Statistical Modelling recent issues

Multilevel models with multivariate mixed response types

Goldstein, H., Carpenter, J., Kenward, M. G, Levin, K. A — Wed, 21 Oct 2009 06:57:22 PDT

We build upon the existing literature to formulate a class of models for multivariate mixtures of Gaussian, ordered or unordered categorical responses and continuous distributions that are not Gaussian, each of which can be defined at any level of a multilevel data hierarchy. We describe a Markov chain Monte Carlo algorithm for fitting such models. We show how this unifies a number of disparate problems, including partially observed data and missing data in generalized linear modelling. The two-level model is considered in detail with worked examples of applications to a prediction problem and to multiple imputation for missing data. We conclude with a discussion outlining possible extensions and connections in the literature. Software for estimating the models is freely available.

Latent trajectory modelling of multivariate binary data

Beath, K. J, Heller, G. Z — Wed, 21 Oct 2009 06:57:22 PDT

Latent trajectory analysis is a form of latent class analysis, where the manifest variables are longitudinal measurements of a single outcome. The latent classes may correspond to either constant increasing or decreasing levels of the outcome over time and describe different severity or course of a disease. Extension to multiple outcomes at each time point allows more accurate determination of classes, with classes based on combination of the outcomes, however requiring models which account for both correlation between outcomes and periods. Three models are described for multiple binary outcomes, observed at each time point: a latent class model where all outcomes are considered independent at all time points, a model incorporating random effects for subject only and one incorporating random effects for subject and period. The methods are applied to data on asthma and allergy symptoms in infants, with symptoms recorded at four time points, and it is shown that the incorporation of subject and period heterogeneity results in lower estimates of the number of latent classes.

Multinomial-Poisson models subject to inequality constraints

Cazzaro, M., Colombi, R. — Wed, 21 Oct 2009 06:57:22 PDT

Lang’s Multinomial-Poisson Homogeneous (MPH) models and Homogeneous Linear Predictor (HLP) Multinomial-Poisson models include as special cases many models for contingency table analysis that have been introduced in the effort to overcome well-known limitations of the log-linear models. Here the definitions of MPH and HLP models are extended to include inequality constraints. It is shown that inequality constrained MPH and HLP models are very flexible and rich family of models for contingency table analysis. The inequality constrained hierarchical multinomial marginal models which are an important sub-class of MPH models are also examined.

Robustness for general design mixed models using the t-distribution

Staudenmayer, J, Lake, E E, Wand, M P — Wed, 21 Oct 2009 06:57:22 PDT

The t-distribution allows the incorporation of outlier robustness into statistical models while retaining the elegance of likelihood-based inference. In this paper, we develop and implement a linear mixed model for the general design of the linear mixed model using the univariate t-distribution. This general design allows a considerably richer class of models to be fit than is possible with existing methods. Included in this class are semi-parametric regression and smoothing and spatial models.

On the estimation of the misclassification table for finite count data with an application in caries research

Lesaffre, E., Kuchenhoff, H., Mwalili, S. M, Declerck, D. — Fri, 17 Jul 2009 06:57:50 PDT

We look at the correction for misclassification of possibly corrupted finite count data in epidemiological studies. In general, the misclassification probabilities are estimated from a validation study and used to correct for the distortion. However, most often the validation study is quite small implying that the misclassification probabilities are impossible to calculate or estimate with high variability if based on the multinomial distribution. To increase efficiency, we propose an approach based on the fact that to determine a count the examiner needs to evaluate all items that make up that count, called the double binomial (DB) approach. We suggest various extensions of the DB approach which might mimic better the scoring behaviour of the examiner relative to a gold standard. We evaluate the performance of our approach(es) to estimate the misclassification probabilities in comparison to the multinomial approach in an analytical way and in a simulation study. Finally, the practical use of our methods is exemplified on an oral health survey examining caries experience in 7-year-old Flemish children involving 16 dental examiners.

Hierarchical dynamic time-to-event models for post-treatment preventive care data on breast cancer survivors

Cooner, F. W, Yu, X., Banerjee, S., Grambsch, P. L, McBean, A M. — Fri, 17 Jul 2009 06:57:50 PDT

This paper considers modelling data arising in post-treatment preventive care settings, where cancer patients who have undergone disease-directed treatment discontinue seeking preventive care services. Clinicians and public health researchers are interested in explaining such behavioural patterns by modelling the time-to-receiving care while accounting for several patient and treatment attributes. A key feature of such data is that a noticeable number of patients would never return for screening, a concept subtly different from censoring, where an individual does not return for screening in the given time frame of the study. Models distinguishing between these two concepts are known as cure rate models and are often preferred for data where a significant part of the population never experienced the endpoint. Building upon recent work on hierarchical cure model framework we propose modelling a sequence of latent events with a piecewise exponential distribution that remedies oversmoothing encountered in existing models with different latent distributions. We investigate simultaneous regression on the cure fraction and the latent event distribution and derive a flexible class of semiparametric cure rate models.

Clustered binary data with random cluster sizes: a dual poisson modelling approach

Ma, R., Jorgensen, B., Willms, J. D. — Fri, 17 Jul 2009 06:57:50 PDT

In the analysis of clustered binary data with random cluster sizes, traditional approaches assuming fixed cluster sizes are generally used. Appropriate inference should take account of both intra-cluster correlation and extra-variation arising from the random cluster sizes. We introduce a dual Poisson random effects model for performing appropriate analyses of such data. Our orthodox best linear unbiased predictor approach to this model depends only on the first- and second- moment assumptions of unobserved random effects. This approach is illustrated with analyses of seed germination data and developmental toxicity data.

Extended truncated Inverse Gaussian-Poisson model

Puig, X., Ginebra, J., Perez-Casany, M. — Fri, 17 Jul 2009 06:57:50 PDT

The inverse Gaussian–Poisson mixture model is very useful when modelling highly skewed non-negative integer data in fields as diverse as linguistics, ecology, market research, bibliometry, engineering and insurance. When using this statistical model on the frequency of word or species frequency data, one typically truncates its sample space at zero to accommodate for the ignorance about the number of words or species that are not observed. In this paper, we show that by truncating the sample space of the inverse Gaussian–Poisson model, one is allowed to extend its parameter space and in that way improve its fit when the frequency of one is larger and the right tail is heavier than is allowed by the unextended model. By fitting the extended model to word frequency count data, we find many instances where the maximum likelihood estimates fall in the extension of the parameter space.

Editorial

Tue, 12 May 2009 01:40:12 PDT

Modelling zero-inflated spatio-temporal processes

Fernandes, M. V., Schmidt, A. M, Migon, H. S — Tue, 12 May 2009 01:40:12 PDT

We consider models for spatio-temporal processes which assume either non-negative values, and often are observed as zero, or discrete values and are also inflated by zeros. Typically, in the first case, the spatial observations are obtained at fixed locations (point-referenced data) over a region D; whereas in the second, the region D is divided into a finite number of regular or irregular subregions (areal level), resulting in observations for each subregion. Our main idea is based on those of zeroinflated models, by assuming that the value observed at location s and time t, Y_t (s), is a realization of a mixture between a Bernoulli distribution with a probability of success _t (s) and a probability density function or probability function p(y_t (s) | .) For both cases, we include spatio-temporal latent processes in the model to account for the possible extra variation present in the mean structure of _t (s) and/or p(y_t(s) | .). In the context of point-referenced data, we model the amount of rainfall over the city of Rio de Janeiro during 75 weeks; whereas in the areal data level case, we consider weekly cases of dengue fever in the city of Rio de Janeiro during the years of 2001–02.

Using decomposed household food acquisitions as inputs of a Kinetic Dietary Exposure Model

Allais, O., Tressou, J. — Tue, 12 May 2009 01:40:12 PDT

Foods naturally contain a number of contaminants that may have different and long-term toxic effects. This paper introduces a novel approach for the assessment of such chronic food risk that integrates the pharmakokinetic properties of a given contaminant. The estimation of such a Kinetic Dietary Exposure Model (KDEM) should be based on long-term consumption data which, for the moment, can only be provided by Household Budget Surveys such as the TNS SECODIP panel in France. A semi-parametric model is proposed to decompose a series of household quantities into individual quantities which are then used as inputs of the KDEM. As an illustration, the risk assessment related to the presence of methylmercury in seafoods is revisited using this novel approach.

Modelling orientation trajectories

Faraway, J. J, Choe, S. B. — Tue, 12 May 2009 01:40:12 PDT

We describe a modelling approach for orientation trajectories. The initial and final orientations of the object are taken as known and the problem of how the object will transition between the endpoints is considered. Orientations are represented as quaternions and mapped to a tangent space. The deviation from the geodesic connecting the endpoints is introduced and called the slerp residual. Modelling the slerp residuals substantially reduces the distortion caused by mapping to the tangent space. Bézier curves are used to compactly model the trajectories and provide a linkage to potential predictors. Data from an experiment to study human motion while reaching to perform a wide variety of grasps are considered. The orientation trajectories of the hand are modelled in several ways resulting in a simple yet interpretable model.

Stochastic volatility models for ordinal-valued time series with application to finance

Muller, G., Czado, C. — Tue, 12 May 2009 01:40:12 PDT

In this paper, we introduce a new class of models, called ordinal-response stochastic volatility models, by combining an ordinal-response model and the idea of stochastic volatility. Corresponding time series occur in high-frequency finance when the stocks are traded on a coarse grid. For parameter estimation, we develop an efficient grouped move multigrid Monte Carlo sampler. This sampler is based on a scale transformation group, whose elements operate on the random samples of a certain conditional distribution. Also volatility estimates are provided. For illustration, we apply our new model class to price changes of the IBM stock. Dependencies on covariates are quantified and compared with theoretical results for such processes.

Modelling transport mode decisions using hierarchical logistic regression models with spatial and cluster effects

Czado, C., Prokopenko, S. — Thu, 19 Feb 2009 07:58:20 PST

This work is motivated by a mobility study conducted in the city of Munich, Germany. The variable of interest is a binary response, which indicates whether public transport has been utilized or not. One of the central questions is to identify areas of low/high utilization of public transport after adjusting for explanatory factors such as trip, individual and household attributes. For the spatial effects a modification of a class of Markov random fields (MRF) models with proper joint distributions introduced by Pettitt et al. (2002) is developed. It contains the intrinsic MRF in the limit and allows for efficient Markov Chain Monte Carlo (MCMC) algorithms. Further cluster effects using group and individual approaches are taken into consideration. The first one models heterogeneity between clusters, while the second one models heterogeneity within clusters. A naive approach to include individual cluster effects results in an unidentifiable model. It is shown how a re-parametrization gives identifiable parameters. This provides a new approach for modeling heterogeneity within clusters. Finally, the proposed model classes are applied to the mobility study.

A time varying hidden Markov model with latent information

Otranto, E. — Thu, 19 Feb 2009 07:58:20 PST

The time varying hidden Markov models are based on the use of some observable variables, which we suppose to drive the transition probabilities. The estimation of the model is conditional on the availability of this information, which is not obvious. In this paper we propose a time varying hidden Markov model with the transition probabilities driven by a latent variable subject to the same Markovian changes of the dependent variable. The model has a state-space form and the latent variable is estimated using a modified Kim filter, so that this information is always available; furthermore, the estimation of this latent variable is useful to forecast the changes in the state. We show the practical characteristics of this model through an example in which the latent variable is the business cycle.

Sharpening P-spline signal regression

Li, B., Marx, B. D. — Thu, 19 Feb 2009 07:58:20 PST

We propose two variations of P-spline signal regression: space-varying penalization signal regression (SPSR) and additive polynomial signal regression (APSR). SPSR uses space-varying roughness penalty according to the estimated coefficients from the partial least-squares (PLS) regression, while APSR expands the linear basis to polynomial bases. SPSR and APSR are motivated in the following two scenarios, respectively: (i) some region(s) of the regressor channels contain more useful information for prediction than others and (ii) the relationship between the response and regressor channels is highly nonlinear. We also extend the methods to the generalized linear regression setting. As illustration, we apply the methods to two published data sets showing highly competitive performance.

Modelling general patterns of digit preference

Camarda, C. G., Eilers, P. H.C., Gampe, J. — Thu, 19 Feb 2009 07:58:20 PST

In many applications data can be interpreted as indirect observations of a latent distribution. A typical example is the phenomenon known as digit preference, i.e. the tendency to round outcomes to pleasing digits. The composite link model (CLM) is a useful framework to uncover such latent distributions. Moreover, when applied to data showing digit preferences, this approach allows estimation of the proportions of counts that were transferred to neighbouring digits. As the estimating equations generally are singular or severely ill-conditioned, we impose smoothness assumptions on the latent distribution and penalize the likelihood function. To estimate the misreported proportions, we use a weighted least-squares regression with an added L₁ penalty. The optimal smoothing parameters are found by minimizing the Akaike’s information Criterion (AIC). The approach is verified by a simulation study and several applications are presented.