Random item effects item response theory (IRT) models, which treat both person and item effects as random, have received much attention for more than a decade. The random item effects approach has several advantages in many practical settings. The present study introduced an explanatory multidimensional random item effects rating scale model. The…

The use of item responses from questionnaire data is ubiquitous in social science research. One side effect of using such data is that researchers must often account for item level missingness. Multiple imputation (Rubin, 1987) is one of the most widely used missing data handling techniques. The traditional multiple imputation approach in…

We present a logistic function of a monotonic polynomial with a lower asymptote, allowing additional flexibility beyond the three-parameter logistic model. We develop a maximum marginal likelihood based approach to estimate the item parameters. The new item response model is demonstrated on math assessment data from a state, and a computationally…

Student growth percentiles (SGPs, Betebenner, 2009) are used to locate a student's current score in a conditional distribution based on the student's past scores. Currently, following Betebenner (2009), quantile regression (QR) is most often used operationally to estimate the SGPs. Alternatively, multidimensional item response theory (MIRT) may…

Student Growth Percentiles (SGP, Betebenner, 2009) are used to locate a student's current score in a conditional distribution based on the student's past scores. Currently, following Betebenner (2009), quantile regression is most often used operationally to estimate the SGPs. Alternatively, multidimensional item response theory (MIRT) may also be…

This research is concerned with two topics in assessing model fit for categorical data analysis. The first topic involves the application of a limited-information overall test, introduced in the item response theory literature, to Structural Equation Modeling (SEM) of categorical outcome variables. Most popular SEM test statistics assess how well…

We present a logistic function of a monotonic polynomial with a lower asymptote, allowing additional flexibility beyond the three-parameter logistic model. We develop a maximum marginal likelihood-based approach to estimate the item parameters. The new item response model is demonstrated on math assessment data from a state, and a computationally…

This research concerns a new proposal for calculating student growth percentiles (SGP, Betebenner, 2009). In Betebenner (2009), quantile regression (QR) is used to estimate the SGPs. However, measurement error in the score estimates, which always exists in practice, leads to bias in the QR-­based estimates (Shang, 2012). One way to address this…

We present a semi-parametric approach to estimating item response functions (IRF) useful when the true IRF does not strictly follow commonly used functions. Our approach replaces the linear predictor of the generalized partial credit model with a monotonic polynomial. The model includes the regular generalized partial credit model at the lowest…

We present a logistic function of a monotonic polynomial with a lower asymptote, allowing additional flexibility beyond the three-parameter logistic model. We develop a maximum marginal likelihood based approach to estimate the item parameters. The new item response model is demonstrated on math assessment data from a state, and a computationally…

In Ramsay curve item response theory (RC-IRT) modeling, the shape of the latent trait distribution is estimated simultaneously with the item parameters. In its original implementation, RC-IRT is estimated via Bock and Aitkin's EM algorithm, which yields maximum marginal likelihood estimates. This method, however, does not produce the…

The present study was motivated by the recognition that standard errors (SEs) of item response theory (IRT) model parameters are often of immediate interest to practitioners and that there is currently a lack of comparative research on different SE (or error variance-covariance matrix) estimation procedures. The present study investigated item…

Lord and Wingersky's (1984) recursive algorithm for creating summed score based likelihoods and posteriors has a proven track record in unidimensional item response theory (IRT) applications. Extending the recursive algorithm to handle multidimensionality is relatively simple, especially with fixed quadrature because the recursions can be defined…

Differential item functioning (DIF) occurs when the probability of responding in a particular category to an item differs for members of different groups who are matched on the construct being measured. The identification of DIF is important for valid measurement. This research evaluates an improved version of Lord's X[superscript 2] Wald test for…

In item response theory (IRT) modeling, the item parameter error covariance matrix plays a critical role in statistical inference procedures. When item parameters are estimated using the EM algorithm, the parameter error covariance matrix is not an automatic by-product of item calibration. Cai proposed the use of Supplemented EM algorithm for…