Least Squares and Minimum MSE Estimators of Variance Components in Mixed Linear Models

The paper deals with the quadratic invariant estimators of the linear functions of variance components in mixed linear model. The estimator with locally minimal mean square error with respect to a parameter ? is derived. Under the condition of normality of the vector Y the theoretical values of MSE of several types of estimators are compared in two different mixed models; under a different types of distributions a simulation study is carried out for the behaviour of derived estimators.     

Inequality constrained estimation of genetic parameters

Summary A method is presented for computing estimates of genetic parameters under linear inequality constraints such that solutions are within theoretical limits. The method produces biased estimators, yet a small scale numerical study, also presented, shows that the inequality constrained estimators have a small mean squared error of prediction than the best of unbiased estimators. The increase in efficiency of estimation is particularly useful for traits where heritability is near the boundary values of zero or one.     

A Note on Balanced Sampling and Robust Genetic Predictors

The concept of balanced sampling is applied to prediction in finite samples using model based inference procedures. Necessary and sufficient conditions are derived for a general linear model with arbitrary covariance structure to yield the expansion estimator as the best linear unbiased predictor for the mean. The analysis is extended to produce a robust estimator for the mean squared error under balanced sampling and the results are discussed in the context of statistical genetics where appropriate sampling produces simple efficient and robust genetic predictors free from unnecessary genetic assumptions.     

Empirical Bayes small area prediction under a zero-inflated lognormal model with correlated random area effects

Many variables of interest in agricultural or economical surveys have skewed distributions and can equal zero. Our data are measures of sheet and rill erosion called Revised Universal Soil Loss Equation - 2 (RUSLE2). Small area estimates of mean RUSLE2 erosion are of interest. We use a zero-inflated lognormal mixed effects model for small area estimation. The model combines a unit-level lognormal model for the positive RUSLE2 responses with a unit-level logistic mixed effects model for the binary indicator that the response is nonzero. In the Conservation Effects Assessment Project (CEAP) data, counties with a higher probability of nonzero responses also tend to have a higher mean among the positive RUSLE2 values. We capture this property of the data through an assumption that the pair of random effects for a county are correlated. We develop empirical Bayes (EB) small area predictors and a bootstrap estimator of the mean squared error (MSE). In simulations, the proposed predictor is superior to simpler alternatives. We then apply the method to construct EB predictors of mean RUSLE2 erosion for South Dakota counties. To obtain auxiliary variables for the population of cropland in South Dakota, we integrate a satellite-derived land cover map with a geographic database of soil properties. We provide an R Shiny application called viscover (available at https://lyux.shinyapps.io/viscover/ ) to visualize the overlay operations required to construct the covariates. On the basis of bootstrap estimates of the mean square error, we conclude that the EB predictors of mean RUSLE2 erosion are superior to direct estimators.     

CLUSTERING POPULATIONS BY MIXED LINEAR MODELS

INTRODUCTIONInevolutionstudiesandplant(oranimal)breedingresearch,clusteranalysesarewidelyusedforgroupingpopulations.Therehavebeenalotofmethodsdevelopedforgroupingpopulations(SneathandSokal,1973;Eve-ritt,1993).Variousmethodsaredifferedinthewaysfordistance(…     

以小时为步长的大兴安岭典型林分地表死可燃物含水率模型预测及外推精度

地表死可燃物含水率是火险天气和火行为预报中的重要指标.本研究基于时滞平衡含水率法(Nelson和Simard方法)及气象要素回归方法,于2010年9—10月对黑龙江省大兴安岭地区盘古林场不同郁闭度的山杨-白桦混交林、红皮云杉纯林,以及采伐迹地(原1∶1樟子松-白桦混交林)地表死可燃物含水率进行以小时为步长的连续测定,建立其预测模型,得到预测误差,并使用相应的模型对其他林分地表死可燃物含水率进行外推精度分析.结果表明:采用Nelson平衡含水率法构建的地表死可燃物含水率变化模型的平均绝对误差、平均相对误差和均方误差根(0.0154、0.104和0.0226)低于Simard法(0.0185、0.117和0.0256)和气象要素回归法(0.0222、0.150和0.0331).在外推效果方面,气象要素回归法的平均绝对误差、平均相对误差和均方误差根(0.0410、0.0300和0.0740)低于Simard法(0.610、0.492和0.846),但前两者均高于Nelson法(0.034、0.021和0.0660),说明以小时为步长的时滞平衡含水率法,尤其是Nelson法适用于大兴安岭地区所测林分.外推虽不能降低误差,但有助于提高现有模型应用至不同林分条件或大尺度范围内的地表死可燃物含水率预测精度和利用率.模型建模和外推误差与不同树种和郁闭度条件差异有关,研究时应根据不同林分和地点选择合适的平衡含水率模型.     

Design-based mapping of tree attributes by 3P sampling

The estimation of individual values (marks) in a finite population of units (e.g., trees) scattered onto a survey region is considered under 3P sampling. For each unit, the mark is estimated by means of an inverse distance weighting interpolator. Conditions ensuring the design-based consistency of maps are considered under 3P sampling. A computationally simple mean squared error estimator is adopted. Because 3P sampling involves the prediction of marks for each unit in the population, prediction errors rather than marks can be interpolated. Then, marks are estimated by the predictions plus the interpolated errors. If predictions are good, prediction errors are more smoothed than raw marks so that the procedure is likely to better meet consistency requirements. The purpose of this paper is to provide theoretical and empirical evidence on the effectiveness of the interpolation based on prediction errors to prove that the proposed strategy is a tool of general validity for mapping forest stands.     

Influence functions and robust Bayes and empirical Bayes small area estimation

We introduce new robust small area estimation procedures basedon area-level models. We first find influence functions correspondingto each individual area-level observation by measuring the divergencebetween the posterior density functions of regression coefficientswith and without that observation. Next, based on these influencefunctions, properly standardized, we propose some new robustBayes and empirical Bayes small area estimators. The mean squarederrors and estimated mean squared errors of these estimatorsare also found. A small simulation study compares the performanceof the robust and the regular empirical Bayes estimators. Whenthe model variance is larger than the sample variance, the proposedrobust empirical Bayes estimators are superior.     

On Method of Moments Estimation in Linear Mixed Effects Models with Measurement Error on Covariates and Response with Application to a Longitudinal Study of Gene-Environment Interaction

We study a linear mixed effects model for longitudinal data, where the response variable and covariates with fixed effects are subject to measurement error. We propose a method of moment estimation that does not require any assumption on the functional forms of the distributions of random effects and other random errors in the model. For a classical measurement error model we apply the instrumental variable approach to ensure identifiability of the parameters. Our methodology, without instrumental variables, can be applied to Berkson measurement errors. Using simulation studies, we investigate the finite sample performances of the estimators and show the impact of measurement error on the covariates and the response on the estimation procedure. The results show that our method performs quite satisfactory, especially for the fixed effects with measurement error (even under misspecification of measurement error model). This method is applied to a real data example of a large birth and child cohort study.     

Integration of the effects of animal and dietary factors on total dry matter intake of dairy cows fed silage-based diets

An empirical regression model for the prediction of total dry matter intake (DMI) of dairy cows was developed and compared with four published intake models. The model was constructed to include both animal and dietary factors, which are known to affect DMI. For model development, a data set based on individual cow data from 10 change-over and four continuous milk production studies was collected (n = 1554). Relevant animal (live weight (LW), days in milk (DIM), parity and breed) and dietary (total and concentrate DMI, concentrate composition, forage digestibility and fermentation quality) data were collected. The model factors were limited to those that are available before the diets are fed to animals, that is, standardized energy corrected milk (sECM) yield, LW, DIM and diet quality (total diet DMI index (TDMI index)). As observed ECM yield is a function of both the production potential of the cow and diet quality, ECM yield standardized for DIM, TDMI index and metabolizable protein concentration was used in modelling. In the individual data set, correlation coefficients between sECM and TDMI index or DIM were much weaker (0.16 and 0.03) than corresponding coefficients with observed ECM (0.65 and 0.46), respectively. The model was constructed with a mixed model regression analysis using cow within trial as a random factor. The following mixed model was estimated for DMI prediction: DMI (kg DM/day) = -2.9 (±0.56)+0.258 (±0.011) × sECM (kg/day) + 0.0148 (±0.0009) × LW (kg) -0.0175 (±0.001) × DIM -5.85 (±0.41) × exp (-0.03 × DIM) + 0.09 (±0.002) × TDMI index. The mixed DMI model was evaluated with a treatment mean data set (207 studies, 992 diets), and the following relationship was found: Observed DMI (kg DM/day) = -0.10 (±0.33) + 1.004 (±0.019) × Predicted DMI (kg DM/day) with an adjusted residual mean square error of 0.362 kg/day. Evaluation of the residuals did not result in a significant mean bias or linear slope bias, and random error accounted for proportionally >0.99 of the error. In conclusion, the DMI model developed is considered robust because of low mean prediction error, accurate and precise validation, and numerically small differences in the parameter values of model variables when estimated with mixed or simple regression models. The Cornell Net Carbohydrate and Protein System was the most accurate of the four other published DMI models evaluated using individual or treatment mean data, but in most cases mean and linear slope biases were relatively high, and, interestingly, there were large differences in both mean and linear slope biases between the two data sets.     

Estimation and comparison of changes in the presence of informative right censoring: conditional linear model

A general linear regression model for the usual least squares estimated rate of change (slope) on censoring time is described as an approximation to account for informative right censoring in estimating and comparing changes of a continuous variable in two groups. Two noniterative estimators for the group slope means, the linear minimum variance unbiased (LMVUB) estimator and the linear minimum mean squared error (LMMSE) estimator, are proposed under this conditional model. In realistic situations, we illustrate that the LMVUB and LMMSE estimators, derived under a simple linear regression model, are quite competitive compared to the pseudo maximum likelihood estimator (PMLE) derived by modeling the censoring probabilities. Generalizations to polynomial response curves and general linear models are also described.     

Evaluation of the Best Linear Unbiased Prediction in Mixed Linear Models with Estimated Variance Components by Means of the MSE of Prediction and the Genetic Selection Differential

Prediction in mixed linear models by Henderson 's (1972) BLUP (Best Linear Unbiased Prediction) requires knowledge of the underlying variance/covariance components to have the property ‘best’. In breeding value prediction these parameters are not known, generally. They have to be replaced by estimations and BLUP becomes estimated BLUP (EBLUP). The aim of this investigation was the evaluation of EBLUP with help of a designed simulation experiment. Criteria used for the evaluation were the mean squared error (MSE) and the (genetic) selection differential (GSD). Besides, an idea of the overestimation of the accuracy of EBLUP by the naive MSE approximation based on the MSE formulas of BLUP with variance component estimations instead of unknown parameters is given.     

Comparison of Regression Methods for Modeling Intensive Care Length of Stay

Intensive care units (ICUs) are increasingly interested in assessing and improving their performance. ICU Length of Stay (LoS) could be seen as an indicator for efficiency of care. However, little consensus exists on which prognostic method should be used to adjust ICU LoS for case-mix factors. This study compared the performance of different regression models when predicting ICU LoS. We included data from 32,667 unplanned ICU admissions to ICUs participating in the Dutch National Intensive Care Evaluation (NICE) in the year 2011. We predicted ICU LoS using eight regression models: ordinary least squares regression on untransformed ICU LoS,LoS truncated at 30 days and log-transformed LoS; a generalized linear model with a Gaussian distribution and a logarithmic link function; Poisson regression; negative binomial regression; Gamma regression with a logarithmic link function; and the original and recalibrated APACHE IV model, for all patients together and for survivors and non-survivors separately. We assessed the predictive performance of the models using bootstrapping and the squared Pearson correlation coefficient (R²), root mean squared prediction error (RMSPE), mean absolute prediction error (MAPE) and bias. The distribution of ICU LoS was skewed to the right with a median of 1.7 days (interquartile range 0.8 to 4.0) and a mean of 4.2 days (standard deviation 7.9). The predictive performance of the models was between 0.09 and 0.20 for R², between 7.28 and 8.74 days for RMSPE, between 3.00 and 4.42 days for MAPE and between −2.99 and 1.64 days for bias. The predictive performance was slightly better for survivors than for non-survivors. We were disappointed in the predictive performance of the regression models and conclude that it is difficult to predict LoS of unplanned ICU admissions using patient characteristics at admission time only.     

Skew-normal random-effects model for meta-analysis of diagnostic test accuracy (DTA) studies

Hierarchical models are recommended for meta-analyzing diagnostic test accuracy (DTA) studies. The bivariate random-effects model is currently widely used to synthesize a pair of test sensitivity and specificity using logit transformation across studies. This model assumes a bivariate normal distribution for the random-effects. However, this assumption is restrictive and can be violated. When the assumption fails, inferences could be misleading. In this paper, we extended the current bivariate random-effects model by assuming a flexible bivariate skew-normal distribution for the random-effects in order to robustly model logit sensitivities and logit specificities. The marginal distribution of the proposed model is analytically derived so that parameter estimation can be performed using standard likelihood methods. The method of weighted-average is adopted to estimate the overall logit-transformed sensitivity and specificity. An extensive simulation study is carried out to investigate the performance of the proposed model compared to other standard models. Overall, the proposed model performs better in terms of confidence interval width of the average logit-transformed sensitivity and specificity compared to the standard bivariate linear mixed model and bivariate generalized linear mixed model. Simulations have also shown that the proposed model performed better than the well-established bivariate linear mixed model in terms of bias and comparable with regards to the root mean squared error (RMSE) of the between-study (co)variances. The proposed method is also illustrated using a published meta-analysis data.     

Extension of the Haseman-Elston regression model to longitudinal data

We propose an extension to longitudinal data of the Haseman and Elston regression method for linkage analysis. The proposed model is a mixed model having several random effects. As response variable, we investigate the sibship sample mean corrected cross-product (smHE) and the BLUP-mean corrected cross product (pmHE), comparing them with the original squared difference (oHE), the overall mean corrected cross-product (rHE), and the weighted average of the squared difference and the squared mean-corrected sum (wHE). The proposed model allows for the correlation structure of longitudinal data. Also, the model can test for gene x time interaction to discover genetic variation over time. The model was applied in an analysis of the Genetic Analysis Workshop 13 (GAW13) simulated dataset for a quantitative trait simulating systolic blood pressure. Independence models did not preserve the test sizes, while the mixed models with both family and sibpair random effects tended to preserve size well.     

Distribution patterns of Cladocera in subarctic Fennoscandian lakes and their potential in environmental reconstruction

Multivariate statistical techniques were used to examine the relationships between surface-sediment cladoceran assemblages and 28 physical and chemical variables in 53 small subarctic lakes from northern Fennoscandia. The lakes were distributed along a steep eco-climatic gradient, spanning boreal corniferous forest to treeless tundra. In general, the sites were small, oligotrophic, and bathymetrically simple, with little or no disturbance in their catchments. From the initial 53 localities, only 36 contained a sufficient number of cladoceran remains for reasonable quantification. From these, a total of 29 cladoceran taxa representing 19 genera were identified, comprising predominantly littoral chydorid species. A constrained redundancy analysis (RDA) and associated Monte Carlo permutation tests indicated that maximum lake depth, sediment organic content, epilimnetic summer temperature, lake perimeter, and lake catchment area made statistically significant (p le; 0.05) contributions to explaining the variance in the cladoceran taxon data. These five variables together accounted for 67.7% of the explained variance, and made a unique contribution of 26.8% to the total variance: all physical determinants independently captured 33.2% of the total variance. The significance of the most powerful explanatory variables is discussed in the paper in detail, and autecological information regarding the most common cladoceran taxa is given. To assess the potential of cladoceran assemblages in environmental reconstruction, quantitative inference models for mean July water and air temperatures were developed for the cladoceran assemblage using partial least squares (PLS) regression. The final prediction model yielded a root mean squared error of prediction (RMSEP). as assessed by jackknifing, of 1.19°C for Cladocera-water temperature data-set, whereas the cladoceran assemblages showed only very weak relationships to mean July air temperature. The overall results emphasize the role of physical factors in regulating species abundance and distributions in these environmentally sensitive ecotonal lakes.     

大兴安岭典型林分地表死可燃物含水率动态变化及预测模型

对春季和秋季大兴安岭地区西林吉林业局山杨-白桦混交林、落叶松林、樟子松林、落叶松-白桦混交林、白桦林5种典型林分不同坡位地表细小死可燃物含水率动态进行研究,构建了不同季节防火期、不同林分地表死可燃物含水率的预测模型,并分析了其预测误差.结果表明: 相同林分地表可燃物含水率在春季和秋季差异显著;在相同季节相同林分下不同坡位可燃物含水率存在差异.采用Nelson模型对地表死可燃物含水率预测的平均绝对误差(MAE)的平均值为0.13,略低于Simard模型(0.14),明显低于气象要素回归模型(0.25).Nelson和Simard模型的预测效果好于气象要素回归模型.秋季模型对地表死可燃物含水率的预测精度好于春季模型和春季秋季混合模型.     

Penalized partial likelihood regression for right-censored data with bootstrap selection of the penalty parameter

The Cox proportional hazards model is often used for estimating the association between covariates and a potentially censored failure time, and the corresponding partial likelihood estimators are used for the estimation and prediction of relative risk of failure. However, partial likelihood estimators are unstable and have large variance when collinearity exists among the explanatory variables or when the number of failures is not much greater than the number of covariates of interest. A penalized (log) partial likelihood is proposed to give more accurate relative risk estimators. We show that asymptotically there always exists a penalty parameter for the penalized partial likelihood that reduces mean squared estimation error for log relative risk, and we propose a resampling method to choose the penalty parameter. Simulations and an example show that the bootstrap-selected penalized partial likelihood estimators can, in some instances, have smaller bias than the partial likelihood estimators and have smaller mean squared estimation and prediction errors of log relative risk. These methods are illustrated with a data set in multiple myeloma from the Eastern Cooperative Oncology Group.     

A note on permutation tests for variance components in multilevel generalized linear mixed models

In many applications of generalized linear mixed models to multilevel data, it is of interest to test whether a random effects variance component is zero. It is well known that the usual asymptotic chi-square distribution of the likelihood ratio and score statistics under the null does not necessarily hold. In this note we propose a permutation test, based on randomly permuting the indices associated with a given level of the model, that has the correct Type I error rate under the null. Results from a simulation study suggest that it is more powerful than tests based on mixtures of chi-square distributions. The proposed test is illustrated using data on the familial aggregation of sleep disturbance.     

Relative need for conservation assessments of vascular plant species among ecoregions

Aim (1) To determine the relative need for conservation assessments of vascular plant species among the world’s ecoregions given under‐assessed species distributions; (2) to evaluate the challenge posed by the lack of financial resources on species assessment efforts; and (3) to demonstrate the utility of nonlinear mixed‐effects models with both homoscedastic and heteroscedastic error structures in the identification of species‐rich ecoregions. Location Global. Methods We identified the world’s ecoregions that contain the highest vascular plant species richness after controlling for area using species–area relationship (SAR) models built within a mixed‐effects multi‐model framework. Using quantitative thresholds, ecoregions with the highest plant species richness, historical habitat loss and projected increase in human population density were deemed to be most in need of conservation assessments of plant species. We used generalized linear models to test if countries that overlap with highly important ecoregions are poorer compared with others. Results We classed ecoregions into nine categories based on the relative need for conservation assessments of vascular plant species. Ecoregions of highest relative need are found mostly in the tropics, particularly Southeast Asia, Central America, Tropical Andes and the Cerrado of South America, and the East African montane region and its surrounding areas. Countries overlapping with ecoregions deemed important for conservation assessments are poorer as measured by their capita gross national income than the other countries. The nonlinear mixed modelling framework was effective in reducing residual spatial autocorrelation compared with nonlinear models comprised of only fixed effects. In contrasting multiple SAR models to identify species‐rich ecoregions, there was not one SAR model that fitted best across all biomes. Not all SAR models displayed homoscedastic errors; therefore it is important to consider models with both homoscedastic and heteroscedastic error structures. Main conclusions We propose that conservation assessments should be conducted first in ecoregions with the greatest predicted species richness, historical habitat loss and future human population increase. As ecoregions deemed to be important for conservation assessments are located in the poorest countries, we urge international aid agencies and botanic gardens to cooperate with both local and international scientists to fund and implement conservation assessment programmes there.