Consider an old test X consisting of s sections and two new tests Y and Z similar to X consisting of p and q sections respectively. All subjects are given test X plus two variable sections from either test Y or Z. Different pairings of variable sections are given to each subsample of subjects. We present a method of estimating the covariance matrix of the combined test (X1, ..., Xs, Y1, ..., Yp, Z1, ..., Zq) and describe an application of these estimation techniques to linear, observed-score, test equating.

In this paper, some psychometric models will be presented that belong to the larger class of latent response models (LRMs). First, LRMs are introduced by means of an application in the field of componential item response theory (Embretson, 1980, 1984). Second, a general definition of LRMs (not specific for the psychometric subclass) is given. Third, some more psychometric LRMs, and examples of how they can be applied, are presented. Fourth, a method for obtaining maximum likelihood (ML) and some maximum a posteriori (MAP) estimates of the parameters of LRMs is presented. This method is then applied to the conjunctive Rasch model. Fifth and last, an application of the conjunctive Rasch model is presented. This model was applied to responses to typical verbal ability items (open synonym items).

In this paper, linear structural equation models with latent variables are considered. It is shown how many common models arise from incomplete observation of a relatively simple system. Subclasses of models with conditional independence interpretations are also discussed. Using an incomplete data point of view, the relationships between the incomplete and complete data likelihoods, assuming normality, are highlighted. For computing maximum likelihood estimates, the EM algorithm and alternatives are surveyed. For the alternative algorithms, simplified expressions for computing function values and derivatives are given. Likelihood ratio tests based on complete and incomplete data are related, and an example on using their relationship to improve the fit of a model is given.

This paper proposes test statistics based on the likelihood ratio principle for testing equality of proportions in correlated data with additional incomplete samples. Powers of these tests are compared through Monte Carlo simulation with those of tests proposed recently by Ekbohm (based on an unbiased estimator) and Campbell (based on a Pearson-Chi-squared type statistic). Even though tests based on the maximum likelihood principle are theoretically expected to be superior to others, at least asymptotically, results from our simulations show that the gain in power could only be slight.

In this paper, we consider a class of models for two-way matrices with binary entries of 0 and 1. First, we consider Boolean matrix decomposition, conceptualize it as a latent response model (LRM) and, by making use of this conceptualization, generalize it to a larger class of matrix decomposition models. Second, probability matrix decomposition (PMD) models are introduced as a probabilistic version of this larger class of deterministic matrix decomposition models. Third, an algorithm for the computation of the maximum likelihood (ML) and the maximum a posteriori (MAP) estimates of the parameters of PMD models is presented. This algorithm is an EM-algorithm, and is a special case of a more general algorithm that can be used for the whole class of LRMs. And fourth, as an example, a PMD model is applied to data on decision making in psychiatric diagnosis.

Two test statistics are proposed for testing the equality of two correlated proportions when some observations are missing on both responses. The performance of these tests in terms of size and power is compared with other tests by means of Monte Carlo simulations. The proposed tests are easily computed and compare favorably with other tests.

Suppose a collection of standard tests is given to all subjects in a random sample, but a different new test is given to each group of subjects in nonoverlapping subsamples. A simple method is developed for displaying the information that the data set contains about the correlational structure of the new tests. This is possible to some extent, even though each subject takes only one new test. The method uses plausible values of the partial correlations among the new tests given the standard tests in order to generate plausible simple correlations among the new tests and plausible multiple correlations between composites of the new tests and the standard tests. The real data example included suggests that the method can be useful in practical problems.

In planned missingness (PM) designs, certain data are set a priori to be missing. PM designs can increase validity and reduce cost; however, little is known about the loss of efficiency that accompanies these designs. The present paper compares PM designs to reduced sample (RN) designs that have the same total number of data points concentrated in fewer participants. In 4 studies, we consider models for both observed and latent variables, designs that do or do not include an “X set” of variables with complete data, and a full range of between- and within-set correlation values. All results are obtained using asymptotic relative efficiency formulas, and thus no data are generated; this novel approach allows us to examine whether PM designs have theoretical advantages over RN designs removing the impact of sampling error. Our primary findings are that (a) in manifest variable regression models, estimates of regression coefficients have much lower relative efficiency in PM designs as compared to RN designs, (b) relative efficiency of factor correlation or latent regression coefficient estimates is maximized when the indicators of each latent variable come from different sets, and (c) the addition of an X set improves efficiency in manifest variable regression models only for the parameters that directly involve the X-set variables, but it substantially improves efficiency of most parameters in latent variable models. We conclude that PM designs can be beneficial when the model of interest is a latent variable model; recommendations are made for how to optimize such a design.

Far-field three-dimensional X-ray diffraction microscopy allows for quick measurement of the centers of mass and volumes of a large number of grains in a polycrystalline material, along with their crystal lattice orientations and internal stresses. However, the grain boundaries—and, therefore, individual grain shapes—are not observed directly. The present paper aims to overcome this shortcoming by reconstructing grain shapes based only on the incomplete morphological data described above. To this end, cross-entropy (CE) optimization is employed to find a Laguerre tessellation that minimizes the discrepancy between its centers of mass and cell sizes and those of the measured grain data. The proposed algorithm is highly parallel and is thus capable of handling many grains (>8,000). The validity and stability of the CE approach are verified on simulated and experimental datasets.

Since Chen's Entity-Relationship (ER) model, conceptual modeling has been playing a fundamental role in relational data design. In this paper we consider an extended ER (EER) model enriched with cardinality constraints, disjointness assertions, and is a relations among both entities and relationships. In this setting, we consider the case of incomplete data, which is likely to occur, for instance, when data from different sources are integrated. In such a context, we address the problem of providing correct answers to conjunctive queries by reasoning on the schema. Based on previous results about decidability of the problem, we provide a query answering algorithm that performs rewriting of the initial query into a recursive Datalog query encoding the information about the schema. We finally show extensions to more general settings.