Crash Frequency Analysis with Generalized Additive Models

2008 ◽  
Vol 2061 (1) ◽  
pp. 39-45 ◽  
Author(s):  
Yuanchang Xie ◽  
Yunlong Zhang
Keyword(s):  
Generalized Linear Models ◽  
Linear Models ◽  
Generalized Additive Model ◽  
Negative Binomial ◽  
Generalized Additive Models ◽  
Additive Model ◽  
Additive Models ◽  
Crash Frequency ◽  
Data Set ◽  
Explanatory Variables

Recent crash frequency studies have been based primarily on generalized linear models, in which a linear relationship is usually assumed between the logarithm of expected crash frequency and other explanatory variables. For some explanatory variables, such a linear assumption may be invalid. It is therefore worthwhile to investigate other forms of relationships. This paper introduces generalized additive models to model crash frequency. Generalized additive models use smooth functions of each explanatory variable and are very flexible in modeling nonlinear relationships. On the basis of an intersection crash frequency data set collected in Toronto, Canada, a negative binomial generalized additive model is compared with two negative binomial generalized linear models. The comparison results show that the negative binomial generalized additive model performs best for both the Akaike information criterion and the fitting and predicting performance.

Climate Influences on Meningitis Incidence in Northwest Nigeria

2014 ◽  
Vol 6 (1) ◽  
pp. 62-76 ◽  
Author(s):  
Auwal F. Abdussalam ◽  
Andrew J. Monaghan ◽  
Vanja M. Dukić ◽  
Mary H. Hayden ◽  
Thomas M. Hopson ◽  
...  
Keyword(s):  
Generalized Linear Models ◽  
Linear Models ◽  
Generalized Additive Models ◽  
Skill Score ◽  
Additive Models ◽  
Maximum Temperature ◽  
Daily Maximum Temperature ◽  
Daily Maximum ◽  
Explanatory Variables ◽  
Score Statistics

Abstract Northwest Nigeria is a region with a high risk of meningitis. In this study, the influence of climate on monthly meningitis incidence was examined. Monthly counts of clinically diagnosed hospital-reported cases of meningitis were collected from three hospitals in northwest Nigeria for the 22-yr period spanning 1990–2011. Generalized additive models and generalized linear models were fitted to aggregated monthly meningitis counts. Explanatory variables included monthly time series of maximum and minimum temperature, humidity, rainfall, wind speed, sunshine, and dustiness from weather stations nearest to the hospitals, and the number of cases in the previous month. The effects of other unobserved seasonally varying climatic and nonclimatic risk factors that may be related to the disease were collectively accounted for as a flexible monthly varying smooth function of time in the generalized additive models, s(t). Results reveal that the most important explanatory climatic variables are the monthly means of daily maximum temperature, relative humidity, and sunshine with no lag; and dustiness with a 1-month lag. Accounting for s(t) in the generalized additive models explains more of the monthly variability of meningitis compared to those generalized linear models that do not account for the unobserved factors that s(t) represents. The skill score statistics of a model version with all explanatory variables lagged by 1 month suggest the potential to predict meningitis cases in northwest Nigeria up to a month in advance to aid decision makers.

scholarly journals Hierarchical generalized additive models: an introduction with mgcv

2018 ◽  
Author(s):  
Eric J Pedersen ◽  
David L. Miller ◽  
Gavin L. Simpson ◽  
Noam Ross
Keyword(s):  
Hierarchical Model ◽  
Generalized Additive Model ◽  
Generalized Additive Models ◽  
Additive Model ◽  
Additive Models ◽  
Complex Structures ◽  
Ecological Data ◽  
Nonlinear Functional ◽  
Functional Relationships ◽  
Statistical Issues

In this paper, we discuss an extension to two popular approaches to modelling complex structures in ecological data: the generalized additive model (GAM) and the hierarchical model (HGLM). The hierarchical GAM (HGAM), allows modelling of nonlinear functional relationships between covariates and outcomes where the shape of the function itself varies between different grouping levels. We describe the theoretical connection between these models, HGLMs and GAMs, explain how to model different assumptions about the degree of inter-group variability in functional response, and show how HGAMs can be readily fitted using existing GAM software, the mgcv package in R. We also discuss computational and statistical issues with fitting these models, and demonstrate how to fit HGAMs on example data.

Modeling of the spatial distribution of Pacific spiny dogfish (Squalus suckleyi) in the Gulf of Alaska using generalized additive and generalized linear models

2013 ◽  
Vol 70 (9) ◽  
pp. 1372-1385 ◽  
Author(s):  
Jason R. Gasper ◽  
Gordon H. Kruse
Keyword(s):  
Spatial Distribution ◽  
Generalized Linear Models ◽  
Linear Models ◽  
Negative Binomial ◽  
Fish Habitat ◽  
Additive Model ◽  
Gulf Of Alaska ◽  
Spiny Dogfish ◽  
Essential Fish Habitat ◽  
Mortality Estimation

The Pacific spiny dogfish (Squalus suckleyi) is a common bycatch species in the Gulf of Alaska. Their spatial distribution is poorly understood, as most catch is discarded at sea. We analyzed spiny dogfish spatial distribution from fishery-dependent and -independent observations of longline gear between 1996 and 2008 using generalized additive and generalized linear models. Poisson, negative binomial, and quasi-Poisson error structures were investigated; the quasi-Poisson generalized additive model fit best. Models showed that spiny dogfish catches were concentrated east of Kodiak Island in waters ≤100 m deep. Results facilitate design of future spiny dogfish assessment surveys and identification of areas in which to focus at-sea observations for fishing mortality estimation, and provide the basis for first-ever designation of spiny dogfish essential fish habitat, despite US legal requirements for essential fish habitat designations since 1996. Identified areas of high bycatch may expedite spatial management by indicating areas in which directed spiny dogfish fisheries could be focused or, conversely, areas in which heightened conservation and catch accounting efforts would be most effective to prevent overfishing of this long-lived, late-maturing species.

scholarly journals Forecasting for smart energy: an accurate and effificient negative binomial additive model

2020 ◽  
Vol 20 (2) ◽  
pp. 1000
Author(s):  
Yousef-Awwad Daraghmi ◽  
Eman Yaser Daraghmi ◽  
Motaz Daadoo ◽  
Samer Alsaadi
Keyword(s):  
Negative Binomial ◽  
Load Forecasting ◽  
Additive Model ◽  
Additive Models ◽  
Electric Load ◽  
Short Term ◽  
Real World Data ◽  
Smooth Functions ◽  
Data Set ◽  
Electric Load Forecasting

<div>Smart energy requires accurate and effificient short-term electric load forecasting to enable effificient</div><div>energy management and active real-time power control. Forecasting accuracy is inflfluenced by the char</div><div>acteristics of electrical load particularly overdispersion, nonlinearity, autocorrelation and seasonal patterns.</div><div>Although several fundamental forecasting methods have been proposed, accurate and effificient forecasting</div><div>methods that can consider all electric load characteristics are still needed. Therefore, we propose a novel</div><div>model for short-term electric load forecasting. The model adopts the negative binomial additive models</div><div>(NBAM) for handling overdispersion and capturing the nonlinearity of electric load. To address the season</div><div>ality, the daily load pattern is classifified into high, moderate, and low seasons, and the autocorrelation of</div><div>load is modeled separately in each season. We also consider the effificiency of forecasting since the NBAM</div><div>captures the behavior of predictors by smooth functions that are estimated via a scoring algorithm which has</div><div>low computational demand. The proposed NBAM is applied to real-world data set from Jericho city, and its</div><div>accuracy and effificiency outperform those of the other models used in this context.</div>

scholarly journals Implementation of a Generalized Additive Model (GAM) for Soybean Maturity Prediction in African Environments

Agronomy ◽  
2021 ◽  
Vol 11 (6) ◽  
pp. 1043
Author(s):  
Guillermo S. Marcillo ◽  
Nicolas F. Martin ◽  
Brian W. Diers ◽  
Michelle Da Fonseca Santos ◽  
Erica Pontes Leles ◽  
...  
Keyword(s):  
Minimum Temperature ◽  
Generalized Additive Model ◽  
Generalized Additive Models ◽  
Additive Model ◽  
Additive Models ◽  
Unbalanced Data ◽  
Genotypic Differences ◽  
Breeding Programs ◽  
Important Trait ◽  
New Crop

Time to maturity (TTM) is an important trait in soybean breeding programs. However, soybeans are a relatively new crop in Africa. As such, TTM information for soybeans is not yet as well defined as in other major producing areas. Multi-environment trials (METs) allow breeders to analyze crop performance across diverse conditions, but also pose statistical challenges (e.g., unbalanced data). Modern statistical methods, e.g., generalized additive models (GAMs), can flexibly smooth a range of responses while retaining observations that could be lost under other approaches. We leveraged 5 years of data from an MET breeding program in Africa to identify the best geographical and seasonal variables to explain site and genotypic differences in soybean TTM. Using soybean cycle features (e.g., minimum temperature, daylength) along with trial geolocation (longitude, latitude), a GAM predicted soybean TTM within 10 days of the average observed TTM (RMSE = 10.3; x = 109 days post-planting). Furthermore, we found significant differences between cultivars (p < 0.05) in TTM sensitivity to minimum temperature and daylength. Our results show potential to advance the design of maturity systems that enhance soybean planting and breeding decisions in Africa.

scholarly journals Hierarchical generalized additive models: an introduction with mgcv

2018 ◽  
Author(s):  
Eric J Pedersen ◽  
David L. Miller ◽  
Gavin L. Simpson ◽  
Noam Ross
Keyword(s):  
Hierarchical Model ◽  
Generalized Additive Model ◽  
Generalized Additive Models ◽  
Additive Model ◽  
Additive Models ◽  
Complex Structures ◽  
Ecological Data ◽  
Nonlinear Functional ◽  
Functional Relationships ◽  
Statistical Issues

In this paper, we discuss an extension to two popular approaches to modelling complex structures in ecological data: the generalized additive model (GAM) and the hierarchical model (HGLM). The hierarchical GAM (HGAM), allows modelling of nonlinear functional relationships between covariates and outcomes where the shape of the function itself varies between different grouping levels. We describe the theoretical connection between these models, HGLMs and GAMs, explain how to model different assumptions about the degree of inter-group variability in functional response, and show how HGAMs can be readily fitted using existing GAM software, the mgcv package in R. We also discuss computational and statistical issues with fitting these models, and demonstrate how to fit HGAMs on example data.

scholarly journals Hierarchical generalized additive models in ecology: an introduction with mgcv

PeerJ ◽  
2019 ◽  
Vol 7 ◽  
pp. e6876 ◽  
Author(s):  
Eric J. Pedersen ◽  
David L. Miller ◽  
Gavin L. Simpson ◽  
Noam Ross
Keyword(s):  
Generalized Additive Model ◽  
Generalized Additive Models ◽  
Additive Model ◽  
Additive Models ◽  
Complex Structures ◽  
Ecological Data ◽  
Mixed Effect ◽  
Nonlinear Functional ◽  
Functional Relationships ◽  
Statistical Issues

In this paper, we discuss an extension to two popular approaches to modeling complex structures in ecological data: the generalized additive model (GAM) and the hierarchical model (HGLM). The hierarchical GAM (HGAM), allows modeling of nonlinear functional relationships between covariates and outcomes where the shape of the function itself varies between different grouping levels. We describe the theoretical connection between HGAMs, HGLMs, and GAMs, explain how to model different assumptions about the degree of intergroup variability in functional response, and show how HGAMs can be readily fitted using existing GAM software, themgcvpackage in R. We also discuss computational and statistical issues with fitting these models, and demonstrate how to fit HGAMs on example data. All code and data used to generate this paper are available at:github.com/eric-pedersen/mixed-effect-gams.

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.

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