We present a class of finite mixture multilevel multidimensional ordinal IRT models for large scale cross-cultural research. Our model is proposed for confirmatory research settings. Our prior for item parameters is a mixture distribution to accommodate situations where different groups of countries have different measurement operations, while countries within these groups are still allowed to be heterogeneous. A simulation study is conducted that shows that all parameters can be recovered. We also apply the model to real data on the two components of affective subjective well-being: positive affect and negative affect. The psychometric behavior of these two scales is studied in 28 countries across four continents.

A Metropolis–Hastings Robbins–Monro (MH-RM) algorithm for high-dimensional maximum marginal likelihood exploratory item factor analysis is proposed. The sequence of estimates from the MH-RM algorithm converges with probability one to the maximum likelihood solution. Details on the computer implementation of this algorithm are provided. The accuracy of the proposed algorithm is demonstrated with simulations. As an illustration, the proposed algorithm is applied to explore the factor structure underlying a new quality of life scale for children. It is shown that when the dimensionality is high, MH-RM has advantages over existing methods such as numerical quadrature based EM algorithm. Extensions of the algorithm to other modeling frameworks are discussed.

A general theory on the use of correlation weights in linear prediction has yet to be proposed. In this paper we take initial steps in developing such a theory by describing the conditions under which correlation weights perform well in population regression models. Using OLS weights as a comparison, we define cases in which the two weighting systems yield maximally correlated composites and when they yield minimally similar weights. We then derive the least squares weights (for any set of predictors) that yield the largest drop in R2 (the coefficient of determination) when switching to correlation weights. Our findings suggest that two characteristics of a model/data combination are especially important in determining the effectiveness of correlation weights: (1) the condition number of the predictor correlation matrix, Rxx, and (2) the orientation of the correlation weights to the latent vectors of Rxx.

Multinomial processing tree models are widely used in many areas of psychology. A hierarchical extension of the model class is proposed, using a multivariate normal distribution of person-level parameters with the mean and covariance matrix to be estimated from the data. The hierarchical model allows one to take variability between persons into account and to assess parameter correlations. The model is estimated using Bayesian methods with weakly informative hyperprior distribution and a Gibbs sampler based on two steps of data augmentation. Estimation, model checks, and hypotheses tests are discussed. The new method is illustrated using a real data set, and its performance is evaluated in a simulation study.

Measures of agreement are used in a wide range of behavioral, biomedical, psychosocial, and health-care related research to assess reliability of diagnostic test, psychometric properties of instrument, fidelity of psychosocial intervention, and accuracy of proxy outcome. The concordance correlation coefficient (CCC) is a popular measure of agreement for continuous outcomes. In modern-day applications, data are often clustered, making inference difficult to perform using existing methods. In addition, as longitudinal study designs become increasingly popular, missing data have become a serious issue, and the lack of methods to systematically address this problem has hampered the progress of research in the aforementioned fields. In this paper, we develop a novel approach to tackle the complexities involved in addressing missing data and other related issues for performing CCC analysis within a longitudinal data setting. The approach is illustrated with both real and simulated data.

Three plausible assumptions of conditional independence in a hierarchical model for responses and response times on test items are identified. For each of the assumptions, a Lagrange multiplier test of the null hypothesis of conditional independence against a parametric alternative is derived. The tests have closed-form statistics that are easy to calculate from the standard estimates of the person parameters in the model. In addition, simple closed-form estimators of the parameters under the alternatives of conditional dependence are presented, which can be used to explore model modification. The tests were applied to a data set from a large-scale computerized exam and showed excellent power to detect even minor violations of conditional independence.

Item calibration is an essential issue in modern item response theory based psychological or educational testing. Due to the popularity of computerized adaptive testing, methods to efficiently calibrate new items have become more important than that in the time when paper and pencil test administration is the norm. There are many calibration processes being proposed and discussed from both theoretical and practical perspectives. Among them, the online calibration may be one of the most cost effective processes. In this paper, under a variable length computerized adaptive testing scenario, we integrate the methods of adaptive design, sequential estimation, and measurement error models to solve online item calibration problems. The proposed sequential estimate of item parameters is shown to be strongly consistent and asymptotically normally distributed with a prechosen accuracy. Numerical results show that the proposed method is very promising in terms of both estimation accuracy and efficiency. The results of using calibrated items to estimate the latent trait levels are also reported.

This paper investigates the precision of parameters estimated from local samples of time dependent functions. We find that time delay embedding, i.e., structuring data prior to analysis by constructing a data matrix of overlapping samples, increases the precision of parameter estimates and in turn statistical power compared to standard independent rows of panel data. We show that the reason for this effect is that the sign of estimation bias depends on the position of a misplaced data point if there is no a priori knowledge about initial conditions of the time dependent function. Hence, we reason that the advantage of time delayed embedding is likely to hold true for a wide variety of functions. We support these conclusions both by mathematical analysis and two simulations.

The paper presents inequalities between four descriptive statistics that can be expressed in the form [P − E(P)]/[1 − E(P)], where P is the observed proportion of agreement of a k × k table with identical categories, and E(P) is a function of the marginal probabilities. Scott’s π is an upper bound of Goodman and Kruskal’s λ and a lower bound of both Bennett et al. S and Cohen’s κ. We introduce a concept for the marginal probabilities of the k×k table called weak marginal symmetry. Using the rearrangement inequality, it is shown that Bennett et al. S is an upper bound of Cohen’s κ if the k×k table is weakly marginal symmetric.