Obtain Parameter Estimates Research Articles

Inference of the generalized-growth model via maximum likelihood estimation: A reflection on the impact of overdispersion

Recently, the generalized-growth model was introduced as a flexible approach to characterize growth dynamics of disease outbreaks during the early ascending phase. In this work, by using classical maximum likelihood estimation to obtain parameter estimates, we evaluate the impact of varying levels of overdispersion on the inference of the growth scaling parameter through comparing Poisson and Negative binomial models. In particular, under exponential and sub-exponential growth scenarios, we evaluate, via simulations, the error rate of making an incorrect characterization of early outbreak growth patterns. Simulation results show that the ability to correctly identify early outbreak growth patterns can be affected by overdispersion even when accounted for using the Negative binomial model. We exemplify our findings using data on five different outbreaks. Overall, our results show that estimates should be interpreted with caution when data are overdispersed.

Evaluating of beef cattle performance and profitability using robust regression analysis

There are several variables affecting the beef cattle performance and profitability. In the related literature, regression analysis is performed to find the contribution of the variables on profitability in different managing systems. Least squares (LS) estimation method is mostly used in regression analysis. However, it is optimal when the distribution of the error terms is normal. In this study, we revise Koknaroglu et al. (2005) study in which regression analysis is used under normality assumption. Different from the mentioned study, we use a robust estimation method called M-estimation since the error terms do not follow a normal distribution according to Shapiro-Wilk normality test. We obtain parameter estimates and their standard errors along with the coefficient of determination. It is observed that the results obtained based on M-estimation are more reliable than their LS counterparts with respect to 𝑅2 criterion.

Regression Analysis with Latent Variables by Partial Least Squares and Four Other Composite Scores: Consistency, Bias and Correction

Compared to the conventional covariance-based SEM (CB-SEM), partial-least-squares SEM (PLS-SEM) has an advantage in computation, which obtains parameter estimates by repeated least squares regression with a single dependent variable each time. Such an advantage becomes increasingly important with big data. However, the estimates of regression coefficients by PLS-SEM are biased in general. This article analytically compares the size of the bias in the regression coefficient estimators of the following methods: PLS-SEM; regression analysis using the Bartlett-factor-scores; regression analysis using the separate and joint regression-factor-scores, respectively; and regression analysis using the unweighted composite scores. A correction to parameter estimates following mode A of PLS-SEM is also proposed. Monte Carlo results indicate that regression analysis using other composite scores can be as good as PLS-SEM with respect to bias and efficiency/accuracy. Results also indicate that corrected estimates following PLS-SEM can be as good as the normal-distribution-based maximum likelihood estimates under CB-SEM.

Two–Stage Instrumental Variables Identification of Polynomial Wiener Systems with Invertible Nonlinearities

Abstract A new two-stage approach to the identification of polynomial Wiener systems is proposed. It is assumed that the linear dynamic system is described by a transfer function model, the memoryless nonlinear element is invertible and the inverse nonlinear function is a polynomial. Based on these assumptions and by introducing a new extended parametrization, the Wiener model is transformed into a linear-in-parameters form. In Stage I, parameters of the transformed Wiener model are estimated using the least squares (LS) and instrumental variables (IV) methods. Although the obtained parameter estimates are consistent, the number of parameters of the transformed Wiener model is much greater than that of the original one. Moreover, there is no unique relationship between parameters of the inverse nonlinear function and those of the transformed Wiener model. In Stage II, based on the assumption that the linear dynamic model is already known, parameters of the inverse nonlinear function are estimated uniquely using the IV method. In this way, not only is the parameter redundancy removed but also the parameter estimation accuracy is increased. A numerical example is included to demonstrate the practical effectiveness of the proposed approach.

Platelets and Hematocrit in the Survival Model of Dengue Hemorrhagic Fever (DHF) Sufferers in Palopo

This study aims to apply cox regression analysis to predict the patient's survival to dengue disease occurring in Palopo. This study uses clinical data, namely the results of laboratory tests to determine the effect on the patient's healing period. Laboratory test results used are platelets and hematocrit. By using the MPLE method to obtain parameter estimation in the cox regression model, it is known that platelets have a stronger effect for patient resistance on DHF than hematocrit. This is based on the p-value obtained from the analysis less than alpha (0.05), which is equal to 0.0433. Patients who had an average platelet below normal when experiencing DHF are longer in their recovery period. In addition, patients with DHF ≤ 2 days, the probability to survive and recover was 90%.

Relational bonds, customer engagement, and service quality

ABSTRACT Relational bonds represent a vital concept in relational marketing. Past research indicates that it can increase customer satisfaction and foster WOM. Although relational bonds have been shown to provide a long-lasting competitive advantage, the theoretical mechanisms underlying these relationships are less clear. This study investigates the relationships among relational bonds, customer engagement, service quality, satisfaction and WOM. A structured, self-administered questionnaire was distributed to customers who received aesthetic medicine services from a large medical center in Taiwan. The survey yielded 500 usable responses, with a response rate of 98.61%. The partial least squares method was utilized to obtain parameter estimates and test proposed hypotheses. Measurement accuracy was assured given satisfactory reliability and convergent/discriminant validity assessments, and all hypotheses were supported. The results indicate that relational bonds affect the extent of customer engagement, which in turn influences service quality. Service quality also leads to customer satisfaction and WOM.

Dependences of the Omori and Gutenberg–Richter parameters

Laboratory experiments on studying the aftershock regime are carried out with sandstone specimens under different axial loading and uniform compression and constant pore pressure. The aftershock sequences are modeled by the scenario of stepwise increasing axial loading of a specimen with strain control ensuring regular generation of aftershock sequences. The experiments are conducted on intact specimens and on the specimens with preliminarily formed shear macrofractures simulating natural faults. The experiments were conducted with multichannel recording of the acoustic emission (AE) signals which made it possible to locate the AE sources. Several types of the dependence of the acoustic activity relaxation parameters (parameters p and c of the modified Omori law and the Gutenberg–Richter b-value) on the level of acting stresses are revealed. The b-value decreases with the growth of axial stresses at all levels of uniform compression. In the case of fracture on the preexisting fault, the Omori relaxation parameter p increases with the growth of axial stresses whereas parameter c (the time delay before the onset of relaxation) decreases with the growth of axial stresses and increases with the rise of the level of uniform compression. In the case of a fracture of an undamaged specimen, parameter p remains unchanged as the axial stresses grow, whereas parameter c increases slightly. Parameter variations in the case of a complex stress state with both varying deviatoric (differential stresses) and spherical parts (effective pressure) of the stress tensor take on a unified form when expressed in terms of Coulomb stresses. It is hypothesized that the time delay of the aftershock activity relaxation is determined by the kinetics of fracture in accordance with the kinetic concept of strength in solids. This hypothesis is supported by exponential dependence of parameter c on stresses and on the effective strength of the medium revealed in the experiments. Under this hypothesis, the dependences of parameter c on the Coulomb stresses can be unified for different effective strength values with the use of Zhurkov’s formula for durability of materials. The obtained parameter estimates for the dependence of c on strength and stresses suggest that the c value is determined by the difference of the strength and the acting stresses, indicating how far the stress state of the medium is from the critical state corresponding to the ultimate strength.

Estimating the incidence and diagnosed proportion of HIV infections in Japan: a statistical modeling study.

BackgroundEpidemiological surveillance of HIV infection in Japan involves two technical problems for directly applying a classical backcalculation method, i.e., (i) all AIDS cases are not counted over time and (ii) people diagnosed with HIV have received antiretroviral therapy, extending the incubation period. The present study aimed to address these issues and estimate the HIV incidence and the proportion of diagnosed HIV infections, using a simple statistical model.MethodsFrom among Japanese nationals, yearly incidence data of HIV diagnoses and patients with AIDS who had not previously been diagnosed as HIV positive, from 1985 to 2017, were analyzed. Using the McKendrick partial differential equation, general convolution-like equations were derived, allowing estimation of the HIV incidence and the time-dependent rate of diagnosis. A likelihood-based approach was used to obtain parameter estimates.ResultsAssuming that the median incubation period was 10.0 years, the cumulative number of HIV infections was estimated to be 29,613 (95% confidence interval (CI): 29,059, 30,167) by the end of 2017, and the proportion of diagnosed HIV infections was estimated at 80.3% (95% CI [78.7%–82.0%]). Allowing the median incubation period to range from 7.5 to 12.3 years, the estimate of the proportion diagnosed can vary from 77% to 84%.DiscussionThe proportion of diagnosed HIV infections appears to have not yet reached 90% among Japanese nationals. Compared with the peak incidence from 2005–2008, new HIV infections have clearly been in a declining trend; however, there are still more than 1,000 new HIV infections per year in Japan. To increase the diagnosed proportion of HIV infections, it is critical to identify people who have difficulty accessing consultation, testing, and care, and to explore heterogeneous patterns of infection.

Estimating recent migration and population-size surfaces.

In many species a fundamental feature of genetic diversity is that genetic similarity decays with geographic distance; however, this relationship is often complex, and may vary across space and time. Methods to uncover and visualize such relationships have widespread use for analyses in molecular ecology, conservation genetics, evolutionary genetics, and human genetics. While several frameworks exist, a promising approach is to infer maps of how migration rates vary across geographic space. Such maps could, in principle, be estimated across time to reveal the full complexity of population histories. Here, we take a step in this direction: we present a method to infer maps of population sizes and migration rates associated with different time periods from a matrix of genetic similarity between every pair of individuals. Specifically, genetic similarity is measured by counting the number of long segments of haplotype sharing (also known as identity-by-descent tracts). By varying the length of these segments we obtain parameter estimates associated with different time periods. Using simulations, we show that the method can reveal time-varying migration rates and population sizes, including changes that are not detectable when using a similar method that ignores haplotypic structure. We apply the method to a dataset of contemporary European individuals (POPRES), and provide an integrated analysis of recent population structure and growth over the last ∼3,000 years in Europe.

Laboratory Modeling of Aftershock Sequences: Stress Dependences of the Omori and Gutenberg–Richter Parameters

Laboratory experiments on studying the aftershock regime are carried out on sandstone specimens at different levels of axial loading and uniform compression and at constant pore pressure. The aftershock sequences are modeled by the scenario of stepwise increasing axial loading of a specimen with strain control, which ensures the regular generation of aftershock sequences. The experiments are conducted on intact specimens and on those with preliminarily formed shear macrofractures simulating natural faults. The multichannel recording of the signals of acoustic emission (AE) during the experiments allowed locating the AE sources. Several types of the dependence of the parameters of relaxation of the acoustic activity—parameters p and c of the modified Omori law and the Gutenberg–Richter b-value—on the level of acting stresses are revealed. The b-value decreases with the growth of axial stresses at all levels of uniform compression. In the case of a fracture on the preexisting fault, the Omori relaxation parameter p increases with the growth of axial stresses; parameter c—the time delay before the onset of relaxation—decreases with the growth of axial stresses and increases with the rise of the level of uniform compression. In the case of a fracture of an undamaged specimen, parameter p remains unchanged with the growth of axial stresses, whereas parameter c increases slightly. Parameter variations in the case of a complex stress state with both varying deviatoric (differential stresses) and spherical parts (effective pressure) of the stress tensor take on a unified form when expressed in terms of Coulomb stresses. It is hypothesized that the time delay of the relaxation of the aftershock activity is determined by the kinetics of a fracture in accordance with the kinetic concept of strength in solids. This hypothesis is supported by the exponential dependences of parameter c on stresses and the effective strength of the medium which are revealed in the experiments. Under this hypothesis, based on Zhurkov’s formula for the durability of materials, it is possible to unify the dependences of parameter c on the Coulomb stresses at different effective strength values. The obtained parameter estimates for the dependence of c on strength and stresses suggest that the c value is determined by the difference of the strength and the acting stresses, thus indicating how far the stress state of the medium is from critically corresponding to the ultimate strength.

Reliability analysis of Birnbaum–Saunders model based on progressive type-II censoring

ABSTRACTThe reliability is derived based on progressively Type-II censored samples, when X and Y are independent Birnbaum–Saunders distributions with the same shape parameter but different scale parameters, and all of these parameters are unknown. The maximum likelihood estimate of R is derived and the approximate variance is constructed by combining delta and Monte Carlo (MC) methods. Then, Bayesian inference is performed to derive R and to predict the times to failure of the items censored in multiple stages of progressively type-II data with two Markov Chain MC (MCMC) algorithms. One algorithm is the hybrid Metropolis-Gibbs methodology, which considers the censored data to be unknown parameters along with model parameters and includes them in MCMC sampler to obtain parameter estimation. In the other algorithm, the unknown parameters are considered in the Metropolis methodology to construct Bayesian estimation and then to predict censored observations. Two illustrative examples are finally provided to examine the performance of the proposed methods.

Estimating reducible stochastic differential equations by conversion to a least-squares problem

Stochastic differential equations (SDEs) are increasingly used in longitudinal data analysis, compartmental models, growth modelling, and other applications in a number of disciplines. Parameter estimation, however, currently requires specialized software packages that can be difficult to use and understand. This work develops and demonstrates an approach for estimating reducible SDEs using standard nonlinear least squares or mixed-effects software. Reducible SDEs are obtained through a change of variables in linear SDEs, and are sufficiently flexible for modelling many situations. The approach is based on extending a known technique that converts maximum likelihood estimation for a Gaussian model with a nonlinear transformation of the dependent variable into an equivalent least-squares problem. A similar idea can be used for Bayesian maximum a posteriori estimation. It is shown how to obtain parameter estimates for reducible SDEs containing both process and observation noise, including hierarchical models with either fixed or random group parameters. Code and examples in R are given. Univariate SDEs are discussed in detail, with extensions to the multivariate case outlined more briefly. The use of well tested and familiar standard software should make SDE modelling more transparent and accessible. Keywords: stochastic processes; longitudinal data; growth curves; compartmental models; mixed-effects; R

REGRESI POISSON BIVARIAT DENGAN KOVARIAN MERUPAKAN FUNGSI DARI VARIABEL BEBAS

Poisson regression is a regression model which often used to analyze the count data. In this study, poisson regression has been used bivariate poisson regression where the regression is a method which is used to model a pair of correlated count data with multiple predictor variables. The model is used covariance which has a function of the independent variable. The purposes of this study is obtain parameter estimates, test statistics of bivariate poisson regression, and determine the factors that influence of infant mortality and maternal mortality. The data is used from the infant mortality and maternal mortality in Central Java 2015. Based on the result, the parameter estimation of poisson bivariate regression model using maximum likelihood (MLE) method. The results obtained from the parameter estimation are not close form so it needs to be done by Newton-Raphson iteration method. In testing the hypothesis using the Maximum Likelihood Ratio Test method (MLRT) by comparing the value between likelihood below H0 and likelihood below population. Partial of parameters model λ1 (infant mortality) there are six independent variables that have significant influence, namely, delivery by health personnel (X1), pregnant women carry out the program K4 (X3), pregnant women who get Fe3 tablet (X4), handling obstetric complication (X5), exclusively breastfed infants (X7), and households living a clean and healthy life (X8). While for model λ2 (maternal death) only variable handling of neonatal complication (X6) which have no significant influence to response variable.

Estimation of agent-based models using sequential Monte Carlo methods

Estimation of agent-based models is currently an intense area of research. Recent contributions have to a large extent resorted to simulation-based methods mostly using some form of simulated method of moments estimation (SMM). There is, however, an entire branch of statistical methods that should appear promising, but has to our knowledge never been applied so far to estimate agent-based models in economics and finance: Markov chain Monte Carlo methods designed for state space models or models with latent variables. This latter class of models seems particularly relevant as agent-based models typically consist of some latent and some observable variables since not all the characteristics of agents would mostly be observable. Indeed, one might often not only be interested in estimating the parameters of a model, but also to infer the time development of some latent variable. However, agent-based models when interpreted as latent variable models would be typically characterized by non-linear dynamics and non-Gaussian fluctuations and, thus, would require a computational approach to statistical inference. Here we resort to Sequential Monte Carlo (SMC) estimation based on a particle filter. This approach is used here to numerically approximate the conditional densities that enter into the likelihood function of the problem. With this approximation we simultaneously obtain parameter estimates and filtered state probabilities for the unobservable variable(s) that drive(s) the dynamics of the observable time series. In our examples, the observable series will be asset returns (or prices) while the unobservable variables will be some measure of agents’ aggregate sentiment. We apply SMC to two selected agent-based models of speculative dynamics with somewhat different flavor. The empirical application to a selection of financial data includes an explicit comparison of the goodness-of-fit of both models.

Model selection for the localized mixture of experts models

ABSTRACTIn this paper, we propose a penalized likelihood method to simultaneous select covariate, and mixing component and obtain parameter estimation in the localized mixture of experts models. We develop an expectation maximization algorithm to solve the proposed penalized likelihood procedure, and introduce a data-driven procedure to select the tuning parameters. Extensive numerical studies are carried out to compare the finite sample performances of our proposed method and other existing methods. Finally, we apply the proposed methodology to analyze the Boston housing price data set and the baseball salaries data set.

The Variance Process Implied in VIX Options: Affine vs. Non-Affine Models

We use the informational content of VIX derivatives to infer implications on the non-affine modeling of the stock returns' variance dynamics. We find that both a non-affine diffusion and variance jumps are necessary to capture the short- and long-term implied volatility distribution. In- and out-of-sample, a linear CEV jump-diffusion model leads to valuation errors that are negligibly affected by the VIX options' maturity and moneyness. For this setup, we obtain parameter estimates that are comparable to the stock option pricing literature. Compared to a linear specification, we find that estimating the diffusion exponent freely does not lead to significantly better results.

Modelling breast cancer tumour growth for a stable disease population.

Statistical models of breast cancer tumour progression have been used to further our knowledge of the natural history of breast cancer, to evaluate mammography screening in terms of mortality, to estimate overdiagnosis, and to estimate the impact of lead-time bias when comparing survival times between screen detected cancers and cancers found outside of screening programs. Multi-state Markov models have been widely used, but several research groups have proposed other modelling frameworks based on specifying an underlying biological continuous tumour growth process. These continuous models offer some advantages over multi-state models and have been used, for example, to quantify screening sensitivity in terms of mammographic density, and to quantify the effect of body size covariates on tumour growth and time to symptomatic detection. As of yet, however, the continuous tumour growth models are not sufficiently developed and require extensive computing to obtain parameter estimates. In this article, we provide a detailed description of the underlying assumptions of the continuous tumour growth model, derive new theoretical results for the model, and show how these results may help the development of this modelling framework. In illustrating the approach, we develop a model for mammography screening sensitivity, using a sample of 1901 post-menopausal women diagnosed with invasive breast cancer.

Extended models for nosocomial infection: parameter estimation and model selection.

We consider extensions to previous models for patient level nosocomial infection in several ways, provide a specification of the likelihoods for these new models, specify new update steps required for stochastic integration, and provide programs that implement these methods to obtain parameter estimates and model choice statistics. Previous susceptible-infected models are extended to allow for a latent period between initial exposure to the pathogen and the patient becoming themselves infectious, and the possibility of decolonization. We allow for multiple facilities, such as acute care hospitals or long-term care facilities and nursing homes, and for multiple units or wards within a facility. Patient transfers between units and facilities are tracked and accounted for in the models so that direct importation of a colonized individual from one facility or unit to another might be inferred. We allow for constant transmission rates, rates that depend on the number of colonized individuals in a unit or facility, or rates that depend on the proportion of colonized individuals. Statistical analysis is done in a Bayesian framework using Markov chain Monte Carlo methods to obtain a sample of parameter values from their joint posterior distribution. Cross validation, deviance information criterion and widely applicable information criterion approaches to model choice fit very naturally into this framework and we have implemented all three. We illustrate our methods by considering model selection issues and parameter estimation for data on methicilin-resistant Staphylococcus aureus surveillance tests over 1 year at a Veterans Administration hospital comprising seven wards.

On Markov-switching periodic ARMA models

ABSTRACTIn this work, we propose a generalization of the classical Markov-switching ARMA models to the periodic time-varying case. Specifically, we propose a Markov-switching periodic ARMA (MS-PARMA) model. In addition of capturing regime switching often encountered during the study of many economic time series, this new model also captures the periodicity feature in the autocorrelation structure. We first provide some probabilistic properties of this class of models, namely the strict periodic stationarity and the existence of higher-order moments. We thus propose a procedure for computing the autocovariance function where we show that the autocovariances of the MS-PARMA model satisfy a system of equations similar to the PARMA Yule–Walker equations. We propose also an easily implemented algorithm which can be used to obtain parameter estimates for the MS-PARMA model. Finally, a simulation study of the performance of the proposed estimation method is provided.

Performance of objective functions and optimisation procedures for parameter estimation in system biology models

Mathematical modelling of signalling pathways aids experimental investigation in system and synthetic biology. Ever increasing data availability prompts the development of large dynamic models with numerous parameters. In this paper, we investigate how the number of unknown parameters affects the convergence of three frequently used optimisation algorithms and four objective functions. We compare objective functions that use data-driven normalisation of the simulations with those that use scaling factors. The data-driven normalisation of the simulation approach implies that simulations are normalised in the same way as the data, making both directly comparable. The scaling factor approach, which is commonly used for parameter estimation in dynamic systems, introduces scaling factors that multiply the simulations to convert them to the scale of the data. Here we show that the scaling factor approach increases, compared to data-driven normalisation of the simulations, the degree of practical non-identifiability, defined as the number of directions in the parameter space, along which parameters are not identifiable. Further, the results indicate that data-driven normalisation of the simulations greatly improve the speed of convergence of all tested algorithms when the overall number of unknown parameters is relatively large (74 parameters in our test problems). Data-driven normalisation of the simulations also markedly improve the performance of the non-gradient-based algorithm tested even when the number of unknown parameters is relatively small (10 parameters in our test problems). As the models and the unknown parameters increase in size, the data-driven normalisation of the simulation approach can be the preferred option, because it does not aggravate non-identifiability and allows for obtaining parameter estimates in a reasonable amount of time.