The standard methodology for many large-scale assessments in education involves regressing latent variables on numerous contextual variables to estimate proficiency distributions. To reduce the number of contextual variables used in the regression and improve estimation, we propose and evaluate principal component analysis on the covariance matrix…

This paper aims to illustrate how data visualization could be utilized to identify errors prior to modeling, using an example with multi-dimensional item response theory (MIRT). MIRT combines item response theory and factor analysis to identify a psychometric model that investigates two or more latent traits. While it may seem convenient to…

The kernel method of test equating is a unified approach to test equating with some advantages over traditional equating methods. Therefore, it is important to evaluate in a comprehensive way the usefulness and appropriateness of the Kernel equating (KE) method, as well as its advantages and disadvantages compared with several popular item…

Modeling multidimensional test data with a unidimensional model can result in serious statistical errors, such as bias in item parameter estimates. Many methods exist for assessing the dimensionality of a test. The current study focused on DIMTEST. Using simulated data, the effects of sample size splitting for use with the ATFIND procedure for…

The use of polytomous items in assessments has increased over the years, and as a result, the validity of these assessments has been a concern. Differential item functioning (DIF) and missing data are two factors that may adversely affect assessment validity. Both factors have been studied separately, but DIF and missing data are likely to occur…

The sample size determination is an important issue for planning research. However, limitations in size have seldom been discussed in the literature. Thus, how to allocate participants into different treatment groups to achieve the desired power is a practical issue that still needs to be addressed when one group size is fixed. The authors focused…

The performance of parameter estimates and standard errors in estimating F. Samejima's graded response model was examined across 324 conditions. Full information maximum likelihood (FIML) was compared with a 3-stage estimator for categorical item factor analysis (CIFA) when the unweighted least squares method was used in CIFA's third stage. CIFA…

The authors examined the robustness of multilevel linear growth curve modeling to misspecification of an autoregressive moving average process. As previous research has shown (J. Ferron, R. Dailey, & Q. Yi, 2002; O. Kwok, S. G. West, & S. B. Green, 2007; S. Sivo, X. Fan, & L. Witta, 2005), estimates of the fixed effects were unbiased, and Type I…

Differential item functioning (DIF) analysis is a statistical technique used for ensuring the equity and fairness of educational assessments. This study formulates a new DIF analysis method using the information similarity index (ISI). ISI compares item information functions when data fits the Rasch model. Through simulations and an international…

This Monte Carlo study investigates the beneficiary effect of including auxiliary variables during estimation of confirmatory factor analysis models with multiple imputation. Specifically, it examines the influence of sample size, missing rates, missingness mechanism combinations, missingness types (linear or convex), and the absence or presence…

Tests of model misfit are often performed to validate the use of a particular model in item response theory. Douglas and Cohen (2001) introduced a general nonparametric approach for detecting misfit under the two-parameter logistic model. However, the statistical properties of their approach, and empirical comparisons to other methods, have not…

Sample-size restrictions limit the contingency table approaches based on asymptotic distributions, such as the Mantel-Haenszel (MH) procedure, for detecting differential item functioning (DIF) in many practical applications. Within this framework, the present study investigated the power and Type I error performance of empirical and inferential…

The standard Pearson correlation coefficient is a biased estimator of the true population correlation, ?, when the predictor and the criterion are range restricted. To correct the bias, the correlation corrected for range restriction, r-sub(c), has been recommended, and a standard formula based on asymptotic results for estimating its standard…

The performance of methods for detecting publication bias in meta-analysis was evaluated using Monte Carlo methods. Four methods of bias detection were investigated: Begg's rank correlation, Egger's regression, funnel plot regression, and trim and fill. Five factors were included in the simulation design: number of primary studies in each…