Item response theory (IRT) is a statistical paradigm for developing educational tests and assessing students. IRT, however, currently lacks an established graphical method for examining model fit for the three-parameter logistic model, the most flexible and popular IRT model in educational testing. A method is presented here to do this. The graph,…

The Hunger Games is an annual event in the fictional country of Panem. Each year, 24 children (tributes) are chosen by lottery from 12 districts to fight to the death in the arena for the entertainment of the Capitol citizens. Using statistical analysis and computer simulations, we will explore the possibility that the Gamemakers, those in charge…

There is great potential in making assessment and learning complementary. In this study, we investigated the feasibility of developing a desktop virtual reality (VR) laboratory simulation on the topic of genetics, with integrated assessment using multiple choice questions based on item response theory (IRT) and feedback based on the cognitive…

Used computer simulation methods to examine the sensitivity of model fit criteria to misspecification of the first-level error structure in two-level models of change and to examine the impact of misspecification estimates on the variance parameters, estimates of the fixed effects, and tests of the fixed effects. Discusses problems caused by…

Used three approaches to understand the effect of the number of variables in the model on model fit in structural equation modeling through computer simulation. Developed a simple formula for the theoretical value of the comparative fit index. (SLD)

The distinction between deterministic and statistical reasoning in the application of models to educational measurement is explicated. Issues addressed include the relationship between data and estimation equations, distinction between parameters and parameter estimates, and power of tests of fit of responses across the ability continuum. (TJH)

Major issues related to index-of-fit conjoint analysis were addressed in this simulation study. Goals were to develop goodness-of-fit criteria for conjoint analysis; develop tests to determine the significance of conjoint analysis results; and calculate the power of the test of the null hypothesis of random data distribution. (SLD)

The influence of sample size (N) and model parsimony on a set of 22 goodness of fit indices was investigated, including those typically used in confirmatory factor analysis and some recently developed indices. For sample data simulated from 2 known population data structures, values for 6 of 22 fit indices were reasonably independent of N and were…

The purpose of the present investigation is to examine the influence of sample size (N) and model complexity on a set of 23 goodness-of-fit (GOF) indices, including those typically used in confirmatory factor analysis. The focus was on two potential problems in assessing GOF: (1) some fit indices are substantially influenced by N so that tests of…

A diabetes-management model is presented, which includes an attitudinal element and depicts relationships among causal elements. LISREL-VI was used to analyze data from 115 Type-I and 105 Type-II patients. The data did not closely fit the model. Results support the importance of the personal meaning of diabetes. (TJH)

This study investigated the distributional properties of the standardized residual that is commonly used in the Rasch model calibration program to develop various indices of item and person fit. The power of the standardized residual to detect measurement disturbances is also addressed. (TJH)

The purpose of this study is to determine an efficient way to reduce the bias in estimates of the Rasch model parameters due to aberrant response patterns. First, the benefits of using one- or two-sided goodness-of-fit tests of patterns with the model are discussed. Then, the consequences of removing non-fitting patterns from Rasch model data are…

To assess problems in hypothesis testing and model comparisons based on normed indices caused by latent class models with sparse contingency tables, a simulation was carried out investigating the distributions of the likelihood ratio statistic, the Pearson statistic chi-square, and a new goodness of fit statistic. (SLD)

Accuracy of three exact person tests for assessing model-data fit in the Rasch model was investigated in a simulation study. Empirical Type I error rates and statistical power of the person tests were computed. The exact person test conditioned on total score is a promising tool for assessing consistency of response patterns with the Rasch model.…

The multitrait-multimethod (MTMM) paradigm is used widely to assess construct validity, but D. A. Kenny and D. A. Kashy (1992) lament that even after 30 years we still do not know how to analyze MTMM data. The Composite Direct Product (CDP) model has recently attracted considerable attention. Its strengths and weaknesses are evaluated, and a…