The R package ltm has been developed for the analysis of multivariate dichotomous and polytomous data using latent variable models, under the Item Response Theory approach. For dichotomous data the Rasch, the Two-Parameter Logistic, and Birnbaum’s Three-Parameter models have been implemented, whereas for polytomous data Semejima’s Graded Response model is available. Parameter estimates are obtained under marginal maximum likelihood using the Gauss-Hermite quadrature rule. The capabilities and features of the package are illustrated using two real data examples.

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High reliability systems generally require individual system components having extremely high reliabilityover long periods of time. Short product development times require reliability tests to be conducted with severe time constraints. Frequently few or no failures occur during such tests, even with acceleration. Thus, it is difficult to assess reliabilitywith traditional life tests that record only failure times. For some components, degradation measures can be taken over time. A relationship between component failure and amountof degradation makes it possible to use degradation models and data to make inferences and predictions about a failure-time distribution. This paper describes degradation reliability models that correspond to physical-failure mechanisms. We explain the connection between degradation reliability models and failuretime reliabilitymodels. Acceleration is modeled byhaving an acceleration model that describes the effect that temperature (or another accelerating vari...

Abstract. Hierarchical or ‘‘multilevel’ ’ regression models typically pa-rameterize the mean response conditional on unobserved latent vari-ables or ‘‘random’ ’ effects and then make simple assumptions regarding their distribution. The interpretation of a regression parameter in such a model is the change in possibly transformed mean response per unit change in a particular predictor having controlled for all conditioning variables including the random effects. An often overlooked limitation of the conditional formulation for nonlinear models is that the interpreta-tion of regression coefficients and their estimates can be highly sensitive to difficult-to-verify assumptions about the distribution of random ef-fects, particularly the dependence of the latent variable distribution on covariates. In this article, we present an alternative parameterization for the multilevel model in which the marginal mean, rather than the conditional mean given random effects, is regressed on covariates. The impact of random effects model violations on the marginal and more traditional conditional parameters is compared through calculation of asymptotic relative biases. A simple two-level example from a study of teratogenicity is presented where the binomial overdispersion depends on the binary treatment assignment and greatly influences likelihood-based estimates of the treatment effect in the conditional model. A second example considers a three-level structure where attitudes toward abortion over time are correlated with person and district level covari-ates. We observe that regression parameters in conditionally specified models are more sensitive to random effects assumptions than their counterparts in the marginal formulation. Key words and phrases: Generalized linear model, latent variable, logis-tic regression, random effects model.

Statistical models in which both fixed and random effects enter nonlinearly are becoming increasingly popular. These models have a wide variety of applications, two of the most common being nonlinear growth curves and overdispersed binomial data. A new SAS/STAT procedure, NLMIXED, fits these models using likelihood-based methods. This paper presents some of the primary features of PROC NLMIXED and illustrates its use with two examples. INTRODUCTION The NLMIXED procedure fits nonlinear mixed models, that is, models in which both fixed and random effects are permitted to have a nonlinear relationship to the response variable. These models can take various forms, but the most common ones involve a conditional distribution for the response variable given the random effects. PROC NLMIXED enables you to specify such a distribution by using either a keyword for a standard form (normal, binomial, Poisson) or SAS programming statements to specify a general distribution. PROC NLMIXED fits the ...

In longitudinal studies measurements are often collected on different types of outcomes for each subject. These may include several longitudinally measured responses (such as blood values relevant to the medical condition under study) and the time at which an event of particular interest occurs (e.g., death, development of a disease or dropout from the study). These outcomes are often separately analyzed; however, in many instances, a joint modeling approach is either required or may produce a better insight into the mechanisms that underlie the phenomenon under study. In this paper we present the R package JM that fits joint models for longitudinal and time-to-event data.

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Stochastic differential equations have shown useful to describe random continuous time processes. Biomedical experiments often imply repeated measurements on a series of experimental units and differences between units can be represented by incorporating ran-dom effects into the model. When both system noise and random effects are considered, stochastic differential mixed-effects models ensue. This class of models enables the simul-taneous representation of randomness in the dynamics of the phenomena being considered and variability between experimental units, thus providing a powerful modeling tool with immediate applications in biomedicine and pharmacokinetic/pharmacodynamic studies. In most cases the likelihood function is not available, and thus maximum likelihood esti-mation of the unknown parameters is not possible. Here we propose a computationally fast approximated maximum likelihood procedure for the estimation of the non-random parameters and the random effects. The method is evaluated on simulations from some famous diffusion processes and on real datasets.

We develop a model that uses repeated observations of a biological community to estimate the number and composition of species in the community. Estimators of community-level attributes are constructed from model-based estimators of occurrence of individual species that incorporate imperfect detection of individuals. Data from the North American Breeding Bird Survey are analyzed to illustrate the variety of ecologically-important quantities that are easily constructed and estimated using our model-based estimators of species occurrence. In particular, we compute site-specific estimates of species richness that honor classical notions of species-area relationships. We suggest extensions of our model to estimate maps of occurrence of individual species and to compute inferences related to the temporal and spatial dynamics of biological communities.

The article proposes an iterative algorithm for the estimation of fixed and ran-dom effects of a nonlinearly aggregated mixed model. The latter arises when an additive Gaussian model is formulated at the disaggregate level on a nonlinear transformation of the responses, but information is available in aggregate form. The nonlinear transformation breaks the linearity of the aggregate model, yielding a nonlinear tight observational constraint. The algorithm rests upon the sequential linearization of the nonlinear aggre-gation constraint around proposals that are iteratively updated until convergence. Likelihood inferences on the hyperparameters are also discussed. As a by product we provide a solution to the problem of disaggregating over the units of analysis the aggregate responses, enforcing the nonlinear observational constraints. Illustrations are provided with reference to the temporal disaggregation prob-lem, concerning the distribution of annual time series flows to the quarters making up the year.