No abstract

This study presents a general framework for single-administration reliability methods, such as Cronbach's alpha, Guttman's lambda-2, and method MS. This general framework was used to derive a new approach to estimating test-score reliability by means of the unrestricted latent class model. This new approach is the latent class reliability coefficient (LCRC). Unlike other single-administration reliability methods, LCRC places few restrictions on the item scores. A simulation study showed that if data are multidimensional or if double monotonicity does not hold, then LCRC is less biased relative to the true reliability than Cronbach's alpha, Guttman's lambda-2, method MS, and the split-half reliability coefficient.Test-score reliability, denoted r XX 0 , is one of the most reported statistics in social and behavioral science research. This study adopts the definition proposed by Lord and Novick (1968, p. 61). Let X be the test score, which is defined as the sum of the J item scores X j ðj ¼ 1; . . . ; J Þ, so that X ¼ P J j¼1 X j . In the population, test score X has expectation m X and variance s 2 X . Let T be the unobservable true score (Lord & Novick, 1968, chaps. 2 and 3), defined as a testee's expectation of X across his or her propensity distribution of independent test repetitions. In the population, T has expectation m T and variance s 2 T . Test-score reliability is defined as the product-moment correlation between two sets of independent test scores from two different but interchangeable tests known as parallel tests (which replace two independent repetitions), and equals the ratio of true score and test score variances,Article

Traditionally latent class (LC) analysis is used by applied researchers as a tool for identifying substantively meaningful clusters. More recently, LC models have also been used as a density estimation tool for categorical variables. We introduce a divisive LC (DLC) model as a density estimation tool that may offer several advantages in comparison to a standard LC model. When using an LC model for density estimation, a considerable number of increasingly large LC models may have to be estimated before sufficient model-fit is achieved. A DLC model consists of a sequence of small LC models. Therefore, a DLC model can be estimated much faster and can easily utilize multiple processor cores, meaning that this model is more widely applicable and practical. In this study we describe the algorithm of fitting a DLC model, and discuss the various settings that indirectly influence the precision of a DLC model as a density estimation tool. These settings are illustrated using a synthetic data example, and the best performing algorithm is applied to a real-data example. The generated data example showed that, using specific decision rules, a DLC model is able to correctly model complex associations amongst categorical variables.

No abstract

We studied four methods for handling incomplete categorical data in statistical modeling: (1) maximum likelihood estimation of the statistical model with incomplete data, (2) multiple imputation using a loglinear model, (3) multiple imputation using a latent class model, (4) and multivariate imputation by chained equations. Each method has advantages and disadvantages, and it is unknown which method should be recommended to practitioners. We reviewed the merits of each method and investigated their effect on the bias and stability of parameter estimates and bias of the standard errors. We found that multiple imputation using a latent class model with many latent classes was the most promising method for handling incomplete categorical data, especially when the number of variables used in the imputation model is large.