Three-part model for fractional response variables with application to Chinese household health insurance coverage

A survey on health insurance was conducted in July and August of 2011 in three major cities in China. In this study, we analyze the household coverage rate, which is an important index of the quality of health insurance. The coverage rate is restricted to the unit interval [0, 1], and it may differ from other rate data in that the “two corners” are nonzero. That is, there are nonzero probabilities of zero and full coverage. Such data may also be encountered in economics, finance, medicine, and many other areas. The existing approaches may not be able to properly accommodate such data. In this study, we develop a three-part model that properly describes fractional response variables with non-ignorable zeros and ones. We investigate estimation and inference under two proportional constraints on the regression parameters. Such constraints may lead to more lucid interpretations and fewer unknown parameters and hence more accurate estimation. A simulation study is conducted to compare the performance of constrained and unconstrained models and show that estimation under constraint can be more efficient. The analysis of household health insurance coverage data suggests that household size, income, expense, and presence of chronic disease are associated with insurance coverage.     

Bayesian model comparison for compartmental models with applications in positron emission tomography

We develop strategies for Bayesian modelling as well as model comparison, averaging and selection for compartmental models with particular emphasis on those that occur in the analysis of positron emission tomography (PET) data. Both modelling and computational issues are considered. Biophysically inspired informative priors are developed for the problem at hand, and by comparison with default vague priors it is shown that the proposed modelling is not overly sensitive to prior specification. It is also shown that an additive normal error structure does not describe measured PET data well, despite being very widely used, and that within a simple Bayesian framework simultaneous parameter estimation and model comparison can be performed with a more general noise model. The proposed approach is compared with standard techniques using both simulated and real data. In addition to good, robust estimation performance, the proposed technique provides, automatically, a characterisation of the uncertainty in the resulting estimates which can be considerable in applications such as PET.     

Modelling small and medium enterprise loan defaults as rare events: the generalized extreme value regression model

A pivotal characteristic of credit defaults that is ignored by most credit scoring models is the rarity of the event. The most widely used model to estimate the probability of default is the logistic regression model. Since the dependent variable represents a rare event, the logistic regression model shows relevant drawbacks, for example, underestimation of the default probability, which could be very risky for banks. In order to overcome these drawbacks, we propose the generalized extreme value regression model. In particular, in a generalized linear model (GLM) with the binary-dependent variable we suggest the quantile function of the GEV distribution as link function, so our attention is focused on the tail of the response curve for values close to one. The estimation procedure used is the maximum-likelihood method. This model accommodates skewness and it presents a generalisation of GLMs with complementary log–log link function. We analyse its performance by simulation studies. Finally, we apply the proposed model to empirical data on Italian small and medium enterprises.     

A note on statistical method for genotype calling of high-throughput single-nucleotide polymorphism arrays

We study the genotype calling algorithms for the high-throughput single-nucleotide polymorphism (SNP) arrays. Building upon the novel SNP-robust multi-chip average preprocessing approach and the state-of-the-art corrected robust linear model with Mahalanobis distance (CRLMM) approach for genotype calling, we propose a simple modification to better model and combine the information across multiple SNPs with empirical Bayes modeling, which could often significantly improve the genotype calling of CRLMM. Through applications to the HapMap Trio data set and a non-HapMap test set of high quality SNP chips, we illustrate the competitive performance of the proposed method.     

Causality and interdependence analysis in linear econometric models with an application to fertility

This paper is an applied analysis of the causal structure of linear multi-equational econometric models. Its aim is to identify the kind of relationships linking the endogenous variables of the model, distinguishing between causal links and feedback loops. The investigation is first carried out within a deterministic framework and then moves on to show how the results may change inside a more realistic stochastic context. The causal analysis is then specifically applied to a linear simultaneous equation model explaining fertility rates. The analysis is carried out by means of a specific RATS programming code designed to show the specific nature of the relationships within the model.     

Improving TAIEX forecasting using fuzzy time series with Box–Cox power transformation

Box–Cox together with our newly proposed transformation were implemented in three different real world empirical problems to alleviate noisy and the volatility effect of them. Consequently, a new domain was constructed. Subsequently, universe of discourse for transformed data was established and an approach for calculating effective length of the intervals was then proposed. Considering the steps above, the initial forecasts were performed using frequently used fuzzy time series (FTS) methods on transformed data. Final forecasts were retrieved from initial forecasted values by proper inverse operation. Comparisons of the results demonstrate that the proposed method produced more accurate forecasts compared with existing FTS on original data.     

Estimation under modified Weibull distribution based on right censored generalized order statistics

In this paper, the maximum likelihood (ML) and Bayes, by using Markov chain Monte Carlo (MCMC), methods are considered to estimate the parameters of three-parameter modified Weibull distribution (MWD(β, τ, λ)) based on a right censored sample of generalized order statistics (gos). Simulation experiments are conducted to demonstrate the efficiency of the proposed methods. Some comparisons are carried out between the ML and Bayes methods by computing the mean squared errors (MSEs), Akaike's information criteria (AIC) and Bayesian information criteria (BIC) of the estimates to illustrate the paper. Three real data sets from Weibull(α, β) distribution are introduced and analyzed using the MWD(β, τ, λ) and also using the Weibull(α, β) distribution. A comparison is carried out between the mentioned models based on the corresponding Kolmogorov–Smirnov (K–S) test statistic, {AIC and BIC} to emphasize that the MWD(β, τ, λ) fits the data better than the other distribution. All parameters are estimated based on type-II censored sample, censored upper record values and progressively type-II censored sample which are generated from the real data sets.     

Generalized estimating equations for mixtures with varying concentrations

A finite mixture model is considered in which the mixing probabilities vary from observation to observation. A parametric model is assumed for one mixture component distribution, while the others are nonparametric nuisance parameters. Generalized estimating equations (GEE) are proposed for the semi‐parametric estimation. Asymptotic normality of the GEE estimates is demonstrated and the lower bound for their dispersion (asymptotic covariance) matrix is derived. An adaptive technique is developed to derive estimates with nearly optimal small dispersion. An application to the sociological analysis of voting results is discussed. The Canadian Journal of Statistics 41: 217–236; 2013 © 2013 Statistical Society of Canada     

A likelihood ratio test for goodness‐of‐fit of recessive and dominant models for case–control studies

Testing goodness‐of‐fit of commonly used genetic models is of critical importance in many applications including association studies and testing for departure from Hardy–Weinberg equilibrium. Case–control design has become widely used in population genetics and genetic epidemiology, thus it is of interest to develop powerful goodness‐of‐fit tests for genetic models using case–control data. This paper develops a likelihood ratio test (LRT) for testing recessive and dominant models for case–control studies. The LRT statistic has a closed‐form formula with a simple $\chi^{2}(1)$ null asymptotic distribution, thus its implementation is easy even for genome‐wide association studies. Moreover, it has the same power and optimality as when the disease prevalence is known in the population. The Canadian Journal of Statistics 41: 341–352; 2013 © 2013 Statistical Society of Canada     

A Markov regime‐switching model for crude‐oil markets: Comparison of composite likelihood and full likelihood

We use the two‐state Markov regime‐switching model to explain the behaviour of the WTI crude‐oil spot prices from January 1986 to February 2012. We investigated the use of methods based on the composite likelihood and the full likelihood. We found that the composite‐likelihood approach can better capture the general structural changes in world oil prices. The two‐state Markov regime‐switching model based on the composite‐likelihood approach closely depicts the cycles of the two postulated states: fall and rise. These two states persist for on average 8 and 15 months, which matches the observed cycles during the period. According to the fitted model, drops in oil prices are more volatile than rises. We believe that this information can be useful for financial officers working in related areas. The model based on the full‐likelihood approach was less satisfactory. We attribute its failure to the fact that the two‐state Markov regime‐switching model is too rigid and overly simplistic. In comparison, the composite likelihood requires only that the model correctly specifies the joint distribution of two adjacent price changes. Thus, model violations in other areas do not invalidate the results. The Canadian Journal of Statistics 41: 353–367; 2013 © 2013 Statistical Society of Canada