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A new family of item response theory models for count data, based on item characteristic curves (ICCs) of binary models, is presented. These models assume a Poisson distribution for the observed scores where the mean is given by the product of a speed parameter and an ICC, for example, the curve of the one-or two-parameter logistic model. Joint and marginal maximum likelihood parameter estimations are discussed and the proposed procedures are evaluated by computer simulation. As an application, item level data from a test measuring processing speed are analyzed and item fit and test information are explored.Keywords count data, Rasch Poisson counts model, item characteristic curve, processing speed Commonly, item response theory (IRT) models are applied to binary or polytomous data. However, especially in intelligence and performance testing, there is also a third type of datacount data-that occurs frequently. For example, processing speed as a factor of intelligence (Jäger, 1982(Jäger, , 1984McGrew, 2005) is often measured by administering a large number of similar tasks under time constraints and counting the number of correctly solved tasks. Also other variables like the number of reading errors (Rasch, 1960) are often measured as count data, as are the fluency scores (the number of original ideas) on divergent thinking tasks for creativity (Guilford, 1967;Torrance, 1974).In the following, we will deal with the analysis of such count data by developing a new family of IRT models. We have the following setup in mind: In a given amount of time, an examinee is presented an (ideally) unlimited number of tasks of a similar type and the number of correctly solved tasks is the score on this group of tasks (alternatively, the number of errors might be observed). We refer to such a collection of tasks as an item. However, the concept of task can be quite loose in the following, because we do not model the tasks themselves but rather the score obtained on the whole item. Furthermore, the speededness of the items is optional.

In a recent genome-wide association study (GWAS), three polymorphisms (rs3756290, RAPGEF6; rs2075677, CSE1L; rs4958581, NMUR2) were suggested as potentially being related to subjective-well-being and life satisfaction. Additionally, associations between the 5-HTTLPR polymorphism (serotonin transporter) and subjective well-being have been reported in other previous studies. In the current study, we therefore sought to further investigate the findings of the GWAS and examine the association between 5-HTTLPR and subjective well-being. A total of 1174 participants (821 females) were recruited and asked to provide information on their demographics, life satisfaction, and positive affect. All participants provided a genetic sample. We found associations between one SNP derived from the GWAS (rs4958581, NMUR2) and life satisfaction. We also replicated findings involving 5-HTTLPR and life satisfaction, but only for the housing, leisure and family life satisfaction variables, and not for overall life satisfaction or positive affect. Our study underlines that research investigating complex traits in the field of behavioral genetics is challenging due to their (a) pleiotropic and (b) polygenic effects, resulting in tiny effect sizes of each marker investigated. The current study also highlights the importance of investigating genetic markers of distinct areas of life satisfaction.

It is shown that deviations of estimated from true values of item difficulty parameters, caused for example by item calibration errors, the neglect of randomness of item difficulty parameters, testlet effects, or rule-based item generation, can lead to systematic bias in point estimation of person parameters in the context of adaptive testing. This effect occurs even when the errors of the item difficulty parameters are themselves unbiased. Analytical calculations as well as simulation studies are discussed.Keywords computerized adaptive testing, biased point estimation, item response theory, calibration errors, differential item functioning, testlets, computerized item generation As many computer-based methods are readily available nowadays, adaptive testing has become a popular and efficient testing method in psychometrics. The basic principle of an adaptive test can be shortly described as follows: An examinee is first given a few items to obtain a crude initial estimate of the person parameter. Then the next item is chosen so that it contributes maximally to the precision of the updated estimate obtained after the examinee has completed the item. Therefore, several item selection criteria have been developed, for example, the criterion of maximal Fisher information, which is probably the most commonly used in practice (van der Linden, 2010). Furthermore, a number of content-and test-specific constraints often have to be taken into account. The item selection process is iteratively repeated and terminates after a certain predefined number of items or when the estimate of the person parameter no longer changes significantly.Item response theory (IRT) models are an essential element of adaptive testing, as they allow for an easy evaluation of the Fisher information for single items. A central feature of IRT models is that they have separate parameters to describe item and person characteristics. However, in this article it is shown that when the true item difficulty parameters of IRT models differ from the estimated ones, a systematic bias in the estimation of person parameters in adaptive testing arises, even when the errors of the difficulty parameters are unbiased.

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