scholarly journals TopREML: a topological restricted maximum likelihood approach to regionalize trended runoff signatures in stream networks

2015 ◽  
Vol 19 (6) ◽  
pp. 2925-2942 ◽  
Author(s):  
M. F. Müller ◽  
S. E. Thompson
Keyword(s):  
Maximum Likelihood ◽  
Covariance Structure ◽  
Restricted Maximum Likelihood ◽  
Best Linear Unbiased Predictor ◽  
Spatial Covariance ◽  
Spatially Correlated ◽  
Sensing Technology ◽  
Likelihood Approach ◽  
Best Linear Unbiased ◽  
Gauged Basins

Abstract. We introduce topological restricted maximum likelihood (TopREML) as a method to predict runoff signatures in ungauged basins. The approach is based on the use of linear mixed models with spatially correlated random effects. The nested nature of streamflow networks is taken into account by using water balance considerations to constrain the covariance structure of runoff and to account for the stronger spatial correlation between flow-connected basins. The restricted maximum likelihood (REML) framework generates the best linear unbiased predictor (BLUP) of both the predicted variable and the associated prediction uncertainty, even when incorporating observable covariates into the model. The method was successfully tested in cross-validation analyses on mean streamflow and runoff frequency in Nepal (sparsely gauged) and Austria (densely gauged), where it matched the performance of comparable methods in the prediction of the considered runoff signature, while significantly outperforming them in the prediction of the associated modeling uncertainty. The ability of TopREML to combine deterministic and stochastic information to generate BLUPs of the prediction variable and its uncertainty makes it a particularly versatile method that can readily be applied in both densely gauged basins, where it takes advantage of spatial covariance information, and data-scarce regions, where it can rely on covariates, which are increasingly observable via remote-sensing technology.

scholarly journals A topological restricted maximum likelihood (TopREML) approach to regionalize trended runoff signatures in stream networks

2015 ◽  
Vol 12 (1) ◽  
pp. 1355-1396 ◽  
Author(s):  
M. F. Müller ◽  
S. E. Thompson
Keyword(s):  
Maximum Likelihood ◽  
Covariance Structure ◽  
Restricted Maximum Likelihood ◽  
Best Linear Unbiased Predictor ◽  
Spatial Covariance ◽  
Spatially Correlated ◽  
Sensing Technology ◽  
Correlated Random Effects ◽  
Best Linear Unbiased ◽  
Gauged Basins

Abstract. We introduce TopREML as a method to predict runoff signatures in ungauged basins. The approach is based on the use of linear mixed models with spatially correlated random effects. The nested nature of streamflow networks is taken into account by using water balance considerations to constrain the covariance structure of runoff and to account for the stronger spatial correlation between flow-connected basins. The restricted maximum likelihood (REML) framework generates the best linear unbiased predictor (BLUP) of both the predicted variable and the associated prediction uncertainty, even when incorporating observable covariates into the model. The method was successfully tested in cross validation analyses on mean streamflow and runoff frequency in Nepal (sparsely gauged) and Austria (densely gauged), where it matched the performance of comparable methods in the prediction of the considered runoff signature, while significantly outperforming them in the prediction of the associated modeling uncertainty. TopREML's ability to combine deterministic and stochastic information to generate BLUPs of the prediction variable and its uncertainty makes it a particularly versatile method that can readily be applied in both densely gauged basins, where it takes advantage of spatial covariance information, and data-scarce regions, where it can rely on covariates, which are increasingly observable thanks to remote sensing technology.

scholarly journals ESTIMASI RATA-RATA LAMA SEKOLAH TINGKAT KECAMATAN DI KABUPATEN PADANG PARIAMAN DENGAN METODE EMPIRICAL BEST LINEAR UNBIASED PREDICTOR

2020 ◽  
Vol 2019 (1) ◽  
pp. 110-116
Author(s):  
Rita Diana ◽  
Rory Rory
Keyword(s):  
Maximum Likelihood ◽  
Small Area ◽  
Small Area Estimation ◽  
Restricted Maximum Likelihood ◽  
Best Linear Unbiased Predictor ◽  
Area Estimation ◽  
Best Linear Unbiased

Rata-rata lama sekolah penduduk umur 25 tahun ke atas merupakan salah satu indikator yang menggambarkan tingkat pendidikan penduduk secara keseluruhan. Dari 19 kabupaten/kota di Sumatera Barat, Kabupaten Padang Pariaman memiliki rata-rata lama sekolah terendah kedua setelah Kabupaten Kepulauan Mentawai. Penanganan rendahnya rata-rata lama sekolah membutuhkan tersedianya data rata-rata lama sekolah yang up to date dan menjangkau level wilayah yang kecil seperti kecamatan dan desa/nagari, agar kebijakan yang diambil pemerintah bisa tepat sasaran. Ketersediaan data tersebut belum mampu diakomodir oleh Badan Pusat Statistik (BPS), karena survei yang dilakukan oleh BPS dirancang untuk pendugaan data area besar, yaitu provinsi dan kabupaten. Salah satu solusi untuk masalah tersebut adalah dengan menggunakan metode estimasi tidak langsung, yaitu Small Area Estimation (SAE). Salah satu estimasi parameter secara tidak langsung berbasiskan model SAE adalah Empirical Best Linear Unbiased Predictor (EBLUP). Tujuan penelitian ini adalah melakukan estimasi rata-rata lama sekolah tingkat kecamatan di Kabupaten Padang Pariaman menggunakan metode EBLUP dengan prosedur maximum likelihood (ML) dan prosedur restricted maximum likelihood (REML). Variabel penyerta yang digunakan dalam penelitian ini yang diduga berpengaruh terhadap variabel respon adalah rasio jumlah SLTA/sederajat per 10.000 penduduk, rata-rata jarak terhadap SLTA/sederajat dan persentase keluarga pertanian. Hasil penelitian menunjukkan SAE metode EBLUP dengan prosedur REML menghasilkan nilai estimasi rata-rata lama sekolah tingkat kecamatan di kabupaten Padang Pariaman memiliki akurasi yang lebih baik dibandingkan dengan hasil estimasi langsung (direct) dan prosedur ML.

scholarly journals GENETIC PARAMETERS OF GIROLANDO CROSSBRED COWS IN DAIRY HERDS IN THE STATE OF ACRE, BRAZIL

2020 ◽  
Vol 23 (1cont) ◽  
Author(s):  
Andressa Pereira Braga ◽  
José Marques Carneiro Júnior ◽  
Antônia Kaylyanne Pinheiro ◽  
Maurício Santos Silva
Keyword(s):  
Maximum Likelihood ◽  
Milk Production ◽  
Genetic Parameters ◽  
Heritability Estimate ◽  
Restricted Maximum Likelihood ◽  
Dairy Herds ◽  
Genetic Progress ◽  
Linear Unbiased Prediction ◽  
Best Linear Unbiased ◽  
Selection For

This study aimed at estimating genetic parameters for milk production and conformation characteristics in Girolando crossbred dairy cows reared in the High and Low Acre region using the restricted maximum likelihood methodology, under an animal model. We estimated the variance components and genetic parameters using the REML/BLUP procedure (Restricted Maximum Likelihood Methodology/Best Linear Unbiased Prediction). The estimated average for milk production for 305 days of lactation (P305) was of 1523.25 ± 481.11 kg, with a heritability of 0.38 for this characteristic. The conformation characteristics showed no significant correlation with milk production. The phenotypical correlations between the linear characteristics of type were, in general, positive and moderate. The P305 obtained in this study can be considered low and indicates that there is a possibility of increasing milk production through selection in herds along with the use of tested and proven bulls. The heritability estimate found (0.38) indicates that there is genetic variability for milk production, demonstrating that selection for this characteristic would result in genetic progress.

subject k(i) gets formulation R, ε if response Y is from formulation T and ε if response Y is from formulation R. The means of T and R are then µ and µ , respectively. Then Var[s ] = σ , the between-subject variance for T , Var[s ] = σ , the between-subject variance for R, Var[s ] = σ , the subject-by-formulation interaction variance, Cov[s ] = ρσ σBR = σ , Var[ε ] = σ and Var[ε ] = σ . Further, we assume that all ε’s are pairwise independent, both within and between subjects. For the special case [ of equal group sizes (n Var[µˆ ] = [ σ − 2σ + ] (σ +σ )/2 /N = σ + (σ )/2 /N where N = 4n. The variances and interactions needed to assess IBE can easily be ob-tained by fitting an appropriate mixed model using proc mixed in SAS. The necessary SAS code for our example will be given below. However, before doing that we need some preliminary results. Using the SAS code we will obtain estimates σˆ , ωˆ , σˆ and σˆ , where ω is the between-subject covariance of R and T, and was earlier denoted by σ . These are normally distributed in the limit with a variance-covariance matrix appropriate to the structure of the fitted model. The model is fitted using REML (restricted maximum likelihood, see Section 6.3 of Chapter 6) and this can be done with SAS proc mixed with the REML option. In addition we fit an unstructured covariance structure using the type =UN option in proc mixed. The estimates of the vari-

2003 ◽  
pp. 366-366
Keyword(s):  
Maximum Likelihood ◽  
Covariance Matrix ◽  
Mixed Model ◽  
Covariance Structure ◽  
Restricted Maximum Likelihood ◽  
Preliminary Results ◽  
Equal Group ◽  
The Subject ◽  
Special Case ◽  
Interaction Variance

Estimation of genotypic correlation and heritability of apricot traits, using restricted maximum likelihood in repeated measures data

2016 ◽  
Vol 96 (3) ◽  
pp. 439-447 ◽  
Author(s):  
Ahmad Ismaili ◽  
Farhad Karami ◽  
Omidali Akbarpour ◽  
Abdolhossein Rezaei Nejad
Keyword(s):  
Maximum Likelihood ◽  
Repeated Measures ◽  
Mixed Model ◽  
Covariance Structure ◽  
Restricted Maximum Likelihood ◽  
Environment Interaction ◽  
Genotypic Correlation ◽  
Model Based ◽  
Repeated Measures Data ◽  
Heritability Estimation

In estimation of genetic parameters in perennial tree species on the basis of analysis of variance (ANOVA), heterogeneity of years and genotype × environment interaction for data sets during the juvenility to maturity life period is ignored. Therefore, a linear mixed model based on restricted maximum likelihood (REML) approximation for modeling of covariance structure of longitudinal data can improve our ability to analyze repeated measures data. In the present research, a modeling of variance-covariance structure by mixed model based on the REML approach has been used for characteristics of 26 apricot genotypes recorded during three years. Fitting unstructured covariance (UN) models for all traits indicated a great heterogeneity of variances among repeated years and the trends of response variables in the genotypes (except for RWC) was due to imperfect correlation of subjects measured in different years. Based on the same structure, positive correlations were estimated among fruit set, potassium content, and yield of pistil in repetitive years, and most traits showed high heritability estimation. To our knowledge, this is the first report in plant that genotypic correlation and heritability and their standard errors are estimated in a repeated measures data over years using REML approximation.

scholarly journals Parentesco na seleção para produtividade e teores de óleo e proteína em soja via modelos mistos

2013 ◽  
Vol 48 (9) ◽  
pp. 1246-1253 ◽  
Author(s):  
Larissa Correia de Melo Pinheiro ◽  
Pedro Ivo Vieira Good God ◽  
Vinícius Ribeiro Faria ◽  
Ane Gabrielle Oliveira ◽  
Aline Akemi Hasui ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Best Linear Unbiased Prediction ◽  
Restricted Maximum Likelihood ◽  
Linear Unbiased Prediction ◽  
Best Linear Unbiased ◽  
Unbiased Prediction

O objetivo deste trabalho foi avaliar influência da informação de parentesco na seleção de progênies de soja quanto à produtividade e aos teores de óleo e proteína, com base no uso de modelos mistos de predição dos valores genéticos. Novecentas progênies F4:6 e 200 progênies F4:7 de soja foram avaliadas nas safras 2010/2011 e 2011/2012, respectivamente. As progênies foram obtidas de cruzamentos múltiplos a partir de 57 progenitores. Os dados foram analisados por meio de modelos aleatórios (quadrados mínimos) e mistos BLUP/REML ("best linear unbiased prediction/restricted maximum likelihood"). Os maiores valores de ganhos preditos foram obtidos com o BLUP/REML. Os valores genéticos preditos com o método BLUP/REML, sem informação de parentesco, apresentaram alta correlação com aqueles obtidos com o modelo aleatório, além de detectada alta coincidência das progênies selecionadas. A inclusão da matriz de parentesco resultou na seleção de progênies diferentes e em maior acurácia na predição dos valores genéticos.

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