Methods & Statistics

Faculty of Social Sciences

Utrecht University

**Supervisors**

Prof. Herbert Hoijtink, Prof. Tineke Oldehinkel,

Prof. Jos van Berkum, Prof. Marian Joels,

Dr Rinke Klein Entink & Dr Rebecca Kuiper

On February 2nd, 2018, Yasin Altinisik will defend his thesis entitled

**Evaluation of inequality constrained hypotheses using an Akaike-type information citerion **

**Summary**

The Akaike information criterion (AIC) is one of the best known information criteria that can be used to evaluate hypotheses containing only equality restrictions on model parameters. The GORIC is a generalization of the AIC that can be utilized to evaluate hypotheses containing equality and/or inequality restrictions on model parameters, but only for normal linear models. This book proposes a new information criterion, the GORICA, that mimics the performance of the GORIC on selecting the best hypothesis in a set of competing hypotheses for normal linear models. The GORICA can be used to evaluate (in)equality constrained hypotheses under a broad range of statistical models: generalized linear models, generalized linear mixed models, structural equation models, and contingency tables. The GORICA is an useful method in evaluating (in)equality constrained hypotheses, because the hypotheses under evaluation can contain either linear restrictions on model parameters or non-linear restrictions on model parameters. For example, the GORICA can be used to evaluate hypotheses containing (in)equality restrictions on odds ratios, which are formulated using non-linear functions of cell probabilities in the context of contingency tables. The GORICA evaluation of (in)equality constrained hypotheses is flexible in the sense that it only requires the estimates of model parameters used in the specification of the hypotheses under evaluation and their covariance matrix as input. These inputs can be obtained using a suitable estimation method such as maximum likelihood estimation, nonparametric bootstrapping, and Gibbs sampling.

**Project**

**Research replication through the evaluation of prior knowledge in the form of informative hypotheses. ****Sparse data big models.
**Research replication is increasingly becoming an important topic. It has two main goals: to reduce the probability of false positives and false negatives; and, to test the generalizability of research conclusions to other (sub)populations and related (but not necessarily exactly the same as in the original study) contexts. Currently the methodologies that are available for research replication are rather limited. In this project a new methodology will be developed, evaluated, and applied. Knowledge derived from existing animal studies, completed waves of cohorts, and expert elicitation will be formalized into informative hypotheses. Subsequently the support in new data for these hypotheses will be quantified using a new model selection criterion: a generalization of the GORIC. The performance of this new approach will be evaluated by means of a simulation study and through its use (in cooperation with other CID researchers) in three case studies: translating the results of animal studies into hypotheses with respect to the development of children; replication of results from a study with respect to attention style as conditional adaptation with different subpopulations and contexts; and, replication of expert expectations with respect to the relation between exposure to stories and the development of social competence and self-regulation.