Parameter estimation of nonlinear mixed-effects models using first-order conditional linearization and the EM algorithm

Nonlinear mixed-effects (NLME) models are flexible enough to handle repeated-measures data from various disciplines. In this article, we propose both maximum-likelihood and restricted maximum-likelihood estimations of NLME models using first-order conditional expansion (FOCE) and the expectation–maximization (EM) algorithm. The FOCE-EM algorithm implemented in the ForStat procedure SNLME is compared with the Lindstrom and Bates (LB) algorithm implemented in both the SAS macro NLINMIX and the S-Plus/R function nlme in terms of computational efficiency and statistical properties. Two realworld data sets an orange tree data set and a Chinese fir (Cunninghamia lanceolata) data set, and a simulated data set were used for evaluation. FOCE-EM converged for all mixed models derived from the base model in the two realworld cases, while LB did not, especially for the models in which random effects are simultaneously considered in several parameters to account for between-subject variation. However, both algorithms had identical estimated parameters and fit statistics for the converged models. We therefore recommend using FOCE-EM in NLME models, particularly when convergence is a concern in model selection.     

Distance-based approach in univariate longitudinal data analysis

In this paper, we propose a methodology to analyze longitudinal data through distances between pairs of observations (or individuals) with regard to the explanatory variables used to fit continuous response variables. Restricted maximum-likelihood and generalized least squares are used to estimate the parameters in the model. We applied this new approach to study the effect of gender and exposure on the deviant behavior variable with respect to tolerance for a group of youths studied over a period of 5 years. Were performed simulations where we compared our distance-based method with classic longitudinal analysis with both AR(1) and compound symmetry correlation structures. We compared them under Akaike and Bayesian information criterions, and the relative efficiency of the generalized variance of the errors of each model. We found small gains in the proposed model fit with regard to the classical methodology, particularly in small samples, regardless of variance, correlation, autocorrelation structure and number of time measurements.     

Functional principal component analysis for the explorative analysis of multisite–multivariate air pollution time series with long gaps

The knowledge of the urban air quality represents the first step to face air pollution issues. For the last decades many cities can rely on a network of monitoring stations recording concentration values for the main pollutants. This paper focuses on functional principal component analysis (FPCA) to investigate multiple pollutant datasets measured over time at multiple sites within a given urban area. Our purpose is to extend what has been proposed in the literature to data that are multisite and multivariate at the same time. The approach results to be effective to highlight some relevant statistical features of the time series, giving the opportunity to identify significant pollutants and to know the evolution of their variability along time. The paper also deals with missing value issue. As it is known, very long gap sequences can often occur in air quality datasets, due to long time failures not easily solvable or to data coming from a mobile monitoring station. In the considered dataset, large and continuous gaps are imputed by empirical orthogonal function procedure, after denoising raw data by functional data analysis and before performing FPCA, in order to further improve the reconstruction.     

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.     

Multivariate linear regression for heterogeneous data

The problem of multivariate regression modelling in the presence of heterogeneous data is dealt to address the relevant issue of the influence of such heterogeneity in assessing the linear relations between responses and explanatory variables. In spite of its popularity, clusterwise regression is not designed to identify the linear relationships within ‘homogeneous’ clusters exhibiting internal cohesion and external separation. A within-clusterwise regression is introduced to achieve this aim and, since the possible presence of a linear relation ‘between’ clusters should be also taken into account, a general regression model is introduced to account for both the between-cluster and the within-cluster regression variation. Some decompositions of the variance of the responses accounted for are also given, the least-squares estimation of the parameters is derived, together with an appropriate coordinate descent algorithms and the performance of the proposed methodology is evaluated in different datasets.     

Segmentation,alignment and statistical analysis of biosignals with application to disease classification

We present a novel methodology for a comprehensive statistical analysis of approximately periodic biosignal data. There are two main challenges in such analysis: (1) the automatic extraction (segmentation) of cycles from long, cyclostationary biosignals and (2) the subsequent statistical analysis, which in many cases involves the separation of temporal and amplitude variabilities. The proposed framework provides a principled approach for statistical analysis of such signals, which in turn allows for an efficient cycle segmentation algorithm. This is achieved using a convenient representation of functions called the square-root velocity function (SRVF). The segmented cycles, represented by SRVFs, are temporally aligned using the notion of the Karcher mean, which in turn allows for more efficient statistical summaries of signals. We show the strengths of this method through various disease classification experiments. In the case of myocardial infarction detection and localization, we show that our method compares favorably to methods described in the current literature.     

Block and Basu bivariate lifetime distribution in the presence of cure fraction

This paper presents estimates for the parameters included in the Block and Basu bivariate lifetime distributions in the presence of covariates and cure fraction, applied to analyze survival data when some individuals may never experience the event of interest and two lifetimes are associated with each unit. A Bayesian procedure is used to get point and confidence intervals for the unknown parameters. Posterior summaries of interest are obtained using standard Markov Chain Monte Carlo methods in rjags package for R software. An illustration of the proposed methodology is given for a Diabetic Retinopathy Study data set.     

A longitudinal analysis of infant and senescent mortality using mixture models

We construct a mixture distribution including infant, exogenous and Gompertzian/non-Gompertzian senescent mortality. Using mortality data from Swedish females 1751–, we show that this outperforms models without these features, and compare its trends in cohort and period mortality over time. We find an almost complete disappearance of exogenous mortality within the last century of period mortality, with cohort mortality approaching the same limits. Both Gompertzian and non-Gompertzian senescent mortality are consistently present, with the estimated balance between them oscillating constantly. While the parameters of the latter appear to be trending over time, the parameters of the former do not.     

An exact density-based empirical likelihood ratio test for paired data

The Wilcoxon rank-sum test and its variants are historically well-known to be very powerful nonparametric decision rules for testing no location difference between two groups given paired data versus a shift alternative. In this title, we propose a new alternative empirical likelihood (EL) ratio approach for testing the equality of marginal distributions given that sampling is from a continuous bivariate population. We show that in various shift alternative scenarios the proposed exact test is superior to the classic nonparametric procedures, which may break down completely or are frequently inferior to the density-based EL ratio test. This is particularly true in the cases where there is a nonconstant shift under the alternative or the data distributions are skewed. An extensive Monte Carlo study shows that the proposed test has excellent operating characteristics. We apply the density-based EL ratio test to analyze real data from two medical studies.     

The Gamma Distribution as a Mixture of Exponential Distributions

A gamma distribution with arbitrary scale parameter θ and shape parameter r < 1 can be represented as a scale mixture of exponential distributions.