High-dimensional maximum marginal likelihood item factor analysis by adaptive quadrature

Although the Bock–Aitkin likelihood-based estimation method for factor analysis of dichotomous item response data has important advantages over classical analysis of item tetrachoric correlations, a serious limitation of the method is its reliance on fixed-point Gauss-Hermite (G-H) quadrature in the solution of the likelihood equations and likelihood-ratio tests. When the number of latent dimensions is large, computational considerations require that the number of quadrature points per dimension be few. But with large numbers of items, the dispersion of the likelihood, given the response pattern, becomes so small that the likelihood cannot be accurately evaluated with the sparse fixed points in the latent space. In this paper, we demonstrate that substantial improvement in accuracy can be obtained by adapting the quadrature points to the location and dispersion of the likelihood surfaces corresponding to each distinct pattern in the data. In particular, we show that adaptive G-H quadrature, combined with mean and covariance adjustments at each iteration of an EM algorithm, produces an accurate fast-converging solution with as few as two points per dimension. Evaluations of this method with simulated data are shown to yield accurate recovery of the generating factor loadings for models of upto eight dimensions. Unlike an earlier application of adaptive Gibbs sampling to this problem by Meng and Schilling, the simulations also confirm the validity of the present method in calculating likelihood-ratio chi-square statistics for determining the number of factors required in the model. Finally, we apply the method to a sample of real data from a test of teacher qualifications.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43596/1/11336_2003_Article_1141.pd

Mouse Chromosome 3

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46995/1/335_2004_Article_BF00648421.pd

Measurement of the gamma ray background in the Davis Cavern at the Sanford Underground Research Facility

Deep underground environments are ideal for low background searches due to the attenuation of cosmic rays by passage through the earth. However, they are affected by backgrounds from γ-rays emitted by 40K and the 238U and 232Th decay chains in the surrounding rock. The LUX-ZEPLIN (LZ) experiment will search for dark matter particle interactions with a liquid xenon TPC located within the Davis campus at the Sanford Underground Research Facility, Lead, South Dakota, at the 4,850-foot level. In order to characterise the cavern background, in-situ γ-ray measurements were taken with a sodium iodide detector in various locations and with lead shielding. The integral count rates (0--3300~keV) varied from 596~Hz to 1355~Hz for unshielded measurements, corresponding to a total flux in the cavern of 1.9±0.4~γ cm−2s−1. The resulting activity in the walls of the cavern can be characterised as 220±60~Bq/kg of 40K, 29±15~Bq/kg of 238U, and 13±3~Bq/kg of 232Th

Dendrochronology and the Complex History of the William Hawk Cabin, Salt Lake City, Utah

The William Hawk Cabin is considered one of the oldest pioneer structures in Salt Lake City, Utah. Tradition suggests that it was originally constructed in 1848 inside the "Old Fort" established by Mormon settlers in 1847, and then moved to its current location between 1850 and 1852. We examined tree rings from 23 Douglas-fir (Pseudotsuga menziesii var. glauca) and eight white fir (Abies concolor) timbers in the cabin to (1) evaluate and refine the suggested range of construction dates of 1848-1852, (2) verify or refute the suggestion that the cabin was originally constructed within the Old Fort, (3) identify any evidence of use of deadwood, timber re-use, stockpiling, or renovation, and (4) determine the provenance of the timbers. We built a 209-year floating chronology from 36 cores crossdated visually and verified statistically with COFECHA. Statistically significant (p < 0.0001) comparisons with established regional chronologies indicated that the Hawk Cabin chronology extends from 1651-1859. Cutting dates ranged from 1832-1860, with strong clusters in 1846 and 1851-1852, and a weaker cluster in 1855. The 1851-1852 cluster accounted for over half of the cutting dates, suggesting that a version of the cabin was built by 1852, and the later timbers were incorporated as part of a major renovation in or after 1860. The 1846 cluster may reflect wood salvaged from road building efforts by the Donner-Reed Party, and suggests that a version of the cabin may have been originally built in the Old Fort, although probably not by Hawk. These results confirm the historical significance of the William Hawk Cabin, and the complexity of its construction history argues for large sample depths in dendroarchaeological studies in semi-arid regions. © 2016 by The Tree-Ring Society.This item is part of the Tree-Ring Research (formerly Tree-Ring Bulletin) archive. For more information about this peer-reviewed scholarly journal, please email the Editor of Tree-Ring Research at [email protected]