A limited dependent variable model for heritability estimation with non-random ascertained samples

In a questionnaire study, a random sample of Dutch families was asked whether they suffered from asthma and related symptoms. From these families, a selected sample was invited to come to the hospital for further phenotyping. Families were selected if at least one family member reported a history of asthma and the twins were 18 years of age or older. Not all families that were thus selected volunteered, leaving us with a fraction of the original sample. The aim of this paper is to describe a limited dependent variable model that can be used in such situations in order to obtain estimates that are representative of the population from which the sample was originally drawn. The model is a linear (DeFries-Fulker) regression model corrected for sample selection. This correction is possible when (some of) the characteristics that determine whether subjects volunteer (or not) are known for all subjects, including those that did not volunteer. The questionnaire study is of interest by itself but serves mainly to provide a concrete illustration of our method. The present model is used to analyze the data and the results are compared to those obtained with other methods: raw (or direct) likelihood estimation, multiple imputation, and sample weighting. Throughout, Rubin's general theory of inference with missing data serves as an integrating framework

Differential Item Functioning in PISA Due to Mode Effects

One of the most important goals of the Programme for International Student Assessment (PISA) is assessing national changes in educational performance over time. These so-called trend results inform policy makers about the development of ability of 15-year-old students within a specific country. The validity of those trend results prescribes invariant test conditions. In the 2015 PISA survey, several alterations to the test administration were implemented, including a switch from paper-based assessments to computer-based assessments for most countries (OECD 2016a). This alteration of the assessment mode is examined by evaluating if the items used to assess trends are subject to differential item functioning across PISA surveys (2012 vs. 2015). Furthermore, the impact on the trend results due to the change in assessment mode of the Netherlands is assessed. The results show that the decrease reported for mathematics in the Netherlands is smaller when results are based upon a separate national calibration.</p

Reliability Issues in High-Stakes Educational Tests

High-stakes tests and examinations often give rise to rather specific measurement problems. Though nowadays item response theory (IRT) has become the standard theoretical framework for educational measurement, in practice, number-correct scores are still prominent in the definition of standards and norms. Therefore, in this chapter methods are developed for relating standards on the number-correct scale to standards on the latent IRT scale. Further, this chapter focuses on two related issues. The first issue is estimating the size of standard errors when equating older versions of a test to the current version. The second issue is estimating the local reliability of number-correct scores and the extra error variance introduced through number-correct scoring rather than using IRT proficiency estimates. It is shown that the first issue can be solved in the framework of maximum a posteriori (MAP) estimation, while the second issue can be solved in the framework of expected a posteriori (EAP) estimation. The examples that are given are derived from simulations studies carried out for linking the nation-wide tests at the end of primary education in the Netherlands