A family of repeated measurements models

A general family of multivariate distributions for repeated measures can be obtained by applying the Laplace transform of a gamma distribution to the integrated intensity function of any continuous distribution on the positive real line. Both clustering and serial dependence can be handled. The response variable may be counts, durations between events, or any continuous positive-valued measurements.     

Tail dependence for skew Laplace distribution and skew Cauchy distribution

ABSTRACT

Coefficient of tail dependence measures the strength of dependence in the tail of a bivariate distribution and it has been found useful in the risk management. In this paper, we derive the upper tail dependence coefficient for a random vector following the skew Laplace distribution and the skew Cauchy distribution, respectively. The result shows that skew Laplace distribution is asymptotically independent in upper tail, however, skew Cauchy distribution has asymptotic upper tail dependence.     

Testing for random effects and serial correlation in spatial autoregressive models

This paper constructs and evaluates tests for random effects and serial correlation in spatial autoregressive panel data models. In these models, ignoring the presence of random effects not only produces misleading inference but inconsistent estimation of the regression coefficients. Two different estimation methods are considered: maximum likelihood and instrumental variables. For each estimator, optimal tests are constructed: Lagrange multiplier in the first case; Neyman's C(α)$C(\alpha )$ in the second. In addition, locally size-robust tests, for individual hypotheses under local misspecification of the unconsidered parameter, are constructed. Extensive Monte Carlo evidence is presented.     

Analysis of a longitudinal ordinal response clinical trial using dynamic models

Summary.  In many areas of pharmaceutical research, there has been increasing use of categorical data and more specifically ordinal responses. In many cases, complex models are required to account for different types of dependences among the responses. The clinical trial that is considered here involved patients who were required to remain in a particular state to enable the doctors to examine their heart. The aim of this trial was to study the relationship between the dose of the drug administered and the time that was spent by the patient in the state permitting examination. The patient's state was measured every second by a continuous Doppler signal which was categorized by the doctors into one of four ordered categories. Hence, the response consisted of repeated ordinal series. These series were of different lengths because the drug effect wore off faster (or slower) on certain patients depending on the drug dose administered and the infusion rate, and therefore the length of drug administration. A general method for generating new ordinal distributions is presented which is sufficiently flexible to handle unbalanced ordinal repeated measurements. It consists of obtaining a cumulative mixture distribution from a Laplace transform and introducing into it the integrated intensity of a binary logistic, continuation ratio or proportional odds model. Then, a multivariate distribution is constructed by a procedure that is similar to the updating process of the Kalman filter. Several types of history dependences are proposed.     

A method of moments estimator of tail dependence in meta-elliptical models

A meta-elliptical model is a distribution function whose copula is that of an elliptical distribution. The tail dependence function in such a bivariate model has a parametric representation with two parameters: a tail parameter and a correlation parameter. The correlation parameter can be estimated by robust methods based on the whole sample. Using the estimated correlation parameter as plug-in estimator, we then estimate the tail parameter applying a modification of the method of moments approach proposed in the paper by Einmahl et al. (2008). We show that such an estimator is consistent and asymptotically normal. Further, we derive the joint limit distribution of the estimators of the two parameters. We illustrate the small sample behavior of the estimator of the tail parameter by a simulation study and on real data, and we compare its performance to that of the competitive estimators.     

A Comparison of Time-Varying Parameter and Multiprocess Mixture Models in the Case of Money-Supply Announcements

This study compares the performance of a recently proposed multiprocess mixture model and a random-walk time-varying parameter (TVP) model, using the interest rate–weekly money relationship for illustrative purposes. For the case of this relationship, which is subject to regime shifts and outliers, the mixture model performs well and the latter model performs poorly. This finding is of general interest, since investigators often adopt random-walk TVP models to accommodate potential regime shifts in regression relationships. The TVP estimation procedure is unlikely to find abrupt shifts, since the estimate of parameter variance is based on the entire data sample. In the face of rapid discontinuous shifts in the parameters, this variance estimate is unrepresentative of the variability during periods of abrupt shift or transient observations.     

A tolerance interval approach for assessment of agreement in method comparison studies with repeated measurements

This paper generalizes the tolerance interval approach for assessing agreement between two methods of continuous measurement for repeated measurement data—a common scenario in applications. The repeated measurements may be longitudinal or they may be replicates of the same underlying measurement. Our approach is to first model the data using a mixed model and then construct a relevant asymptotic tolerance interval (or band) for the distribution of appropriately defined differences. We present the methodology in the general context of a mixed model that can incorporate covariates, heteroscedasticity and serial correlation in the errors. Simulation for the no-covariate case shows good small-sample performance of the proposed methodology. For the longitudinal data, we also describe an extension for the case when the observed time profiles are modelled nonparametrically through penalized splines. Two real data applications are presented.     

A new class of mixture models for differential gene expression in DNA microarray data

One of the fundamental issues in analyzing microarray data is to determine which genes are expressed and which ones are not for a given group of subjects. In datasets where many genes are expressed and many are not expressed (i.e., underexpressed), a bimodal distribution for the gene expression levels often results, where one mode of the distribution represents the expressed genes and the other mode represents the underexpressed genes. To model this bimodality, we propose a new class of mixture models that utilize a random threshold value for accommodating bimodality in the gene expression distribution. Theoretical properties of the proposed model are carefully examined. We use this new model to examine the problem of differential gene expression between two groups of subjects, develop prior distributions, and derive a new criterion for determining which genes are differentially expressed between the two groups. Prior elicitation is carried out using empirical Bayes methodology in order to estimate the threshold value as well as elicit the hyperparameters for the two component mixture model. The new gene selection criterion is demonstrated via several simulations to have excellent false positive rate and false negative rate properties. A gastric cancer dataset is used to motivate and illustrate the proposed methodology.     

A comparison of univariate and multivariate multilevel models for repeated measures of use of antenatal care in Uttar Pradesh

Summary.  We compare two different multilevel modelling approaches to the analysis of repeated measures data to assess the effect of mother level characteristics on women's use of prenatal care services in Uttar Pradesh, India. We apply univariate multilevel models to our data and find that the model assumptions are severely violated and the parameter estimates are not stable, particularly for the mother level random effect. To overcome this we apply a multivariate multilevel model. The correlation structure shows that, once the decision has been made regarding use of antenatal care by the mother for her first observed birth in the data, she does not tend to change this decision for higher order births.