Mixed percolation on the square lattice

1984 ◽  
Vol 21 (2) ◽  
pp. 247-259 ◽  
Author(s):  
John C. Wierman
Keyword(s):  
Mixed Models ◽  
Mixed Model ◽  
Percolation Model ◽  
Square Lattice ◽  
Underlying Graph ◽  
Self Duality ◽  
Random Elements

In a planar percolation model, faces of the underlying graph, as well as the sites and bonds, may be viewed as random elements. With this viewpoint, Whitney duality allows construction of a planar dual percolation model for each planar percolation model, which applies to mixed models with sites, bonds, and faces open or closed at random. Using self-duality for percolation models on the square lattice, information is obtained about the percolative region in the mixed model.

Mixed percolation on the square lattice

1984 ◽  
Vol 21 (02) ◽  
pp. 247-259 ◽  
Author(s):  
John C. Wierman
Keyword(s):  
Mixed Models ◽  
Mixed Model ◽  
Percolation Model ◽  
Square Lattice ◽  
Underlying Graph ◽  
Self Duality ◽  
Random Elements

In a planar percolation model, faces of the underlying graph, as well as the sites and bonds, may be viewed as random elements. With this viewpoint, Whitney duality allows construction of a planar dual percolation model for each planar percolation model, which applies to mixed models with sites, bonds, and faces open or closed at random. Using self-duality for percolation models on the square lattice, information is obtained about the percolative region in the mixed model.

scholarly journals Mixed Models as a Tool for Comparing Groups of Time Series in Plant Sciences

Plants ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 362
Author(s):  
Ioannis Spyroglou ◽  
Jan Skalák ◽  
Veronika Balakhonova ◽  
Zuzana Benedikty ◽  
Alexandros G. Rigas ◽  
...  
Keyword(s):  
Time Series ◽  
Random Effects ◽  
Mixed Models ◽  
Mixed Model ◽  
Repeated Measurements ◽  
Time Series Models ◽  
Additional Time ◽  
Biotic Stresses ◽  
Viable Solution ◽  
Long Time

Plants adapt to continual changes in environmental conditions throughout their life spans. High-throughput phenotyping methods have been developed to noninvasively monitor the physiological responses to abiotic/biotic stresses on a scale spanning a long time, covering most of the vegetative and reproductive stages. However, some of the physiological events comprise almost immediate and very fast responses towards the changing environment which might be overlooked in long-term observations. Additionally, there are certain technical difficulties and restrictions in analyzing phenotyping data, especially when dealing with repeated measurements. In this study, a method for comparing means at different time points using generalized linear mixed models combined with classical time series models is presented. As an example, we use multiple chlorophyll time series measurements from different genotypes. The use of additional time series models as random effects is essential as the residuals of the initial mixed model may contain autocorrelations that bias the result. The nature of mixed models offers a viable solution as these can incorporate time series models for residuals as random effects. The results from analyzing chlorophyll content time series show that the autocorrelation is successfully eliminated from the residuals and incorporated into the final model. This allows the use of statistical inference.

scholarly journals Optimal models in the yield analysis of new flax cultivars

2018 ◽  
Vol 98 (4) ◽  
pp. 897-907
Author(s):  
Gaofeng Jia ◽  
Helen M. Booker
Keyword(s):  
Mixed Models ◽  
Statistical Power ◽  
Mixed Model ◽  
Trial Data ◽  
Residual Error ◽  
Yield Data ◽  
Symmetry Model ◽  
Compound Symmetry ◽  
Future Data ◽  
Variety Performance

Multi-environment trials are conducted to evaluate the performance of cultivars. In a combined analysis, the mixed model is superior to an analysis of variance for evaluating and comparing cultivars and dealing with an unbalanced data structure. This study seeks to identify the optimal models using the Saskatchewan Variety Performance Group post-registration regional trial data for flax. Yield data were collected for 15 entries in post-registration tests conducted in Saskatchewan from 2007 to 2016 (except 2011) and 16 mixed models with homogeneous or heterogeneous residual errors were compared. A compound symmetry model with heterogeneous residual error (CSR) had the best fit, with a normal distribution of residuals and a mean of zero fitted to the trial data for each year. The compound symmetry model with homogeneous residual error (CS) and a model extending the CSR to higher dimensions (DIAGR) were the next best models in most cases. Five hundred random samples from a two-stage sampling method were produced to determine the optimal models suitable for various environments. The CSR model was superior to other models for 396 out of 500 samples (79.2%). The top three models, CSR, CS, and DIAGR, had higher statistical power and could be used to access the yield stability of the new flax cultivars. Optimal mixed models are recommended for future data analysis of new flax cultivars in regional tests.

scholarly journals The Impact of Misspecified Random Effect Distribution in a Weibull Regression Mixed Model

Stats ◽  
2018 ◽  
Vol 1 (1) ◽  
pp. 48-76
Author(s):  
Freddy Hernández ◽  
Viviana Giampaoli
Keyword(s):  
Weibull Distribution ◽  
Random Effects ◽  
Mixed Models ◽  
Fixed Effects ◽  
Mixed Model ◽  
Random Effect ◽  
Estimation Procedure ◽  
Weibull Regression ◽  
Two Parameters ◽  
The Impact

Mixed models are useful tools for analyzing clustered and longitudinal data. These models assume that random effects are normally distributed. However, this may be unrealistic or restrictive when representing information of the data. Several papers have been published to quantify the impacts of misspecification of the shape of the random effects in mixed models. Notably, these studies primarily concentrated their efforts on models with response variables that have normal, logistic and Poisson distributions, and the results were not conclusive. As such, we investigated the misspecification of the shape of the random effects in a Weibull regression mixed model with random intercepts in the two parameters of the Weibull distribution. Through an extensive simulation study considering six random effect distributions and assuming normality for the random effects in the estimation procedure, we found an impact of misspecification on the estimations of the fixed effects associated with the second parameter σ of the Weibull distribution. Additionally, the variance components of the model were also affected by the misspecification.

Full Credibility with Generalized Linear and Mixed Models

2009 ◽  
Vol 39 (1) ◽  
pp. 61-80 ◽  
Author(s):  
José Garrido ◽  
Jun Zhou
Keyword(s):  
Mixed Models ◽  
Mixed Model ◽  
Linear Mixed Model ◽  
Linear Models ◽  
Link Function ◽  
Analysis Method ◽  
Risk Class ◽  
Statistical Analysis Method ◽  
Car Insurance ◽  
Insurance Data

AbstractGeneralized linear models (GLMs) are gaining popularity as a statistical analysis method for insurance data. For segmented portfolios, as in car insurance, the question of credibility arises naturally; how many observations are needed in a risk class before the GLM estimators can be considered credible? In this paper we study the limited fluctuations credibility of the GLM estimators as well as in the extended case of generalized linear mixed model (GLMMs). We show how credibility depends on the sample size, the distribution of covariates and the link function. This provides a mechanism to obtain confidence intervals for the GLM and GLMM estimators.

Poisson mixed models for predicting number of fires

2019 ◽  
Vol 28 (3) ◽  
pp. 237
Author(s):  
Miguel Boubeta ◽  
María José Lombardía ◽  
Manuel Marey-Pérez ◽  
Domingo Morales
Keyword(s):  
Forest Fires ◽  
Mixed Models ◽  
Mixed Model ◽  
Parametric Bootstrap ◽  
Temporal Correlation ◽  
Autoregressive Process ◽  
Burned Area ◽  
Time Effects ◽  
North West ◽  
Temporal Models

Wildfires are considered one of the main causes of forest destruction. In recent years, the number of forest fires and burned area in Mediterranean regions have increased. This problem particularly affects Galicia (north-west of Spain). Conventional modelling of the number of forest fires in small areas may have a high error. For this reason, four area-level Poisson mixed models with time effects are proposed. The first two models contain independent time effects, whereas the random effects of the other models are distributed according to an autoregressive process AR(1). A parametric bootstrap algorithm is given to measure the accuracy of the plug-in predictor of fire number under the temporal models. A significant prediction improvement is observed when using Poisson regression models with random time effects. Analysis of historical data finds significant meteorological and socioeconomic variables explaining the number of forest fires by area and reveals the presence of a temporal correlation structure captured by the area-level Poisson mixed model with AR(1) time effects.

Generalized linear mixed models for multi-reader multi-case studies of diagnostic tests

2015 ◽  
Vol 26 (3) ◽  
pp. 1373-1388 ◽  
Author(s):  
Wei Liu ◽  
Norberto Pantoja-Galicia ◽  
Bo Zhang ◽  
Richard M Kotz ◽  
Gene Pennello ◽  
...  
Keyword(s):  
Mixed Models ◽  
Diagnostic Tests ◽  
Fixed Effects ◽  
Mixed Model ◽  
Linear Mixed Model ◽  
Generalized Linear Mixed Models ◽  
Characteristic Curve ◽  
Linear Mixed Models ◽  
Parametric Bootstrap ◽  
Pseudo Likelihood

Diagnostic tests are often compared in multi-reader multi-case (MRMC) studies in which a number of cases (subjects with or without the disease in question) are examined by several readers using all tests to be compared. One of the commonly used methods for analyzing MRMC data is the Obuchowski–Rockette (OR) method, which assumes that the true area under the receiver operating characteristic curve (AUC) for each combination of reader and test follows a linear mixed model with fixed effects for test and random effects for reader and the reader–test interaction. This article proposes generalized linear mixed models which generalize the OR model by incorporating a range-appropriate link function that constrains the true AUCs to the unit interval. The proposed models can be estimated by maximizing a pseudo-likelihood based on the approximate normality of AUC estimates. A Monte Carlo expectation-maximization algorithm can be used to maximize the pseudo-likelihood, and a non-parametric bootstrap procedure can be used for inference. The proposed method is evaluated in a simulation study and applied to an MRMC study of breast cancer detection.

Linear mixed model better than repeated measures analysis

2019 ◽  
Vol 30 (6) ◽  
pp. NP1-NP2 ◽  
Author(s):  
Işıl Kutluturk Karagoz ◽  
Berhan Keskin ◽  
Flora Özkalaycı ◽  
Ali Karagöz
Keyword(s):  
Mixed Models ◽  
Repeated Measures ◽  
Mixed Model ◽  
Linear Mixed Model ◽  
Linear Time ◽  
Case Series ◽  
Model Fit ◽  
Repeated Measures Analysis ◽  
Technical Issues ◽  
Better Than

We have some criticism regarding some technical issues. Mixed models have begun to play a pivotal role in statistical analyses and offer many advantages over more conventional analyses regarding repeated variance analyses. First, they allow to avoid conducting multiple t-tests; second, they can accommodate for within-patient correlation; third, they allow to incorporate not only a random coefficient, but also a random slope, typically ‘linear’ time in longitudinal case series when there are enough data and patients’ trajectories vary a lot and improving model fit.

Analysis of covariance in agronomy and crop research

2011 ◽  
Vol 91 (4) ◽  
pp. 621-641 ◽  
Author(s):  
Rong-Cai Yang ◽  
Patricia Juskiw
Keyword(s):  
Regression Analysis ◽  
Spatial Variation ◽  
Mixed Models ◽  
Mixed Model ◽  
Statistical Technique ◽  
Analysis Of Covariance ◽  
Statistical Software ◽  
Mixed Model Analysis ◽  
Crop Research ◽  
Advanced Topic

Yang, R.-C. and Juskiw, P. 2011. Analysis of covariance in agronomy and crop research. Can. J. Plant Sci. 91: 621–641. Analysis of covariance (ANCOVA) is a statistical technique that combines the methods of the analysis of variance (ANOVA) and regression analysis. However, ANCOVA is an advanced topic that often appears towards the end of many textbooks, and thus, it is either taught cursorily or ignored completely in many statistics classes. Additionally, many elaborated applications of ANCOVA to agronomy and crop research along with uses of the latest statistical software are rarely described in textbooks or classes. The objectives of this paper are to provide an overview on conventional ANCOVA and to introduce more advanced uses of ANCOVA under mixed models. We describe three elaborate applications including (i) the use of ANCOVA for dissecting dosage responses for different treatments, (ii) stability of treatments across multiple environments and (iii) removal of spatial variation that is not effectively controlled by blocking. These analyses illustrate that ANCOVA is either a simpler analysis or provides more information than conventional statistical methods. We provide a technical appendix ( Appendix A ) on principles and theory underlying mixed-model analysis of ANCOVA along with SAS programs ( Appendix B ) for more uses and in-depth understanding of this powerful technique in agronomy and crop research.

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