Survival analysis is an important analytic method in the social and medical sciences. Also known under the name time-to-event analysis, this method provides parameter estimation and model fitting commonly conducted via maximum-likelihood. Bayesian survival analysis offers multiple advantages over the frequentist approach for measurement…

In this digital ITEMS module, Dr. Roy Levy describes Bayesian approaches to psychometric modeling. He discusses how Bayesian inference is a mechanism for reasoning in a probability-modeling framework and is well-suited to core problems in educational measurement: reasoning from student performances on an assessment to make inferences about their…

Analysts of discrete data often face the challenge of managing the tendency of inflation on certain values. When treated improperly, such phenomenon may lead to biased estimates and incorrect inferences. This study extends the existing literature on single-value inflated models and develops a general framework to handle variables with more than…

Immediacy is one of the necessary criteria to show strong evidence of treatment effect in single case experimental designs (SCEDs). With the exception of Natesan and Hedges (2017) no inferential statistical tool has been used to demonstrate or quantify it until now. We investigate and quantify immediacy by treating the change-points between the…

Simulation modeling is an effective tool for solving problems that cannot be explained analytically or when data cannot be collected. This is done by simulating the observed behavior of a problem under study using a computer program. In math education, this can develop knowledge and fundamental competencies of simulation modeling at a higher level…

This Monte Carlo simulation study compares methods to estimate the effects of programs with multiple versions when assignment of individuals to program version is not random. These methods use generalized propensity scores, which are predicted probabilities of receiving a particular level of the treatment conditional on covariates, to remove…

The Monte Carlo method is one of the basic simulation statistical methods which can be used both to demonstrate basic probability and statistical concepts as well as to analyse the behaviour stochastic models. The introduction part of the article provides a brief description of the Monte Carlo method. The main part of the article is concentrated…

Data simulation and Monte Carlo simulation studies are important skills for researchers and practitioners of educational and psychological measurement, but there are few resources on the topic specific to item response theory. Even fewer resources exist on the statistical software techniques to implement simulation studies. This article presents…

In item response theory (IRT) modeling, the Fisher information matrix is used for numerous inferential procedures such as estimating parameter standard errors, constructing test statistics, and facilitating test scoring. In principal, these procedures may be carried out using either the expected information or the observed information. However, in…

Pseudocontingencies are inferences about correlations in the environment that are formed on the basis of statistical regularities like skewed base rates or varying base rates across environmental contexts. Previous research has demonstrated that pseudocontingencies provide a pervasive mechanism of inductive inference in numerous social judgment…

The Monte Carlo method and related multiple imputation methods are traditionally used in math, physics and science to estimate and analyze data and are now becoming standard tools in analyzing business and financial problems. However, few sources explain the application of the Monte Carlo method for individuals and business professionals who are…

The variance formula derived for a two-stage sampling design without replacement employs the joint inclusion probabilities in the first-stage selection of clusters. One of the difficulties encountered in data analysis is the lack of information about such joint inclusion probabilities. One way to solve this issue is by applying Hájek's…

Many important high-stakes decisions--college admission, academic performance evaluation, and even job promotion--depend on accurate and reliable scores from valid large-scale assessments. However, examinees sometimes cheat by copying answers from other test-takers or practicing with test items ahead of time, which can undermine the effectiveness…

Studies analyzing clustered data sets using both multilevel models (MLMs) and ordinary least squares (OLS) regression have generally concluded that resulting point estimates, but not the standard errors, are comparable with each other. However, the accuracy of the estimates of OLS models is important to consider, as several alternative techniques…

Stan is a probabilistic programming language for specifying statistical models. A Stan program imperatively defines a log probability function over parameters conditioned on specified data and constants. As of version 2.14.0, Stan provides full Bayesian inference for continuous-variable models through Markov chain Monte Carlo methods such as the…