A general method is presented for estimating variance components when the experimental design has one random way of classification and a possibly unbalanced fixed classification. The procedure operates on a sample covariance matrix in which the fixed classes play the role of variables and the random classes correspond to observations. Cases are considered which assume (i) homogeneous and (ii) nonhomogeneous error variance, and (iii) arbitrary scale factors in the measurements and homogeneous error variance. The results include maximum-likelihood estimations of the variance components and scale factors, likelihood-ratio tests of the goodness-of-fit of the model assumed for the design, and large-sample variances and covariances of the estimates. Applications to mental test data are presented. In these applications the subjects constitute the random dimension of the design, and a classification of the mental tests according to objective features of format or content constitute the fixed dimensions.

A new paired comparison method, based upon choices between lotteries, is developed for the measurement of utilities of objects with respect to the utility of receiving nothing, i.e., the status quo. The method is used to estimate the utilities of four birthday gifts. These objects had also been studied in an earlier experiment which used choices between single objects and pairs of objects to determine a rational origin. A comparison of the results of the two experiments indicates that both methods scale objects with respect to the same rational origin and unit of measurement.

A random effects probit model is developed for the case in which the same units are sampled repeatedly at each level of an independent variable. Because the observed proportions may be correlated under these conditions, estimating their trend with respect to the independent variable is no longer a standard problem for probit, logit or loglinear analysis. Using a qualitative analogue of a random regressions model, we employ instead marginal maximum likelihood to estimate the average latent trend line. Likelihood ratio tests of the hypothesis of no trend in the average line, and the hypothesis of no differences in average trend lines between experimental treatments, are proposed. We illustrate the model both with simulated data and with observed data from a clinical experiment in which psychiatric patients on two drug therapies are rated on five occasions for the presence or absence of symptoms.

Maximum likelihood estimation of item parameters in the marginal distribution, integrating over the distribution of ability, becomes practical when computing procedures based on an EM algorithm are used. By characterizing the ability distribution empirically, arbitrary assumptions about its form are avoided. The Em procedure is shown to apply to general item-response models lacking simple sufficient statistics for ability. This includes models with more than one latent dimension.

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 up to 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.

The problem of estimation in the method of successive categories is reconsidered and a new least squares solution is obtained. An empirical comparison of this solution with Gulliksen's solution is presented.

A method of estimating the parameters of the normal ogive model for dichotomously scored item-responses by maximum likelihood is demonstrated. Although the procedure requires numerical integration in order to evaluate the likelihood equations, a computer implemented Newton-Raphson solution is shown to be straightforward in other respects. Empirical tests of the procedure show that the resulting estimates are very similar to those based on a conventional analysis of item “difficulties” and first factor loadings obtained from the matrix of tetrachoric correlation coefficients. Problems of testing the fit of the model, and of obtaining invariant parameters are discussed.

A multivariate logistic latent trait model for items scored in two or more nominal categories is proposed. Statistical methods based on the model provide 1) estimation of two item parameters for each response alternative of each multiple choice item and 2) recovery of information from “wrong” responses when estimating latent ability. An application to a large sample of data for twenty vocabulary items shows excellent fit of the model according to a chi-square criterion. Item and test information curves are compared for estimation of ability assuming multiple category and dichotomous scoring of these items. Multiple scoring proves substantially more precise for subjects of less than median ability, and about equally precise for subjects above the median.

A three-component model for comparative judgment which allows for individual differences in preference is proposed. An implication of the model is that errors in the observed proportions due to sampling individuals in paired comparisons experiments are correlated. By neglecting this correlation, Mosteller's test for the method of paired comparisons tends to accept falsely the goodness of fit of the Case V solution. It is shown that bounds may be set for the correlation effect which make a valid test possible in some cases and provide useful standard errors for the estimated affective values.

A scheme for choosing a few individuals whose preferences for given objects are most representative of those of a larger group of individuals is proposed. The method involves (a) quantifying the preferences of each individual so as to discriminate optimally among objects, (b) testing statistically whether or not a common preference continuum may be assumed for the quantified preferences, (c) constructing a linear estimator of values for the objects on this continuum, if it may be assumed, and (d) selecting as judges the least number of individuals whose quantified preferences, when used with this estimator, determine values for the objects with acceptable accuracy. A numerical example based on food preferences is presented.

We present WALLABY pilot data release 1, the first public release of H i pilot survey data from the Wide-field ASKAP L-band Legacy All-sky Blind Survey (WALLABY) on the Australian Square Kilometre Array Pathfinder. Phase 1 of the WALLABY pilot survey targeted three $60\,\mathrm{deg}^{2}$ regions on the sky in the direction of the Hydra and Norma galaxy clusters and the NGC 4636 galaxy group, covering the redshift range of $z \lesssim 0.08$ . The source catalogue, images and spectra of nearly 600 extragalactic H i detections and kinematic models for 109 spatially resolved galaxies are available. As the pilot survey targeted regions containing nearby group and cluster environments, the median redshift of the sample of $z \approx 0.014$ is relatively low compared to the full WALLABY survey. The median galaxy H i mass is $2.3 \times 10^{9}\,{\rm M}_{{\odot}}$ . The target noise level of $1.6\,\mathrm{mJy}$ per 30′′ beam and $18.5\,\mathrm{kHz}$ channel translates into a $5 \sigma$ H i mass sensitivity for point sources of about $5.2 \times 10^{8} \, (D_{\rm L} / \mathrm{100\,Mpc})^{2} \, {\rm M}_{{\odot}}$ across 50 spectral channels ( ${\approx} 200\,\mathrm{km \, s}^{-1}$ ) and a $5 \sigma$ H i column density sensitivity of about $8.6 \times 10^{19} \, (1 + z)^{4}\,\mathrm{cm}^{-2}$ across 5 channels ( ${\approx} 20\,\mathrm{km \, s}^{-1}$ ) for emission filling the 30′′ beam. As expected for a pilot survey, several technical issues and artefacts are still affecting the data quality. Most notably, there are systematic flux errors of up to several 10% caused by uncertainties about the exact size and shape of each of the primary beams as well as the presence of sidelobes due to the finite deconvolution threshold. In addition, artefacts such as residual continuum emission and bandpass ripples have affected some of the data. The pilot survey has been highly successful in uncovering such technical problems, most of which are expected to be addressed and rectified before the start of the full WALLABY survey.

We present the most sensitive and detailed view of the neutral hydrogen ( ${\rm H\small I}$ ) emission associated with the Small Magellanic Cloud (SMC), through the combination of data from the Australian Square Kilometre Array Pathfinder (ASKAP) and Parkes (Murriyang), as part of the Galactic Australian Square Kilometre Array Pathfinder (GASKAP) pilot survey. These GASKAP-HI pilot observations, for the first time, reveal ${\rm H\small I}$ in the SMC on similar physical scales as other important tracers of the interstellar medium, such as molecular gas and dust. The resultant image cube possesses an rms noise level of 1.1 K ( $1.6\,\mathrm{mJy\ beam}^{-1}$ ) $\mathrm{per}\ 0.98\,\mathrm{km\ s}^{-1}$ spectral channel with an angular resolution of $30^{\prime\prime}$ ( ${\sim}10\,\mathrm{pc}$ ). We discuss the calibration scheme and the custom imaging pipeline that utilises a joint deconvolution approach, efficiently distributed across a computing cluster, to accurately recover the emission extending across the entire ${\sim}25\,\mathrm{deg}^2$ field-of-view. We provide an overview of the data products and characterise several aspects including the noise properties as a function of angular resolution and the represented spatial scales by deriving the global transfer function over the full spectral range. A preliminary spatial power spectrum analysis on individual spectral channels reveals that the power law nature of the density distribution extends down to scales of 10 pc. We highlight the scientific potential of these data by comparing the properties of an outflowing high-velocity cloud with previous ASKAP+Parkes ${\rm H\small I}$ test observations.

The Variables and Slow Transients Survey (VAST) on the Australian Square Kilometre Array Pathfinder (ASKAP) is designed to detect highly variable and transient radio sources on timescales from 5 s to $\sim\!5$ yr. In this paper, we present the survey description, observation strategy and initial results from the VAST Phase I Pilot Survey. This pilot survey consists of $\sim\!162$ h of observations conducted at a central frequency of 888 MHz between 2019 August and 2020 August, with a typical rms sensitivity of $0.24\ \mathrm{mJy\ beam}^{-1}$ and angular resolution of $12-20$ arcseconds. There are 113 fields, each of which was observed for 12 min integration time, with between 5 and 13 repeats, with cadences between 1 day and 8 months. The total area of the pilot survey footprint is 5 131 square degrees, covering six distinct regions of the sky. An initial search of two of these regions, totalling 1 646 square degrees, revealed 28 highly variable and/or transient sources. Seven of these are known pulsars, including the millisecond pulsar J2039–5617. Another seven are stars, four of which have no previously reported radio detection (SCR J0533–4257, LEHPM 2-783, UCAC3 89–412162 and 2MASS J22414436–6119311). Of the remaining 14 sources, two are active galactic nuclei, six are associated with galaxies and the other six have no multi-wavelength counterparts and are yet to be identified.

In this paper, we describe the system design and capabilities of the Australian Square Kilometre Array Pathfinder (ASKAP) radio telescope at the conclusion of its construction project and commencement of science operations. ASKAP is one of the first radio telescopes to deploy phased array feed (PAF) technology on a large scale, giving it an instantaneous field of view that covers $31\,\textrm{deg}^{2}$ at $800\,\textrm{MHz}$. As a two-dimensional array of 36$\times$12 m antennas, with baselines ranging from 22 m to 6 km, ASKAP also has excellent snapshot imaging capability and 10 arcsec resolution. This, combined with 288 MHz of instantaneous bandwidth and a unique third axis of rotation on each antenna, gives ASKAP the capability to create high dynamic range images of large sky areas very quickly. It is an excellent telescope for surveys between 700 and $1800\,\textrm{MHz}$ and is expected to facilitate great advances in our understanding of galaxy formation, cosmology, and radio transients while opening new parameter space for discovery of the unknown.

The Rapid ASKAP Continuum Survey (RACS) is the first large-area survey to be conducted with the full 36-antenna Australian Square Kilometre Array Pathfinder (ASKAP) telescope. RACS will provide a shallow model of the ASKAP sky that will aid the calibration of future deep ASKAP surveys. RACS will cover the whole sky visible from the ASKAP site in Western Australia and will cover the full ASKAP band of 700–1800 MHz. The RACS images are generally deeper than the existing NRAO VLA Sky Survey and Sydney University Molonglo Sky Survey radio surveys and have better spatial resolution. All RACS survey products will be public, including radio images (with $\sim$ 15 arcsec resolution) and catalogues of about three million source components with spectral index and polarisation information. In this paper, we present a description of the RACS survey and the first data release of 903 images covering the sky south of declination $+41^\circ$ made over a 288-MHz band centred at 887.5 MHz.

Ice shelves play a critical role in modulating dynamic loss of ice from the grounded portion of the Antarctic Ice Sheet and its contribution to sea-level rise. Measurements of ice-shelf motion provide insights into processes modifying buttressing. Here we investigate the effect of seasonal variability of basal melting on ice flow of Ross Ice Shelf. Velocities were measured from November 2015 to December 2016 at 12 GPS stations deployed from the ice front to 430 km upstream. The flow-parallel velocity anomaly at each station, relative to the annual mean, was small during early austral summer (November–January), negative during February–April, and positive during austral winter (May–September). The maximum velocity anomaly reached several metres per year at most stations. We used a 2-D ice-sheet model of the RIS and its grounded tributaries to explore the seasonal response of the ice sheet to time-varying basal melt rates. We find that melt-rate response to changes in summer upper-ocean heating near the ice front will affect the future flow of RIS and its tributary glaciers. However, modelled seasonal flow variations from increased summer basal melting near the ice front are much smaller than observed, suggesting that other as-yet-unidentified seasonal processes are currently dominant.