Related papers: On an EM-based closed-form solution for 2 paramete…
Parameter estimation is one of the most important tasks in statistics, and is key to helping people understand the distribution behind a sample of observations. Traditionally parameter estimation is done either by closed-form solutions…
We propose a class of Item Response Theory models for items with ordinal polytomous responses, which extends an existing class of multidimensional models for dichotomously-scored items measuring more than one latent trait. In the proposed…
Marginal maximum likelihood estimation (MMLE) in item response theory (IRT) is highly sensitive to aberrant responses, such as careless answering and random guessing, which can reduce estimation accuracy. To address this issue, this study…
Loss tomography has been studied for more than 10 years and a number of estimators have been proposed. The estimators can be divided into two classes: maximum likelihood and non-maximum likelihood. The maximum likelihood estimators rely on…
We propose a structural equation model, which reduces to a multidimensional latent class item response theory model, for the analysis of binary item responses with non-ignorable missingness. The missingness mechanism is driven by two sets…
In this paper, we address the identification problem for the systems characterized by linear time-invariant dynamics with bilinear observation models. More precisely, we consider a suitable parametric description of the system and formulate…
Item parameter estimation in pharmacometric item response theory (IRT) models is predominantly performed using the Laplace estimation algorithm as implemented in NONMEM. In psychometrics a wide range of different software tools, including…
Joint maximum likelihood (JML) estimation is one of the earliest approaches to fitting item response theory (IRT) models. This procedure treats both the item and person parameters as unknown but fixed model parameters and estimates them…
This paper deals with parameter estimation when the data are randomly right censored. The maximum likelihood estimates from censored samples are obtained by using the expectation-maximization (EM) and Monte Carlo EM (MCEM) algorithms. We…
We provide a general theory of the expectation-maximization (EM) algorithm for inferring high dimensional latent variable models. In particular, we make two contributions: (i) For parameter estimation, we propose a novel high dimensional EM…
The testlet model is a popular statistical approach widely used by researchers and practitioners to address local item dependence (LID), a violation of the local independence assumption in item response theory (IRT) which can cause various…
We consider likelihood-based two-step estimation of latent variable models, in which just the measurement model is estimated in the first step and the measurement parameters are then fixed at their estimated values in the second step where…
Traditional methods for determining assessment item parameters, such as difficulty and discrimination, rely heavily on expensive field testing to collect student performance data for Item Response Theory (IRT) calibration. This study…
The EM algorithm is a method for finding the maximum likelihood estimate of a model in the presence of missing data. Unfortunately, EM does not produce a parameter covariance matrix for standard errors. Supplemented EM (SEM; Meng & Rubin,…
In this paper, we study a generalization of the two-groups model in the presence of covariates --- a problem that has recently received much attention in the statistical literature due to its applicability in multiple hypotheses testing…
Incorporating Item Response Theory (IRT) into NLP tasks can provide valuable information about model performance and behavior. Traditionally, IRT models are learned using human response pattern (RP) data, presenting a significant bottleneck…
Evaluation of large language models (LLMs) is increasingly critical, yet standard benchmarking methods rely on average accuracy, overlooking both the inherent stochasticity of LLM outputs and the heterogeneity of benchmark items. Item…
Expectation Maximization (EM) is among the most popular algorithms for estimating parameters of statistical models. However, EM, which is an iterative algorithm based on the maximum likelihood principle, is generally only guaranteed to find…
This paper introduces a flexible Bayesian nonparametric Item Response Theory (IRT) model, which applies to dichotomous or polytomous item responses, and which can apply to either unidimensional or multidimensional scaling. This is an…
We consider the estimation accuracy of individual strength parameters of a Thurstone choice model when each input observation consists of a choice of one item from a set of two or more items (so called top-1 lists). This model accommodates…