CALENDAR YEAR EFFECT MODELING FOR CLAIMS RESERVING IN HGLM

2019 ◽  
Vol 49 (03) ◽  
pp. 763-786 ◽  
Author(s):  
Patrizia Gigante ◽  
Liviana Picech ◽  
Luciano Sigalotti
Keyword(s):  
Fixed Effects ◽  
Linear Models ◽  
Parametric Bootstrap ◽  
Predictive Distribution ◽  
Linear Predictor ◽  
Calendar Effects ◽  
Year Effect ◽  
Run Off ◽  
Likelihood Approach ◽  
Risk Parameters

AbstractClaims reserving models are usually based on data recorded in run-off tables, according to the origin and the development years of the payments. The amounts on the same diagonal are paid in the same calendar year and are influenced by some common effects, for example, claims inflation, that can induce dependence among payments. We introduce hierarchical generalized linear models (HGLM) with risk parameters related to the origin and the calendar years, in order to model the dependence among payments of both the same origin year and the same calendar year. Besides the random effects, the linear predictor also includes fixed effects. All the parameters are estimated within the model by the h-likelihood approach. The prediction for the outstanding claims and an approximate formula to evaluate the mean square error of prediction are obtained. Moreover, a parametric bootstrap procedure is delineated to get an estimate of the predictive distribution of the outstanding claims. A Poisson-gamma HGLM with origin and calendar year effects is studied extensively and a numerical example is provided. We find that the estimates of the correlations can be significant for payments in the same calendar year and that the inclusion of calendar effects can determine a remarkable impact on the prediction uncertainty.

COMPOUND POISSON CLAIMS RESERVING MODELS: EXTENSIONS AND INFERENCE

2018 ◽  
Vol 48 (3) ◽  
pp. 1137-1156 ◽  
Author(s):  
Shengwang Meng ◽  
Guangyuan Gao
Keyword(s):  
Linear Models ◽  
Mean Squared Error ◽  
Predictive Distribution ◽  
Compound Poisson ◽  
Poisson Models ◽  
Squared Error ◽  
Run Off ◽  
Mean And Variance ◽  
The Individual ◽  
Over Dispersion

AbstractWe consider compound Poisson claims reserving models applied to the paid claims and to the number of payments run-off triangles. We extend the standard Poisson-gamma assumption to account for over-dispersion in the payment counts and to account for various mean and variance structures in the individual payments. Two generalized linear models are applied consecutively to predict the unpaid claims. A bootstrap is used to estimate the mean squared error of prediction and to simulate the predictive distribution of the unpaid claims. We show that the extended compound Poisson models make reasonable predictions of the unpaid claims.

Accuracy of p-values of approximate tests in testing for equality of means under unequal variances

2009 ◽  
Vol 59 (6) ◽  
Author(s):  
Júlia Volaufová
Keyword(s):  
Fixed Effects ◽  
Linear Models ◽  
Parametric Bootstrap ◽  
Small Sample ◽  
P Value ◽  
Sample Sizes ◽  
F Test ◽  
P Values ◽  
Unequal Variances ◽  
Equality Of Means

AbstractSeemingly, testing for fixed effects in linear models with variance-covariance components has been solved for decades. However, even in simple situations such as in fixed one-way model with heteroscedastic variances (a multiple means case of the Behrens-Fisher problem) the questions of statistical properties of various approximations of test statistics are still alive. Here we present a brief overview of several approaches suggested in the literature as well as those available in statistical software, accompanied by a simulation study in which the accuracy of p-values is studied. Our interest is limited here to the Welch’s test, the Satterthwaite-Fai-Cornelius test, the Kenward-Roger test, the simple ANOVA F-test, and the parametric bootstrap test. We conclude that for small sample sizes, regardless the number of compared means and the heterogeneity of variance, the ANOVA F-test p-value performs the best. For higher sample sizes (at least 5 per group), the parametric bootstrap performs well, and the Kenward-Roger test also performs well.

241 Skeletal Muscle Mitochondrial Capacities Are Impacted by Breed and Temperament in Young Angus and Brahman Steers

2021 ◽  
Vol 99 (Supplement_3) ◽  
pp. 127-127
Author(s):  
Chloey P Guy ◽  
Lauren T Wesolowski ◽  
Audrey L Earnhardt ◽  
Dustin Law ◽  
Don A Neuendorff ◽  
...  
Keyword(s):  
Skeletal Muscle ◽  
Fixed Effects ◽  
Linear Models ◽  
Citrate Synthase ◽  
Volume Density ◽  
Skeletal Muscle Mitochondria ◽  
Mitochondrial Volume ◽  
Mitochondrial Volume Density ◽  
Brahman Steers ◽  
The Impact

Abstract Temperament impacts skeletal muscle mitochondria in Brahman heifers, but this has not been investigated in steers or between cattle breeds. We hypothesized mitochondrial measures would be greater in Angus than Brahman, temperamental than calm steers, and the trapezius (TRAP) than the longissimus thoracis (LT) muscle. Samples from calm (n = 13 per breed), intermediate (n = 12 per breed), and temperamental (n=13 per breed) Angus and Brahman steers (mean±SD 10.0±0.8 mo) were evaluated for mitochondrial enzyme activities via colorimetry. Calm and temperamental LT samples were evaluated for oxidative phosphorylation (P) and electron transfer (E) capacities by high-resolution respirometry. Data were analyzed using linear models with fixed effects of breed, muscle, temperament, and all interactions. Brahman tended to have greater mitochondrial volume density (citrate synthase activity; CS) than Angus (P = 0.08), while intrinsic (relative to CS) mitochondrial function (cytochrome c oxidase activity) was greater in Angus than Brahman (P = 0.001) and greater in TRAP than LT (P = 0.008). Angus exhibited greater integrative (per mg tissue) and intrinsic P with complex I (PCI), P with complexes I+II (PCI+II), maximum noncoupled E, and E with complex II (ECII; P ≤ 0.04) and tended to have greater intrinsic leak (P = 0.1) than Brahman. Contribution of PCI to total E was greater in Angus than Brahman (P = 0.01), while contribution of ECII to total E was greater in Brahman than Angus (P = 0.05). A trend for the interaction of breed and temperament (P = 0.07) indicated calm Angus had the greatest intrinsic ECII (P ≤ 0.03) while intrinsic ECII was similar between temperamental Angus and calm and temperamental Brahman. Integrative PCI+II and ECII, and the contribution of PCI and PCI+II to overall E tended to be greater in temperamental than calm steers (P ≤ 0.09), while intrinsic ECII tended to be greater in calm than temperamental steers (P = 0.07). The impact of these mitochondrial differences on meat quality measures remains to be determined.

scholarly journals 150PREGNANCY AND PARTURITION FOLLOWING TRANSFER OF BOVINE EMBRYOS CULTURED IN TWO MEDIA UNDER TWO OXYGEN CONCENTRATIONS

2004 ◽  
Vol 16 (2) ◽  
pp. 197 ◽  
Author(s):  
A. Fischer-Brown ◽  
R. Monson ◽  
D. Northey ◽  
T. Kuhlka ◽  
J. Rutledge
Keyword(s):  
Birth Weight ◽  
Pregnancy Rate ◽  
Repeated Measures ◽  
Fixed Effects ◽  
Linear Models ◽  
Statistical Significance ◽  
Bovine Embryos ◽  
Crown Rump Length ◽  
Oxygen Treatment

Developmental aberrations following transfer of in vitro-produced bovine embryos can result in early gestational losses and offspring abnormalities. An ongoing study tests the hypothesis that such aberrations occur with equal frequency among commonly employed culture systems. In year 1, embryos were produced using oocytes from abattoir-derived ovaries (breed unspecified) and a proven Angus bull selected for low birth weight. IVC treatments were 2×2 factorial for medium (KSOMaa or SOFaa) and oxygen concentration (5% or 20%). Angus recipients (n=61; 32 cows, 29 heifers) were randomly allotted to treatments for Day 7 transfers. Pregnancy was diagnosed with ultrasound several times during gestation (Table 1). At parturition calf weight, shoulder height, chest circumference, crown-rump length, and humeral and femoral length data were collected. Statistical analyses (Statistical Analysis System, Cary, NC) were logistic regression with a binomial distribution for pregnancy rate, and the general linear models procedure for calf measurements; included were fixed effects of medium, oxygen, and their interaction, with additional fixed effects of dam parity and calf sex where appropriate. No significant effects of medium or oxygen were found for pregnancy rate or calf measurements other than birth weight. Mean birth weight was higher in the KSOM, 20% oxygen treatment (Table 1), and medium-oxygen interaction for calf weight was also significant (P<0.01). In year 2 embryos were produced using the same Angus bull and Angus oocytes. Angus recipients (n=38; 32 cows, 6 heifers) were randomly allotted to treatments. Fetal crown-rump lengths were measured by ultrasound weekly from Days 33 to 54 and were analyzed as repeated measures using the mixed procedure. Pregnancy outcome and LS means for crown-rump lengths are included in Table 1. Though insufficient recipient numbers preclude determination of statistical significance, of interest is the relatively small fetal size in early gestation and large birth weights in the KSOM, 20% oxygen treatment. This treatment also contained a Day 33 pregnancy, subsequently lost by Day 40, in which the fetus was too small to obtain an accurate measurement. Fetal growth will continue to be monitored throughout gestation. Data will be collected at parturition as in year 1, and pooled analyses will be done. Table 1

scholarly journals The Analysis of Reproduction in Population of the Slovak Spotted Dairy Cows

2019 ◽  
Vol 67 (6) ◽  
pp. 1419-1426
Author(s):  
Jozef Bujko ◽  
Juraj Candrák ◽  
Peter Strapák ◽  
Július Žitný ◽  
Cyril Hrnčár ◽  
...  
Keyword(s):  
Dairy Cows ◽  
Fixed Effects ◽  
Linear Models ◽  
Correlation Coefficients ◽  
Calving Interval ◽  
Factors Affecting ◽  
Actual Computation ◽  
Reproduction Traits ◽  
Days Open ◽  
Basic Statistical Analysis

The aim of study was to analyse the reproduction and factors affecting on reproduction traits of dairy cows in population of Slovak Spotted cattle from 2007 to 2016 the results for 37,274 dairy cows: days to first service (DFS), days open (DO), number of inseminations per conception (NIC), age of first calving (AFC) and calving interval (CI). The basic statistical analysis were analysed using the SAS version 9.3. For the actual computation a linear models with fixed effects was used: For the actual computation a linear models with fixed effects was used: yijklm = μ + HYSi + BTj+ Fk+ Bl +eijklm. The linear model represents coefficients determination R2 = 0.452117% (P < 0.001) for DFS, R2 = 0.377715% (P < 0.001) for DO, R2 = 0.348442% (P < 0.001) for NIC and R2 = 0.317128% (P < 0.001) for CI with all fixed effects. Correlation coefficients among DFS with DO, NIC, AFC and CI were r = 0.37275, r = -0.06881, r = 0.06493 and r = 0.08348. These coefficients were highly statistically significant (P < 0.001).

scholarly journals Association of casein micelle size and enzymatic curd strength and dry matter curd yield

2019 ◽  
Vol 49 (3) ◽  
Author(s):  
Denise Ribeiro de Freitas ◽  
Fernando Nogueira de Souza ◽  
Jamil Silvano de Oliveira ◽  
Diêgo dos Santos Ferreira ◽  
Cristiane Viana Guimarães Ladeira ◽  
...  
Keyword(s):  
Fixed Effects ◽  
Dry Matter ◽  
Linear Models ◽  
Favorable Effect ◽  
Casein Micelle ◽  
Casein Micelles ◽  
Micelle Size ◽  
Milk Protein Content ◽  
Bulk Tank ◽  
Cheese Production

ABSTRACT: The aim of the present study was to explore the association between milk protein content and casein micelle size and to examine the effects of casein micelle size on enzymatic curd strength and dry matter curd yield using reduced laboratory-scale cheese production. In this research, 140 bulk tank milk samples were collected at dairy farms. The traits were analyzed using two linear models, including only fixed effects. Smaller micelles were associated with higher κ-casein and lower αs-casein contents. The casein micellar size (in the absence of the αs-casein and κ-casein effects) did not affect the enzymatic curd strength; however, smaller casein micelles combined with higher fat, lactose, casein and κ-casein contents exhibited a favorable effect on the dry matter curd yield. Overall, results of the present study provide new insights into the importance of casein micelle size for optimizing cheese production.

scholarly journals Catalytic prior distributions with application to generalized linear models

2020 ◽  
Vol 117 (22) ◽  
pp. 12004-12010
Author(s):  
Dongming Huang ◽  
Nathan Stein ◽  
Donald B. Rubin ◽  
S. C. Kou
Keyword(s):  
Generalized Linear Models ◽  
Linear Models ◽  
Synthetic Data ◽  
Interval Estimation ◽  
Likelihood Estimation ◽  
Predictive Distribution ◽  
Point Estimation ◽  
Tuning Parameter ◽  
Working Model ◽  
Coverage Accuracy

A catalytic prior distribution is designed to stabilize a high-dimensional “working model” by shrinking it toward a “simplified model.” The shrinkage is achieved by supplementing the observed data with a small amount of “synthetic data” generated from a predictive distribution under the simpler model. We apply this framework to generalized linear models, where we propose various strategies for the specification of a tuning parameter governing the degree of shrinkage and study resultant theoretical properties. In simulations, the resulting posterior estimation using such a catalytic prior outperforms maximum likelihood estimation from the working model and is generally comparable with or superior to existing competitive methods in terms of frequentist prediction accuracy of point estimation and coverage accuracy of interval estimation. The catalytic priors have simple interpretations and are easy to formulate.

Analysis of Glacier Run-Off and Meteorological Observations

1972 ◽  
Vol 11 (63) ◽  
pp. 303-318 ◽  
Author(s):  
Gudmundur Gudmundsson ◽  
Guttormur Sigbjarnarson
Keyword(s):  
Spectral Analysis ◽  
Linear Relationship ◽  
Impulse Response ◽  
Linear Models ◽  
Time Lag ◽  
Diurnal Variations ◽  
Frequency Range ◽  
Western Margin ◽  
Run Off ◽  
Meteorological Observations

Abstract Linear models of the relationships between meteorological observations and the flow of river Tungnaá at the western margin of glacier Vatnajökull were investigated by means of spectral analysis and estimation of the impulse response. Most of the variation of Tungnaá is confined to the lowest frequencies and the diurnal variations. The temperature has most effect on the rapid variations around 1 cycle/day whereas the largest coherences with the precipitation are in the lowest frequencies. The wind explains over 20% of the variations in the frequency range from 0–1 cycle/day, but this is partly due to its coherence with the precipitation. The time lag between changes in the temperature and the river is about 2 h, but the time lag between precipitation and the river is longer. Analysis of longer records of daily observations from Ϸjórsá shows that the coherence of the run-off and temperature increases at frequencies too low to be estimated from these data. At frequencies over 1 cycle/day most of the observed variations of the river cannot be explained by means of a linear relationship with the meteorological series.

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.

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