An Introduction to Generalized Linear Models, Second Edition

Dobson, Annette

doi:10.1201/9781420057683

Cited by 1,363 publications

(1,441 citation statements)

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“…The time series of residuals was assumed to be realized from a second order stationary random function with zero mean that was characterised by a marginal distribution function and a temporal correlation function. In the mixed model context the f m ( ) are referred to as the fixed effects and the r m ( ) as the random effects (Dobson, 1990).…”

Section: Temporal Modelling Of Groundwater Levelsmentioning

confidence: 99%

Spatio-temporal modelling of the status of groundwater droughts

Marchant

Bloomfield

2018

Journal of Hydrology

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An empirical (geo)statistical modelling scheme is developed to address the challenges of modelling the severity and distribution of groundwater droughts given their spatially and temporally heterogeneous nature and given typically highly irregular groundwater level observations in space and time. The scheme is tested using GWL measurements from 948 observation boreholes across the Chalk aquifer (UK) to estimate monthly groundwater drought status from 1960 to 2013. For each borehole, monthly GWLs are simulated using empirical mixed models where the fixed effects are based on applying an impulse response function to the local monthly precipitation. Modelled GWLs are standardised using the Standardised Groundwater Index (SGI) and the monthly SGI values interpolated across the aquifer to produce spatially distributed monthly maps of SGI drought status for 54 years for the Chalk. The mixed models include fewer parameters than comparable lumped parameter groundwater models while explaining a similar proportion (more than 65%) of GWL variation. In addition, the empirical modelling approach enables confidence bounds on the predicted GWLs and SGI values to be estimated without the need for prior information about catchment or aquifer parameters. The results of the modelling scheme are illustrated for three major episodes of multi-annual drought (1975-1976; 1988-1992; 2011-2012). They agree with previous documented analyses of the groundwater droughts while providing for the first time a systematic, spatially coherent characterisation of the events. The scheme is amenable to use in near real time to provide short term forecasts of groundwater drought status if suitable forecasts of the driving meteorology are available.

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Section: Temporal Modelling Of Groundwater Levelsmentioning

confidence: 99%

Spatio-temporal modelling of the status of groundwater droughts

Marchant

Bloomfield

2018

Journal of Hydrology

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“…This summary is necessarily brief; for a more comprehensive introduction to the general theory, see Krzanowski (1998, Ch. 5-8) or Dobson (2001).…”

Section: Generalized Linear Models For Rainfall Modelling Descriptionmentioning

confidence: 99%

Multi-site stochastic modelling of daily rainfall in Uganda

Kigobe

McIntyre

Wheater

et al. 2011

Hydrological Sciences Journal

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The availability of precipitation records in Uganda has significantly decreased since the 1970s, severely limiting the data available for hydrological modelling. This problem has been addressed in this study by using the generalized linear modelling (GLM) framework to develop stochastic daily rainfall models that have the capability for extending and infilling historic data sets. We have used a relatively sparse raingauge network in the Kyoga basin (in the Upper Nile) to reproduce spatial and temporal patterns of precipitation by fitting occurrence (logistic) and amounts (gamma) models as functions of dominant seasonal, climate and geographical controls. The GLMs were able to reproduce rainfall properties when predefined climatic zones are modelled independently. We were not able to represent the spatial variability of the equatorial climate with one integrated basin scale model, however this is not thought to preclude application to basin scale hydrological modelling.Key words generalized linear models; rainfall; stochastic models; climate change; Uganda; Kyoga; ENSO Modélisation stochastique multi-sites de la pluie journalière en Ouganda Résumé La disponibilité des données de précipitations en Ouganda a considérablement diminué depuis les années 1970, limitant fortement les données disponibles pour la modélisation hydrologique. Ce problème a été abordé dans cette étude dans le cadre de la modélisation linéaire généralisée (MLG), afin de développer des modèles stochastiques de pluie journalière qui puissent étendre et compléter les données historiques. Nous avons utilisé un réseau de pluviomètres de relativement faible densité dans le bassin du Kyoga (dans le Nil Supérieur), afin de reproduire les patrons spatiaux et temporels des précipitations en modélisant l'occurence (logistique) et les volumes (gamma) comme fonctions des forçages dominants saisonniers, climatiques et géographiques. Les MLG sont en mesure de reproduire les propriétés des pluies lorsque des zones climatiques pré-définies sont modélisées de façon indépendante. Nous n'avons pas pu représenter la variabilité spatiale du climat équatorial avec un modèle à l'échelle intégrée du bassin, cependant ceci ne semble pas devoir empêcher la mise en oeuvre d'une modélisation hydrologique à l'échelle du bassin.

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“…Tests for the significance of the effects in the models were done using the Wald statistic (Dobson, 1990). Such statistics are based on the asymptotic normality property of maximum likelihood estimates and computed as the generalized inner product of the parameter estimates with the respective variancecovariance matrix.…”

Section: Differences Among Habitats and Altitudesmentioning

confidence: 99%

The effect of local environmental heterogeneity on species diversity of alpine dung beetles (Coleoptera: Scarabaeidae)

Negro¹,

Palestrini²,

Giraudo³

et al. 2011

Eur. J. Entomol.

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Abstract. The relative effects of two components of mountain environmental heterogeneity, altitude (1500, 1700 and 2000 m a.s.l.) and habitat (pastures, coniferous forests, wet meadows, scrub and anthropogenic woods) on the diversity of dung beetles in an Italian alpine valley were determined. The additive gamma diversity analysis indicated that differences among habitats (ßH) were always smaller than those among altitudes (ßA), irrespective of the measures used; it also showed that the contribution of ßA to -diversity was higher than expected by chance for all the measures of species diversity used, whereas the contribution of ßH was significantly higher in the case of one measure only. Generalized linear models confirmed that altitude was the most important factor associated with local diversity, with all the diversity parameters considered progressively and significantly increasing with increasing altitude. Indicator species analyses revealed that dung beetle altitudinal and habitat diversity patterns depended on local choice of species, with preferences for altitudinal levels being more numerous and apparent than those for habitats. Despite the minor effect of habitat differences, comparing a three-habitat with a single-habitat scenario it was possible to demonstrate that greater habitat heterogeneity is associated with a significantly greater diversity of dung beetles. This study suggests that preservation of local environmental heterogeneity by means of traditional pastoral activities should be encouraged as a means of conserving the diversity of dung beetle species in the Alps.

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An Introduction to Generalized Linear Models, Second Edition

Cited by 1,363 publications

References 0 publications

Spatio-temporal modelling of the status of groundwater droughts

Spatio-temporal modelling of the status of groundwater droughts

Multi-site stochastic modelling of daily rainfall in Uganda

The effect of local environmental heterogeneity on species diversity of alpine dung beetles (Coleoptera: Scarabaeidae)

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