A Comparison of Anchor-Item Designs for the Concurrent Calibration of Large Banks of Likert-Type Items

Current interest in measuring quality of life is generating interest in the construction of computerized adaptive tests (CATs) with Likert-type items. Calibration of an item bank for use in CAT requires collecting responses to a large number of candidate items. However, the number is usually too large to administer to each subject in the calibration sample. The concurrent anchor-item design solves this problem by splitting the items into separate subtests, with some common items across subtests; then administering each subtest to a different sample; and finally running estimation algorithms once on the aggregated data array, from which a substantial number of responses are then missing. Although the use of anchor-item designs is widespread, the consequences of several configuration decisions on the accuracy of parameter estimates have never been studied in the polytomous case. The present study addresses this question by simulation, comparing the outcomes of several alternatives on the configuration of the anchor-item design. The factors defining variants of the anchor-item design are (a) subtest size, (b) balance of common and unique items per subtest, (c) characteristics of the common items, and (d) criteria for the distribution of unique items across subtests. The results of this study indicate that maximizing accuracy in item parameter recovery requires subtests of the largest possible number of items and the smallest possible number of common items; the characteristics of the common items and the criterion for distribution of unique items do not affect accuracy.

Energy estimation of cosmic rays with the Engineering Radio Array of the Pierre Auger Observatory

The Auger Engineering Radio Array (AERA) is part of the Pierre Auger Observatory and is used to detect the radio emission of cosmic-ray air showers. These observations are compared to the data of the surface detector stations of the Observatory, which provide well-calibrated information on the cosmic-ray energies and arrival directions. The response of the radio stations in the 30-80 MHz regime has been thoroughly calibrated to enable the reconstruction of the incoming electric field. For the latter, the energy deposit per area is determined from the radio pulses at each observer position and is interpolated using a two-dimensional function that takes into account signal asymmetries due to interference between the geomagnetic and charge-excess emission components. The spatial integral over the signal distribution gives a direct measurement of the energy transferred from the primary cosmic ray into radio emission in the AERA frequency range. We measure 15.8 MeV of radiation energy for a 1 EeV air shower arriving perpendicularly to the geomagnetic field. This radiation energy-corrected for geometrical effects-is used as a cosmic-ray energy estimator. Performing an absolute energy calibration against the surface-detector information, we observe that this radio-energy estimator scales quadratically with the cosmic-ray energy as expected for coherent emission. We find an energy resolution of the radio reconstruction of 22% for the data set and 17% for a high-quality subset containing only events with at least five radio stations with signal.