p = .730) or days (p = .916; grand mean = 183.7 mmHg [178.4, 189.1]). LOP varied significantly between participants (p = .011, standard error = 47.3 mmHg). 47% of LOP variance was between participants, 18% and 6% was within participants between days and legs, respectively, and 28% was associated with random error. The relative error variance was 14.4 mmHg. Pulse pressure (PP) (p = .005) and TC (p = .040) were positively associated with LOP. A LMM including PP and TC predicted LOP with a mean absolute difference of 11.1 mmHg [9.7, 12.6] compared to measured LOP. ConclusionsThe relative error variance suggests that clinicians should measure LOP consistently for each patient to ensure BFR safety and effectiveness.

Stein’s Lemma for generalized skew-elliptical random vectors

This paper generalizes Stein's Lemma recently obtained for elliptical class distributions to the generalized skew-elliptical family of distributions. Stein's Lemma provides a useful tool for deriving covariances between functions of component random variables. This Lemma has applications in finance, notably for portfolio selection and hence for the capital asset pricing model (CAPM), as well as technical applications such as the computation of moments. It also leads to important propositions concerning the mean and variance of generalized skew-elliptical variables.

Reliability-based design of truck escape ramps

The design method of truck escape ramps (TERs) presented by the Transportation Association of Canada and other organizations is deterministic and assumes fixed values of the design speed, rolling resistance, and ramp grade. This paper presents a reliability-based method for TER design based on the first-order second-moment (FOSM) method and the advanced FOSM (AFOSM) method. These methods rely on the distribution of the component random variables. Each method was used to analyze a TER with one grade and two grades. The FOSM is simple and can be easily used by practitioners, even with calculators. The AFOSM is more complicated but more accurate as it considers the design points in determining the probability of failure. The AFOSM method was used to establish design graphs for the required length of TERs. Application of the proposed method is illustrated using actual TERs in the United States and considering a hypothetical design scenario.

Modelling the multilevel structure and mixed effects of the factors influencing the energy consumption of electric vehicles

To improve the accuracy of estimation of the energy consumption of electric vehicles (EVs) and to enable the alleviation of range anxiety through the introduction of EV charging stations at suitable locations for the near future, multilevel mixed-effects linear regression models were used in this study to estimate the actual energy efficiency of EVs. The impacts of the heterogeneity in driving behaviour among various road environments and traffic conditions on EV energy efficiency were extracted from long-term daily trip-based energy consumption data, which were collected over 12months from 68 in-use EVs in Aichi Prefecture in Japan. Considering the variations in energy efficiency associated with different types of EV ownership, different external environments, and different driving habits, a two-level random intercept model, three two-level mixed-effects models, and two three-level mixed-effects models were developed and compared. The most reasonable nesting structure was determined by comparing the models, which were designed with different nesting structures and different random variance component specifications, thereby revealing the potential correlations and non-constant variability of the energy consumption per kilometre (ECPK) and improving the estimation accuracy by 7.5%.

International Tourists Spending in Northern Thailand: Multilevel Linear Regression Based Hierarchical Data

This paper applies the multilevel linear regression (MLM) model to investigate factors that affect international tourists' spending per day when travelling in the northern region of Thailand. Four hundred questionnaires were collected by a convenience sampling method in 9 provinces of northern Thailand (Chiang Mai, Chiang Rai, Lamphun, Lampang, Uttaradit, Pitsanulok, Sukhothai, Kampaeng Phet and Nakonsawan) from October, 2015 to December, 2015. The results represent the mixed affected model which contains significant fixed effect explanatory variables (age, intention of revisit, and the attitude to reuse domestic land transportation) and random variance components, including individual income. In addition, the MLM can explain that the overall international tourists' spending per day in the region level (level 1) statistically depends on the individual income in the province level (level 2).

Analyzing bivariate ordinal data with CUB margins

Statistical modelling for ordinal data has received a considerable attention in the literature, and a consolidated theory relying on Generalized Linear Model approach has been developed. In this article, we present an innovative technique for modelling bivariate ordinal data. In particular, we consider the method introduced by Plackett for constructing a one-parameter bivariate distribution from given margins, and we apply it in order to represent correlated ordinal variables which individually follows a CUB model. This is a univariate mixture distribution defined by the convex Combination of a Uniform and a shifted Binomial distribution whose parameters may be related to rater's covariates. The article shows how the bivariate distribution can be defined and how its characterizing parameter, which describes the association between the component random variables, can be related to the subject's covariates. The proposed approach is applied to the study of two key drivers of extra virgin olive oil consumption in Italy. The technique allows a representation of the data whose meaning can be easily interpreted providing useful information for management support.

Multivariate Bernoulli distribution

In this paper, we consider the multivariate Bernoulli distribution as a model to estimate the structure of graphs with binary nodes. This distribution is discussed in the framework of the exponential family, and its statistical properties regarding independence of the nodes are demonstrated. Importantly the model can estimate not only the main effects and pairwise interactions among the nodes but also is capable of modeling higher order interactions, allowing for the existence of complex clique effects. We compare the multivariate Bernoulli model with existing graphical inference models - the Ising model and the multivariate Gaussian model, where only the pairwise interactions are considered. On the other hand, the multivariate Bernoulli distribution has an interesting property in that independence and uncorrelatedness of the component random variables are equivalent. Both the marginal and conditional distributions of a subset of variables in the multivariate Bernoulli distribution still follow the multivariate Bernoulli distribution. Furthermore, the multivariate Bernoulli logistic model is developed under generalized linear model theory by utilizing the canonical link function in order to include covariate information on the nodes, edges and cliques. We also consider variable selection techniques such as LASSO in the logistic model to impose sparsity structure on the graph. Finally, we discuss extending the smoothing spline ANOVA approach to the multivariate Bernoulli logistic model to enable estimation of non-linear effects of the predictor variables.

Stochastic simulation of bivariate gamma distribution: a frequency-factor based approach

A frequency-factor based approach for stochastic simulation of bivariate gamma distribution is proposed. The approach involves generation of bivariate normal samples with a correlation coefficient consistent with the correlation coefficient of the corresponding bivariate gamma samples. Then the bivariate normal samples are transformed to bivariate gamma samples using the well-known general equation of hydrological frequency analysis. We demonstrate that the proposed bivariate gamma simulation approach is capable of generating random sample pairs which not only have the desired marginal densities of component random variables but also their correlation coefficient. Scatter plots of simulated bivariate sample pairs also exhibit appropriate linear patterns (dependence structure) that are commonly observed in environmental and hydrological applications. Caution should also be exercised when specifying combinations of coefficients of skewness and the correlation coefficient for bivariate gamma simulation.

Stein's Lemma for elliptical random vectors

For the family of multivariate normal distribution functions, Stein's Lemma presents a useful tool for calculating covariances between functions of the component random variables. Motivated by applications to corporate finance, we prove a generalization of Stein's Lemma to the family of elliptical distributions.

A STATISTICAL REASON FOR THE APPEARANCE OF 1/F SPECTRA FROM NOT PERFECTLY CONTINUOUS PROCESSES

The objective of this paper is the derivation of the spectral estimate for data from a stochastic process that does not perfectly match the common supposition of stochastic continuity. The used model is a Randomly Indexed Random Walk that supposes the data of every sampling interval as the sum of a finite random number of random independent increments. This corresponds to the discreteness of the state space of electron devices. Random increments indicate the transitions between the current state and a randomly selected next one. Transitions are pointlike events occurring at random instants in time. Randomness in time influences the stochastic properties of the recorded data in such a way that the fixed variance of single random increments turns into a random one of the equidistantly recorded data. Thus, despite of the independence of increments, the data appear as positively correlated. The standard spectral estimate yields the 1/f pattern if the random variance component approaches the magnitude of the fixed variance component.

On extremal distributions and sharp $\bolds{L_p}$-bounds\\ for sums of multilinear forms

In this paper we present a study of the problem of approximating the expectations of functions of statistics in independent and dependent random variables in terms of the expectations of functions of the component random variables. We present results providing sharp analogues of the Burkholder--Rosenthal inequalities and related estimates for the expectations of functions of sums of dependent nonnegative r.v.'s and conditionally symmetric martingale differences with bounded conditional moments as well as for sums of multilinear forms. Among others, we obtain the following sharp inequalities: $E(\sum_{k=1}^n X_k)^t\le 2 \max (\sum_{k=1}^n EX_k^t, (\sum_{k=1}^n a_k)^t)$ for all nonnegative r.v.'s $X_1, \ldots, X_n$ with $E(X_k\mid X_1, \ldots, X_{k-1})\le a_k$, $EX_k^t<\infty$, $k=1, \ldots, n$, $1#x003C;t#x003C;2$; $E(\sum_{k=1}^n X_k)^t\le E\theta^t(1) \max (\sum_{k=1}^n b_k, (\sum_{k=1}^n a_k^s)^{t/s})$ for all nonnegative r.v.'s $X_1, \ldots, X_n$ with $E(X_k^s\mid X_1, \ldots, X_{k-1})\le a_k^s$, $E(X_k^t\mid X_1, \ldots, X_{k-1})\le b_k$, $k=1, \ldots, n$, $1#x003C;t#x003C;2$, $0#x003C;s\le t-1$ or $t\ge 2$, $0#x003C;s\le 1$, where $\theta(1)$ is a Poisson random variable with parameter 1. As applications, new decoupling inequalities for sums of multilinear forms are presented and sharp Khintchine--Marcinkiewicz--Zygmund inequalities for generalized moving averages are obtained. The results can also be used in the study of a wide class of nonlinear statistics connected to problems of long-range dependence and in an econometric setup, in particular, in stabilization policy problems and in the study of properties of moving average and autocorrelation processes. The results are based on the iteration of a series of key lemmas that capture the essential extremal properties of the moments of the statistics involved.

Genotype by environment interactions in lamb weight and carcass composition traits

AbstractThe systematic use of the same genotype in several different environments provides information that can be used to estimate genotype by environment interaction (G ✕ E) variances and parameters. Data from the UK Suffolk Sire Referencing Scheme Ltd were used to investigate a range of sire and dam by environment interactions in lamb weight (at 8 weeks and scanning) and body composition traits (muscle and fat depth). These interactions were calculated in a DFREML mixed model containing direct additive, maternal additive, maternal environmental random variance components and the covariance between direct and maternal additive effects. Sire interactions with year, flock and flock-year and dam effects within and between litters were investigated. The addition of all G ✕ E (co)variance components resulted in an improved fit of the model for all traits. Sire interactions accounted for between 2 and 3% of the phenotypic variance in all traits, usually at the expense of both additive effects. Maternal litter environmental variance components ranged from 10% (fat depth and muscle depth) to 20% (8-week weight) of phenotypic variance. Most of this variation was found in the residual component of variance when the term was omitted from the model. When fitting sire G✕ E components in a model the covariance between direct and maternal additive genetic effects, as a proportion of phenotypic variance, was reduced to a low level (from –0·36 to –0·08 for 8-week weight). Genotype by environment interactions form a significant source of variation in lamb growth and composition traits and reduce the high negative correlation between additive effects found previously in these traits.

The Concentration-Response Relation between Air Pollution and Daily Deaths

Studies on three continents have reported associations between various measures of airborne particles and daily deaths. Sulfur dioxide has also been associated with daily deaths, particularly in Europe. Questions remain about the shape of those associations, particularly whether there are thresholds at low levels. We examined the association of daily concentrations of black smoke and SO(2) with daily deaths in eight Spanish cities (Barcelona, Bilbao, Castellón, Gijón, Oviedo, Valencia, Vitoria, and Zaragoza) with different climates and different environmental and social characteristics. We used nonparametric smoothing to estimate the shape of the concentration-response curve in each city and combined those results using a metasmoothing technique developed by Schwartz and Zanobetti. We extended their method to incorporate random variance components. Black smoke had a nearly linear association with daily deaths, with no evidence of a threshold. A 10 microg/m(3) increase in black smoke was associated with a 0.88% increase in daily deaths (95% confidence interval, 0.56%-1.20%). SO(2) had a less plausible association: Daily deaths increased at very low concentrations, but leveled off and then decreased at higher concentrations. These findings held in both one- and two-pollutant models and held whether we optimized our weather and seasonal model in each city or used the same smoothing parameters in each city. We conclude that the association with particle levels is more convincing than for SO(2), and without a threshold. Linear models provide an adequate estimation of the effect of particulate air pollution on mortality at low to moderate concentrations.