The variability among data may have quite complex structure and the splitting of variation into its individual components is important in many areas of applications. In particular, the study of variation through a class of linear models known as random and mixed models is a central topic in statistics with wide ramifications in both theory and applications. Sometimes these models are called components of variance models since the interest in the model lies in investigating the variances of the effects of factor levels which are assumed to be randomly selected from a large population of levels. These variances are also known as variance components since the total variance can be expressed as the sum of these variances and the error variance. Knowledge of the variance components, i.e., the information on the relative importance and magnitude of the sources of variability in the data is of critical importance in many problems since the isolation of the total variance into the individual components of variance would result in the physical elimination of the sources of variability in question.

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A bibliography on variance components an introduction and an update: 1984-2002

Summary This article provides (1) a comprehensive coverage of the literature on designs for estimating variance components, and (2) a review of recent applications of such designs in genetics, statistical process control, and quality improvement. In addition, recent methods of estimation of variance components and model forms, other than the linear, are discussed. The latter developments have a direct effect on the choice of design. Some suggested ideas for future research directions are also given.

Designs for Variance Components Estimation: Past and Present

Cerambyx welensii Kuster is one of the greatest threats to Quercus suber L. and Quercus ilex L. in Spain. Efficient control methods for this species are currently being tested, and the use of traps baited with food-related products for their monitoring and control has been proposed. Cerambyx welensii adults prefer to colonize old or decayed trees, in which cortical exudates frequently release fermentation odors. Fermentation-related compounds, such as ethanol, have been cited as attractants to various hardwood woodborers (as Cerambyx cerdo L.), used either alone or sometimes in combination with other host odors. In this work, we conducted field experiments to ascertain whether chemical blends mimicking fermentation odors were attractive for C. welensii. To this end, we used three types of traps (multiple funnel, cross-vane and single-funnel) baited with six synthetic blends including one or more fermentation-related chemicals (ethanol, ethyl acetate, 3-methyl-1-butanol, acetaldehyde, 2-methyl-1-propanol and 2-methyl-1-butanol), various food-related products (beer, melon and red wine mixed with peach juice) and host monoterpenes (α-pinene, β-pinene, limonene, α-phellandrene and camphene). At high release rates (5–11 g/day), various synthetic blends proved attractive irrespective of trap type. Our results contribute to understand the impact of volatile organic compounds in host selection by woodborers infesting deciduous trees. The results hold promise for optimizing trapping strategies to control C. welensii within an integrated pest management framework.

Field attraction of Cerambyx welensii to fermentation odors and host monoterpenes

The purpose of this paper is to investigate the determinants influencing the costs of cardiovascular disease in the regional health service in Italy’s Apulia region from 2014 to 2016. Data for patients with acute myocardial infarction (AMI), heart failure (HF), and atrial fibrillation (AF) were collected from the hospital discharge registry. Generalized linear models (GLM), and generalized linear mixed models (GLMM) were used to identify the role of random effects in improving the model performance. The study was based on socio-demographic variables and disease-specific variables (diagnosis-related group, hospitalization type, hospital stay, surgery, and economic burden of the hospital discharge form). Firstly, both models indicated an increase in health costs in 2016, and lower spending values for women (p < 0.001) were shown. GLMM indicates a significant increase in health expenditure with increasing age (p < 0.001). Day-hospital has the lowest cost, surgery increases the cost, and AMI is the most expensive pathology, contrary to AF (p < 0.001). Secondly, AIC and BIC assume the lowest values for the GLMM model, indicating the random effects’ relevance in improving the model performance. This study is the first that considers real data to estimate the economic burden of CVD from the regional health service’s perspective. It appears significant for its ability to provide a large set of estimates of the economic burden of CVD, providing information to managers for health management and planning.

https://www.mdpi.com/1660-4601/18/9/4652/pdf

Identification of Health Expenditures Determinants: A Model to Manage the Economic Burden of Cardiovascular Disease

The green peach aphid, Myzus persicae (Sulzer), is a generalist insect herbivore capable of using a wide range of cultivated plants and weeds. In this laboratory study, we examined the inter-clonal variation in M. persicae’s ability to exploit the wild peach Prunus davidiana, a source of genetic resistance to aphids used by peach breeding programs. An initial screening of a set of sexually reproducing clones collected from commercial orchards planted with susceptible varieties found significant genetic variation in aphid survival on P. davidiana. Comparison of two clones (Fr2 and Fr12) found marked differences in colony sizes achieved. A detailed analysis of probing and feeding behavior showed that the clone exhibiting the highest performance on P. davidiana (Fr2) initiated probing earlier than the lower performing clone (Fr12). Periods of non-probing were also significantly shorter for this clone. Finally, Fr2 produced more and longer events of watery saliva injection into sieve elements. We discuss these results in terms of host plant adaptation by aphids and their capacity to overcome plant-resistance genes.

Intra-specific variation of behavioral signals in suppressing plant defenses in the green peach aphid Myzus persicae, feeding on the resistant wild peach Prunus davidiana

Generalized linear models provide a methodology for doing regression and ANOV A-type analysis with data whose errors are not necessarily normally-distributed. Common applications in agriculture include categorical data, survival analysis, bioassay, etc. Most of the literature and most of the available computing software for generalized linear models applies to cases in which all model effects are fixed. However, many agricultural research applications lead to mixed or random effects models: split-plot experiments, animaland plant-breeding studies, multi-location studies, etc. Recently, through a variety of efforts in a number of contexts, a general framework for generalized linear models with random effects, the "generalized linear mixed model," has been developed. The purpose of this presentation is to present an overview of the methodology for generalized mixed linear models. Relevant background, estimating equations, and general approaches to interval estimation and hypothesis testing will be presented. Methods will be illustrated via a small data set involving binary data.

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W. W. Stroup

Papers

Generalized linear mixed models - an overview