Given sample data, how do you calculate the value of a parameter? While this question is impossible to answer, it is frequently encountered in statistics classes when students are introduced to the distinction between a sample and a population (or between a statistic and a parameter). It is not uncommon for teachers of statistics to also confuse…

Multisite cluster randomized trials (MCRTs), in which, the intermediate-level clusters (e.g., classrooms) are randomly assigned to the treatment or control condition within each site (e.g., school), are among the most commonly used experimental designs across a broad range of disciplines. MCRTs often align with the theory that programs are…

The logistic and confined exponential curves are frequently used in studies of growth and learning. These models, which are nonlinear in their parameters, can be estimated using structural equation modeling software. This paper proposes a single combined model, a weighted combination of both models. Mplus, Proc Calis, and lavaan code for the model…

The meta-analytic-predictive (MAP) approach is a Bayesian method to incorporate historical controls in new trials that aims to increase the statistical power and reduce the required sample size. Here we investigate how to calculate the sample size of the new trial when historical data is available, and the MAP approach is used in the analysis. In…

Latent transition analysis is an informative statistical tool for depicting heterogeneity in learning as latent profiles. We present a Monte Carlo simulation study to guide researchers in selecting fit indices for identifying the correct number of profiles. We simulated data representing profiles of learners within a typical pre- post- follow…

Among all, Cronbach's Alpha and McDonald's Omega are commonly used for reliability estimations. The alpha uses inter-item correlations while omega is based on a factor analysis result. This study uses simulated ordinal data sets to test whether the alpha and omega produce different estimates. Their performances were compared according to the…

When designing a study for causal mediation analysis, it is crucial to conduct a power analysis to determine the sample size required to detect the causal mediation effects with sufficient power. However, the development of power analysis methods for causal mediation analysis has lagged far behind. To fill the knowledge gap, I proposed a…

Factor mixture modeling (FMM) is generally complex with both unobserved categorical and unobserved continuous variables. We explore the potential of item parceling to reduce the model complexity of FMM and improve convergence and class enumeration accordingly. To this end, we conduct Monte Carlo simulations with three types of data, continuous,…

Measuring change in an educational or psychological construct over time is often achieved by repeatedly administering the same items to the same examinees over time and fitting a second-order latent growth curve model. However, latent growth modeling with full information maximum likelihood (FIML) estimation becomes computationally challenging…

There is a great deal of research about item response theory (IRT) conducted by simulations. Item and ability parameters are estimated with varying numbers of replications under different test conditions. However, it is not clear what the appropriate number of replications should be. The aim of the current study is to develop guidelines for the…

Contamination of responses due to extreme and midpoint response style can confound the interpretation of scores, threatening the validity of inferences made from survey responses. This study incorporated person-level covariates in the multidimensional item response tree model to explain heterogeneity in response style. We include an empirical…

We derive sample-allocation formulas that maximize the power of several mediation tests in two-level-group-randomized studies under a linear cost structure and fixed budget. The results suggest that the optimal individual sample size is typically smaller than that associated with the detection of a main effect and is frequently less than 10 under…

Statistical mediation analysis allows researchers to identify the most important mediating constructs in the causal process studied. Identifying specific mediators is especially relevant when the hypothesized mediating construct consists of multiple related facets. The general definition of the construct and its facets might relate differently to…

Parallel analysis (PA) assesses the number of factors in exploratory factor analysis. Traditionally PA compares the eigenvalues for a sample correlation matrix with the eigenvalues for correlation matrices for 100 comparison datasets generated such that the variables are independent, but this approach uses the wrong reference distribution. The…

Previous research includes frequent admonitions regarding the importance of establishing connectivity in data collection designs prior to the application of Rasch models. However, details regarding the influence of characteristics of the linking sets used to establish connections among facets, such as locations on the latent variable, model-data…