Analysis of fixed effects linear models under heteroscedastic errors

1998 ◽  
Vol 37 (4) ◽  
pp. 399-408 ◽  
Author(s):  
Todd Smith ◽  
Shyamal D. Peddada
2021 ◽  
Vol 99 (Supplement_3) ◽  
pp. 127-127
Author(s):  
Chloey P Guy ◽  
Lauren T Wesolowski ◽  
Audrey L Earnhardt ◽  
Dustin Law ◽  
Don A Neuendorff ◽  
...  

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.


2004 ◽  
Vol 16 (2) ◽  
pp. 197 ◽  
Author(s):  
A. Fischer-Brown ◽  
R. Monson ◽  
D. Northey ◽  
T. Kuhlka ◽  
J. Rutledge

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


Author(s):  
Jozef Bujko ◽  
Juraj Candrák ◽  
Peter Strapák ◽  
Július Žitný ◽  
Cyril Hrnčár ◽  
...  

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).


2019 ◽  
Vol 49 (03) ◽  
pp. 763-786 ◽  
Author(s):  
Patrizia Gigante ◽  
Liviana Picech ◽  
Luciano Sigalotti

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.


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 ◽  
...  

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.


1993 ◽  
Vol 18 (1) ◽  
pp. 1-40 ◽  
Author(s):  
Robert J. Boik

This article considers two related issues concerning the analysis of interactions in complex linear models. The first issue concerns the omnibus test for interaction. Apparently, it is not well known that the usual F test for interaction can be replaced, in many applications, by a test that is more powerful against a certain class of alternatives. The competing test is based on the maximal product interaction contrast F statistic and achieves its power advantage by focusing solely on product contrasts. The maximal product interaction F test is reviewed and three new results are reported: (a) An extended table of exact critical values is computed, (b) a table of moment functions useful for approximating the p-value corresponding to an observed maximal F statistic is computed, and (c) a simulation study concerning the null distribution of the maximal F statistic when data are unbalanced or covariates are present is reported. It is conjectured that lack of balance or presence of covariates has no effect on the null distribution. The simulation results support the conjecture. The second issue concerns follow-up tests when the omnibus test is significant. It appears that researchers, in general, do not perform coherent follow-up tests on interactions. To make it easier for researchers to do so, an exposition on the use of product interaction contrasts and partial interactions in complex fixed-effects models is provided. The recommended omnibus and follow-up tests are illustrated on an educational data set analyzed using SAS ( SAS Institute, 1988 ) and SPSS (1990) .


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