Fitting multi-population mortality models to socio-economic groups

2020 ◽  
pp. 1-29
Author(s):  
Jie Wen ◽  
Andrew J.G. Cairns ◽  
Torsten Kleinow
Keyword(s):  
Goodness Of Fit ◽  
Information Criterion ◽  
Age Effects ◽  
Period Effects ◽  
Mortality Models ◽  
Bayes Information Criterion ◽  
The Common ◽  
Population Mortality ◽  
Index Of Multiple Deprivation ◽  
Special Case

Abstract We compare results for 12 multi-population mortality models fitted to 10 distinct socio-economic groups in England, subdivided using the Index of Multiple Deprivation. Using the Bayes Information Criterion to compare models, we find that a special case of the common age effect (CAE) model fits best in a variety of situations, achieving the best balance between goodness of fit and parsimony. We provide a detailed discussion of key models to highlight which features are important. Group-specific period effects are found to be more important than group-specific age effects, and non-parametric age effects deliver significantly better results than parametric (e.g. linear) age effects. We also find that the addition of cohort effects is beneficial in some cases but not all. The preferred CAE model has the additional benefit of being coherent in the sense of Hyndman et al. ((2013) Demography50(1), 261–283); some of the other models considered are not.

scholarly journals Clustering-Based Extensions of the Common Age Effect Multi-Population Mortality Model

Risks ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 45
Author(s):  
Simon Schnürch ◽  
Torsten Kleinow ◽  
Ralf Korn
Keyword(s):  
Goodness Of Fit ◽  
Age Effect ◽  
Age Effects ◽  
Clustering Methods ◽  
Domain Specific ◽  
Mortality Model ◽  
Effect Model ◽  
Out Of Sample ◽  
The Common ◽  
Population Mortality

We introduce four variants of the common age effect model proposed by Kleinow, which describes the mortality rates of multiple populations. Our model extensions are based on the assumption of multiple common age effects, each of which is shared only by a subgroup of all considered populations. This makes the models more realistic while still keeping them as parsimonious as possible, improving the goodness of fit. We apply different clustering methods to identify suitable subgroups. Some of the algorithms are borrowed from the unsupervised learning literature, while others are more domain-specific. In particular, we propose and investigate a new model with fuzzy clustering, in which each population’s individual age effect is a linear combination of a small number of age effects. Due to their good interpretability, our clustering-based models also allow some insights in the historical mortality dynamics of the populations. Numerical results and graphical illustrations of the considered models and their performance in-sample as well as out-of-sample are provided.

Modeling Period Effects in Multi-Population Mortality Models: Applications to Solvency II

2014 ◽  
Vol 18 (1) ◽  
pp. 150-167 ◽  
Author(s):  
Rui Zhou ◽  
Yujiao Wang ◽  
Kai Kaufhold ◽  
Johnny Siu-Hang Li ◽  
Ken Seng Tan
Keyword(s):  
Solvency Ii ◽  
Period Effects ◽  
Mortality Models ◽  
Population Mortality

Evaluating the Goodness of Fit of Stochastic Mortality Models

2009 ◽  
Author(s):  
Kevin Dowd ◽  
Andrew J. G. Cairns ◽  
David P. Blake ◽  
Guy Coughlan ◽  
David Epstein ◽  
...  
Keyword(s):  
Goodness Of Fit ◽  
Stochastic Mortality ◽  
Stochastic Mortality Models ◽  
Mortality Models

scholarly journals Parsimonious Predictive Mortality Modeling by Regularization and Cross-Validation with and without Covid-Type Effect

Risks ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 5
Author(s):  
Karim Barigou ◽  
Stéphane Loisel ◽  
Yahia Salhi
Keyword(s):  
Life Insurance ◽  
Cross Validation ◽  
Cohort Effect ◽  
Information Criterion ◽  
Mortality Forecasting ◽  
Hand Model ◽  
Regularization Techniques ◽  
Bayes Information Criterion ◽  
The One ◽  
Regularized Model

Predicting the evolution of mortality rates plays a central role for life insurance and pension funds. Standard single population models typically suffer from two major drawbacks: on the one hand, they use a large number of parameters compared to the sample size and, on the other hand, model choice is still often based on in-sample criterion, such as the Bayes information criterion (BIC), and therefore not on the ability to predict. In this paper, we develop a model based on a decomposition of the mortality surface into a polynomial basis. Then, we show how regularization techniques and cross-validation can be used to obtain a parsimonious and coherent predictive model for mortality forecasting. We analyze how COVID-19-type effects can affect predictions in our approach and in the classical one. In particular, death rates forecasts tend to be more robust compared to models with a cohort effect, and the regularized model outperforms the so-called P-spline model in terms of prediction and stability.

scholarly journals Comparison of growth models to describe growth from birth to 6 years in a Beninese cohort of children with repeated measurements

BMJ Open ◽  
2020 ◽  
Vol 10 (9) ◽  
pp. e035785
Author(s):  
Shukrullah Ahmadi ◽  
Florence Bodeau-Livinec ◽  
Roméo Zoumenou ◽  
André Garcia ◽  
David Courtin ◽  
...  
Keyword(s):  
Growth Model ◽  
Goodness Of Fit ◽  
Growth Models ◽  
Information Criterion ◽  
Height Growth ◽  
Sub Saharan Africa ◽  
Individual Growth ◽  
Secondary Outcome ◽  
Growth Trajectories ◽  
Best Fitting

ObjectiveTo select a growth model that best describes individual growth trajectories of children and to present some growth characteristics of this population.SettingsParticipants were selected from a prospective cohort conducted in three health centres (Allada, Sekou and Attogon) in a semirural region of Benin, sub-Saharan Africa.ParticipantsChildren aged 0 to 6 years were recruited in a cohort study with at least two valid height and weight measurements included (n=961).Primary and secondary outcome measuresThis study compared the goodness-of-fit of three structural growth models (Jenss-Bayley, Reed and a newly adapted version of the Gompertz growth model) on longitudinal weight and height growth data of boys and girls. The goodness-of-fit of the models was assessed using residual distribution over age and compared with the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). The best-fitting model allowed estimating mean weight and height growth trajectories, individual growth and growth velocities. Underweight, stunting and wasting were also estimated at age 6 years.ResultsThe three models were able to fit well both weight and height data. The Jenss-Bayley model presented the best fit for weight and height, both in boys and girls. Mean height growth trajectories were identical in shape and direction for boys and girls while the mean weight growth curve of girls fell slightly below the curve of boys after neonatal life. Finally, 35%, 27.7% and 8% of boys; and 34%, 38.4% and 4% of girls were estimated to be underweight, wasted and stunted at age 6 years, respectively.ConclusionThe growth parameters of the best-fitting Jenss-Bayley model can be used to describe growth trajectories and study their determinants.

Ba-, Si- and vacancy-rich phlogopites from the talc-bearing sulfide ore deposit of La Creuse, Beaujolais, France

2018 ◽  
Vol 82 (5) ◽  
pp. 1187-1210
Author(s):  
Marie-Lola Pascal ◽  
Michel Fonteilles ◽  
Véronique Tournis ◽  
Benoît Baptiste ◽  
Jean-Louis Robert ◽  
...  
Keyword(s):  
Goodness Of Fit ◽  
Monoclinic Space Group ◽  
Excess Charge ◽  
Formula Unit ◽  
X Ray Diffraction ◽  
Ore Deposit ◽  
Sulfide Ore ◽  
The Common ◽  
The Stability ◽  
High Level

ABSTRACTBa-rich and Si-rich phlogopites occur in the talc-bearing rocks of the La Creuse sulfide ore deposit in Beaujolais, France. They form a group of compositions completely separated from the common Al-rich phlogopites that occur in the surrounding talc-free metasiltites and metarhyolites, with higher Ba and Mg and lower Al contents. The Ba-rich phlogopites have a relatively narrow compositional range (0.24 to 0.80 Ba per formula unit, for 44 valencies) with high and constant Si (5.8 atoms per formula unit, apfu) and Mg + Fe (5.6 apfu), probably buffered by the presence of talc. Compared to low-Al phlogopites from talc-free rocks, the excess charge introduced by the BaK–1 substitution is compensated by interlayer vacancies. Such a high level of interlayer vacancy (0.56 pfu), related to the talc-producing metasomatic conditions, is essential for the stability of this special group of Ba-rich and Si-rich phlogopites.Single crystal X-ray diffraction analyses were performed. Ba-rich and Si-rich phlogopite is monoclinic, space group C2/m, (R = 5.31%) with a = 5.3185(5), b = 9.2136(9), c = 10.1349(11) Å and β = 100.131(11)°. The occupancies of Mg/Fe and K/Ba were refined exploring different vacancies. The solutions giving the best R factor (4.77%) and goodness-of-fit (1.06) are obtained with 15% < vacancy < 40% at the interlayer site.

scholarly journals Model Selection in Peptide-receptor Radionuclide Therapy for an Accurate Determination of Time Integrated Activity Coefficients

2021 ◽  
Vol 2019 (1) ◽  
pp. 012079
Author(s):  
N Atikah ◽  
A Riana ◽  
A Dwi ◽  
Z Anwari ◽  
Misrawati ◽  
...  
Keyword(s):  
Model Selection ◽  
Activity Coefficients ◽  
Radionuclide Therapy ◽  
Goodness Of Fit ◽  
Accurate Determination ◽  
Peptide Receptor Radionuclide Therapy ◽  
Information Criterion ◽  
Selection Function ◽  
Pharmacokinetic Data ◽  
Peptide Receptor

Abstract Calculation of accurate time-integrated activity coefficients (TIACs) is desirable in nuclear medicine dosimetry. The accuracy of the calculated TIACs is highly dependent on the fit function. However, systematic studies of determining a good function for peptide-receptor radionuclide therapy (PRRT) in different patients have not been reported in the literature. The aim of this study was to individually determine the best function for the calculation of TIACs in tumor and kidneys using a model selection based on the goodness of fit criteria and Corrected Akaike Information Criterion (AICc). The data used in this study was pharmacokinetic data of 111In-DOTATATE in tumor and kidneys obtained from 4 PRRT patients. Eleven functions with various parameterizations were formulated to describe the biokinetic data of 111In-DOTATATE in tumor and kidneys. The model selection was performed by choosing the best function from the function with sufficient goodness of fit based on the smallest AICc. Based on the results of model selection, function A 1 -(λ 1+λphys )t was selected as the best function for all tumor and kidneys in patients with meningioma tumors. By using this function, the calculated of TIACs could be more accurate for future patients with meningioma tumor.

scholarly journals Tornumonkpe Distribution: Statistical Properties and Goodness of Fit

2021 ◽  
pp. 12-22
Author(s):  
Barinaadaa John Nwikpe
Keyword(s):  
Goodness Of Fit ◽  
Real Life ◽  
Mathematical Expression ◽  
Information Criterion ◽  
Moment Generating Function ◽  
Data Sets ◽  
The Moment ◽  
The One ◽  
Coefficient Of Skewness ◽  
New Distribution

A new sole parameter probability distribution named the Tornumonkpe distribution has been derived in this paper. The new model is a blend of gamma (2,  and gamma(3  distributions. The shape of its density for different values of the parameter has been shown.  The mathematical expression for the moment generating function, the first three raw moments, the second and third moments about the mean, the distribution of order statistics, coefficient of variation and coefficient of skewness has been given. The parameter of the new distribution was estimated using the method of maximum likelihood. The goodness of fit of the Tornumonkpe distribution was established by fitting the distribution to three real life data sets. Using -2lnL, Bayesian Information Criterion (BIC), and Akaike Information Criterion(AIC) as criterial for selecting the best fitting model, it was revealed that the new distribution outperforms the one parameter exponential, Shanker and Amarendra distributions for the data sets used.

scholarly journals Longitudinal Pattern of Aerenchyma Formation Using the Ti-Gompertz Model in Rice Adventitious Roots

2021 ◽  
Vol 12 ◽  
Author(s):  
Yun Chen ◽  
Guoming Li ◽  
Buhong Zhao ◽  
Yajun Zhang ◽  
Kun Liu ◽  
...  
Keyword(s):  
Adventitious Roots ◽  
Goodness Of Fit ◽  
Gompertz Model ◽  
Root Apex ◽  
Information Criterion ◽  
Ordinary Least Squares ◽  
Parameter Estimates ◽  
Aerenchyma Formation ◽  
Root Aerenchyma ◽  
Longitudinal Pattern

The longitudinal pattern of root aerenchyma formation of its relationship with the function of adventitious roots in rice remains unclear. In this study, the percentage of the aerenchyma area to the cross-sectional area (i.e., aerenchyma percentage) was fit with four non-linear models, namely, W0-Gompertz, Ti-Gompertz, logistic, and von Bertalanffy. Goodness-of-fit criteria such as the R2, the Akaike information criterion (AIC), and the Bayesian information criterion (BIC) were used to select the model. The bias of the parameters was evaluated using the difference between the ordinary least squares-based parameter estimates and the mean of 1,000 bootstrap-based parameter estimates and the symmetry of the distributions of these parameters. The results showed that the Ti-Gompertz model, which had a high goodness-of-fit with an R2 close to 1, lower AIC and BIC values, parameter estimates close to being unbiased, and good linear approximation, provided the best fit for the longitude pattern of rice aerenchyma formation with different root lengths among the competing models. Using the second- and third-order derivatives according to the distance from the root apex, the critical points of Ti-Gompertz were calculated. The rapid stage for aerenchyma formation was from the maximum acceleration point (1.38–1.76 cm from the root apex) to the maximum deceleration point (3.13–4.19 cm from the root apex). In this stage, the aerenchyma percentage increased by 5.3–15.7% per cm, suggesting that the cortical cells tended to die rapidly for the aerenchyma formation rather than for the respiration cost during this stage. Meanwhile, the volume of the aerenchyma of the entire roots could be computed using the integral function of the Ti-Gompertz model. We proposed that the longitudinal pattern of root aerenchyma formation modeled by the Ti-Gompertz model helped to deeply understand the relationship between the anatomical traits and physiological function in rice adventitious roots.

scholarly journals Contrast response functions in the visual wulst of the alert burrowing owl: a single-unit study

2016 ◽  
Vol 116 (4) ◽  
pp. 1765-1784 ◽  
Author(s):  
Pedro Gabrielle Vieira ◽  
João Paulo Machado de Sousa ◽  
Jerome Baron
Keyword(s):  
Single Unit ◽  
Goodness Of Fit ◽  
Dynamic Range ◽  
Information Criterion ◽  
Future Research ◽  
Response Functions ◽  
Athene Cunicularia ◽  
Low Contrast ◽  
Burrowing Owl ◽  
Contrast Response

The neuronal representation of luminance contrast has not been thoroughly studied in birds. Here we present a detailed quantitative analysis of the contrast response of 120 individual neurons recorded from the visual wulst of awake burrowing owls ( Athene cunicularia). Stimuli were sine-wave gratings presented within the cell classical receptive field and optimized in terms of eye preference, direction of drift, and spatiotemporal frequency. As contrast intensity was increased from zero to near 100%, most cells exhibited a monotonic response profile with a compressive, at times saturating, nonlinearity at higher contrasts. However, contrast response functions were found to have a highly variable shape across cells. With the view to capture a systematic trend in the data, we assessed the performance of four plausible models (linear, power, logarithmic, and hyperbolic ratio) using classical goodness-of-fit measures and more rigorous statistical tools for multimodel inferences based on the Akaike information criterion. From this analysis, we conclude that a high degree of model uncertainty is present in our data, meaning that no single descriptor is able on its own to capture the heterogeneous nature of single-unit contrast responses in the wulst. We further show that the generalizability of the hyperbolic ratio model established, for example, in the primary visual cortex of cats and monkeys is not tenable in the owl wulst mainly because most neurons in this area have a much wider dynamic range that starts at low contrast. The challenge for future research will be to understand the functional implications of these findings.

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