Determining the mean–variance relationship in generalized linear models—A parametric robust way

2011 ◽  
Vol 141 (1) ◽  
pp. 197-203 ◽  
Author(s):  
Tsung-Shan Tsou
Keyword(s):  
Generalized Linear Models ◽  
Linear Models ◽  
The Mean ◽  
Mean Variance

scholarly journals Association Between Pulsatile Components of Blood Pressure and Severe Tooth Loss in Rural Ecuador: The Three Villages Study

2020 ◽  
Vol 11 ◽  
pp. 215013272092867 ◽  
Author(s):  
Oscar H. Del Brutto ◽  
Robertino M. Mera ◽  
Bettsy Y. Recalde ◽  
Andrew P. Torpey ◽  
John P. Hill ◽  
...  
Keyword(s):  
Blood Pressure ◽  
Arterial Hypertension ◽  
Generalized Linear Models ◽  
Tooth Loss ◽  
Linear Models ◽  
Community Dwelling ◽  
Multivariate Models ◽  
Mediation Analyses ◽  
The Mean ◽  
Relevant Covariates

Background: Arterial hypertension has been associated with severe tooth loss, but differential associations with individual components of blood pressure (BP) have scarcely been investigated. We assessed the independent associations between pulsatile/steady components of BP and severe tooth loss in community-dwelling adults residing in 3 rural Ecuadorian villages. Methods: Individuals aged ≥40 years living in Atahualpa, El Tambo, and Prosperidad were identified during door-to-door surveys. Data collection focused on the number of remaining teeth and measurements of pulsatile/steady components of BP. Multivariate models were fitted to assess independent associations between pulsatile/steady BP components and severe tooth loss, after adjusting for relevant covariates. Results: A total of 1543 individuals were included. Oral exams identified 426 (28%) individuals with severe tooth loss. BP levels ≥140/90 mm Hg were determined in 481 (31%) individuals. The mean pulse pressure (PP) level was 55.3 ± 19 mm Hg. For systolic BP (SBP), the mean level was 133.1 ± 23.5 mm Hg, and for diastolic BP (DBP) it was 77.8 ± 11.5 mm Hg. Univariate models showed significant associations between severe tooth loss and SBP and PP, but not with DBP. However, the significance was taken away in fully adjusted generalized linear models. Age remained as an independent significant covariate in models using SBP and PP. Causal mediation analyses disclosed that percentages of the effect of severe tooth loss mediated by age were 99.5% for SBP and 98.9% for PP. Conclusion: This study shows that age captures most of the effect of the association between pulsatile components of BP and severe tooth loss.

scholarly journals The opposite effects of routine metabolic rate and metabolic rate during startle responses on variation in the predictability of behaviour in hermit crabs

Behaviour ◽  
2016 ◽  
Vol 153 (13-14) ◽  
pp. 1545-1566 ◽  
Author(s):  
Mariana Velasque ◽  
Mark Briffa
Keyword(s):  
Metabolic Rate ◽  
Generalized Linear Models ◽  
Startle Response ◽  
Linear Models ◽  
Elevated Temperatures ◽  
Hermit Crabs ◽  
Routine Metabolic Rate ◽  
Intraindividual Variation ◽  
The Mean ◽  
Pagurus Bernhardus

Studies on animal behaviour have suggested a link between personality and energy expenditure. However, most models assume constant variation within individuals, even though individuals vary between observations. Such variation is called intraindividual variation in behaviour (IIV). We investigate if IIV in the duration of the startle response is associated with metabolic rates (MR) in the hermit crabPagurus bernhardus. We repeatedly measured startle response durations and MR during each observation. We used double hierarchical generalized linear models to ask whether among and IIV in behaviour was underpinned by MR. We found no association between the mean duration of the startle responses and either routine MR or MR during startle response. Nevertheless, we found that IIV increased with MR during startle responses and decreased with routine MR. These results indicate that crabs with higher MR during startle responses behave less predictably, and that predictability is reduced during exposure to elevated temperatures.

scholarly journals Movement distances for four small mammals in two Atlantic forests fragments, Southern Brazil

2021 ◽  
Vol 16 (1) ◽  
pp. 11-18
Author(s):  
Daniela Oliveira de Lima ◽  
Luana Gabriele Arenhart Braun ◽  
Fabrício Luiz Skupien ◽  
Daniele Pereira Rodrigues ◽  
Jady de Oliveira Sausen
Keyword(s):  
Body Weight ◽  
Generalized Linear Models ◽  
Linear Models ◽  
Animal Movement ◽  
Individual Performance ◽  
Southern Brazil ◽  
Climatic Effects ◽  
Independent Variables ◽  
The Mean ◽  
Didelphis Albiventris

Animal movement has an important role in individual performance, species reproduction, population demography, and conservation, especially in fragmented landscapes. The distance moved by an individual may vary depending on individual needs, such as the search for food resources and sexual partners. Here we investigated which factors affect the distances between successive captures (hereafter DSC) for Akodon montensis, Oligoryzomys nigripes, Sooretamys angouya, and Didelphis albiventris. This study was conducted from April 2015 to October 2016 in two fragments in the south of Atlantic Forest biome through capture, mark and recapture technique. DSC was analyzed using Generalized Linear Models with Poisson distribution where the independent variables were sex, whether the animal was active or not in terms of reproduction, body weight, and climatic season. The mean DSC was greater for D. albiventris (44.6 ± 28.8 m), followed by S. angouya (31.9 ± 25.7 m), O. nigripes (25.8 ± 22.5 m) and A. montensis (18.9 ± 22.0 m). Males of all species moved larger DSC than females. Considering the rodents, reproductive animals also moved larger DSC than non-reproductive animals. Sex may have masked the effect of body weight, as males tend to be larger than females. Climatic effects were tested for A. montensis and O. nigripes, however, with diverse effects.

Generalized Linear Models

2021 ◽  
pp. 195-208
Author(s):  
Andy Hector
Keyword(s):  
Regression Analysis ◽  
Maximum Likelihood ◽  
Generalized Linear Models ◽  
Linear Models ◽  
Square Root ◽  
Link Function ◽  
Data Transformations ◽  
Normal Distributions ◽  
Equal Variance ◽  
The Mean

This chapter revisits a regression analysis to explore the normal least squares assumption of approximately equal variance. It also considers some of the data transformations that can be used to achieve this. A linear regression of transformed data is compared with a generalized linear-model equivalent that avoids transformation by using a link function and non-normal distributions. Generalized linear models based on maximum likelihood use a link function to model the mean (in this case a square-root link) and a variance function to model the variability (in this case the gamma distribution, where the variance increases as the square of the mean). The Box–Cox family of transformations is explained in detail.

Analysis of factors affecting superovulatory responses in ruminants

1995 ◽  
Vol 124 (1) ◽  
pp. 61-70 ◽  
Author(s):  
J. A. Woolliams ◽  
Z. W. Luo ◽  
B. Villanueva ◽  
D. Waddington ◽  
P. J. Broadbent ◽  
...  
Keyword(s):  
Generalized Linear Models ◽  
Linear Models ◽  
Negative Binomial ◽  
Commercial Application ◽  
Data Set ◽  
Factors Affecting ◽  
Binomial Distributions ◽  
Breeding Schemes ◽  
Over Dispersion ◽  
Mean Variance

SUMMARYData on ovulation rate and numbers of ova and transferable embryos recovered from superovulated cattle and sheep were analysed using generalized linear models, quasi-likelihood, restricted maximum likelihood (REML) and generalized linear mixed models (GLMMS). The data pertained to the operation of nucleus breeding schemes in cattle and the commercial application of embryo transfer in sheep.Results of the analyses showed that generalized linear models involving Poisson and Binomial distributions were inappropriate because of over-dispersion, and that analyses using quasi-likelihood to model negative binomial and β-binomial distributions were more suitable. Factors identified as important in determining the results in cattle were the number of previous superovulations (a higher proportion of transferable embryos were obtained in the initial flush compared to subsequent recoveries in two out of three sets of data), the donor (significant in all analyses with repeated recoveries) and its mate (significant in some analyses). In sheep, the use of pFSH or hMG for superovulation increased embryo yields above those obtained with PMSG + GnRH. Analyses of a further data set for sheep showed the effect of breed was ambiguous.The effects of donors and their mates were treated as random effects in analyses involving REML and GLMMS. Results showed that the repeatability of the number of transferable embryos produced per donor ranged between 0·13 and 0·23 in three sets of data and was significant in all cases. In these analyses the variance among mates was not significantly different from zero.The results of analyses were used to develop a random generator to simulate the numbers of ova and embryos recovered from a cow following superovulation. By sampling from negative binomial distributions where the scale factor used for each cow was a normally distributed deviate, distributions were obtained which had the same mean, variance and repeatability as those observed.

scholarly journals Correcting for vessel avoidance in acoustic-abundance estimates for herring

2008 ◽  
Vol 65 (6) ◽  
pp. 1036-1045 ◽  
Author(s):  
Vidar Hjellvik ◽  
Nils Olav Handegard ◽  
Egil Ona
Keyword(s):  
Generalized Linear Models ◽  
Linear Models ◽  
Clupea Harengus ◽  
Target Strength ◽  
Correction Factors ◽  
Correction Procedure ◽  
True Density ◽  
Abundance Estimates ◽  
The Mean ◽  
Specific Experiment

AbstractHjellvik, V., Handegard, N. O., and Ona, E. 2008. Correcting for vessel avoidance in acoustic-abundance estimates for herring. – ICES Journal of Marine Science, 65: 1036–1045. When a research vessel passes over a school or layer of herring (Clupea harengus), the fish may avoid the vessel by swimming downwards and horizontally. If the orientation of the fish is changed in this process, the mean target strength may also be altered. Consequently, the echo abundance measured by the relatively narrow echosounder beam does not always reflect the true density of the school in the undisturbed situation. This avoidance behaviour has been quantified in several experiments where a stationary, submerged transducer has been used to measure the changes in echo abundance during the passage of a survey vessel. Two approaches for correcting the echo abundance for avoidance are presented. The first is to correct in each depth layer separately, but this does not account for diving during vessel passage. The second is to correct the total echo abundance based on the mean depth of the fish at passage. Generalized linear models are fitted to the experimental data in both approaches. The parameters are estimated with uncertainty, which is taken into account when the fitted models are used for correcting standard survey data. The models were fitted to data from various experiments conducted during the period 1996–2004. The avoidance response differed strongly between experiments, indicating that correction factors estimated from one specific experiment should not be used uncritically in a standard correction procedure.

Sign in / Sign up

Export Citation Format

Share Document