Biomedical subjects

Frank Rijmen

Publications and source records attributed to Frank Rijmen.

4 recordsLinked to original sources

PubMed2006

Statistical inference in generalized linear mixed models: a review.

We present a review of statistical inference in generalized linear mixed models (GLMMs). GLMMs are an extension of generalized linear models and are suitable for the analysis of non-normal data with a clustered structure. A GLMM contains parameters common to all clusters (fixed regression effects and variance components) and cluster-specific parameters. The latter parameters are assumed to be randomly drawn from a population distribution. The parameters of this population distribution (the variance components) have to be estimated together with the fixed effects. We focus on the case in which the cluster-specific parameters are normally distributed. The cluster-specific effects are integrated out of the likelihood so that the fixed effects and variance components can be estimated. Unfortunately, the integral over the cluster-specific effects is intractable for most GLMMs with a normal mixing distribution. Within a classical statistical framework, we distinguish between two broad classes of methods to handle this intractable integral: methods that rely on a numerical approximation to the integral and methods that use an analytical approximation to the integrand. Finally, we present an overview of available methods for testing hypotheses about the parameters of GLMMs.

Analysis of Variance↗

PubMed2005

Mixed model estimation methods for the Rasch model.

Mixed models take the dependency between observations based on the same person into account by introducing one or more random effects. After introducing the mixed model framework, it is explained, by taking the Rasch model as a generic example, how item response models can be conceptualized as generalized linear and nonlinear mixed models. Common estimation methods for generalized linear and nonlinear models are discussed. In a simulation study, the performance of four estimation methods is assessed for the Rasch model under different conditions regarding the number of items and persons, and the degree of interindividual differences. The estimation methods included in the study are: an approximation of the integral over the random effect by means of Gaussian quadrature; direct maximization with a sixth-order Laplace approximation to the integrand; a linearized approximation of the nonlinear model employing PQL2; and finally a Bayesian MCMC method. It is concluded that the estimation methods perform almost equally well, except for a slightly worse recovery of the variance parameter for PQL2 and MCMC.

Data Interpretation, Statistical↗

PubMed2003

A latent class model for individual differences in the interpretation of conditionals.

We investigated the hypothesis that there are three levels of performance associated with conditional reasoning: (1) Unsophisticated reasoners solve a modus tollens by accepting the invited inferences, treating the conditional as if it were a biconditional. (2) Reasoners of an intermediate level can resist the invited inferences, but cannot find the line of reasoning needed to endorse modus tollens. (3) Sophisticated reasoners do not draw the invited inferences either, but they do master the strategy to solve a modus tollens. On a first set of six problems, solved by 214 adolescents, an unrestricted latent class analysis revealed the existence of a large subgroup of reasoners with a biconditional interpretation of the conditional, and a smaller subgroup with a conditional interpretation. On a second set of 24 problems, solved by the same participants, a restricted latent class model corroborated the existence of a large subgroup of unsophisticated reasoners and a smaller subgroup of reasoners of an intermediate level. No evidence was found for the existence of a subgroup of sophisticated reasoners. As expected, the class of biconditional reasoners was associated with the class of unsophisticated reasoners, and the class of conditional reasoners was associated with the class of reasoners of an intermediate level. Furthermore, the former showed a biconditonal response pattern on truth table tasks, whereas the latter showed a conditional response pattern.

Adolescent↗

PubMed2003

A nonlinear mixed model framework for item response theory.

Mixed models take the dependency between observations based on the same cluster into account by introducing 1 or more random effects. Common item response theory (IRT) models introduce latent person variables to model the dependence between responses of the same participant. Assuming a distribution for the latent variables, these IRT models are formally equivalent with nonlinear mixed models. It is shown how a variety of IRT models can be formulated as particular instances of nonlinear mixed models. The unifying framework offers the advantage that relations between different IRT models become explicit and that it is rather straightforward to see how existing IRT models can be adapted and extended. The approach is illustrated with a self-report study on anger.

Anger↗