We consider two-level models where a continuous response R and continuous covariates C are assumed missing at random. Inferences based on maximum likelihood or Bayes are routinely made by estimating their joint normal distribution from observed data R[subscript obs] and C[subscript obs]. However, if the model for R given C includes random…

This note extends the results in the 2016 article by Raykov, Marcoulides, and Li to the case of correlated errors in a set of observed measures subjected to principal component analysis. It is shown that when at least two measures are fallible, the probability is zero for any principal component--and in particular for the first principal…

Probability and chance are essential concepts, not just in statistics but in real life. We present an adaptable activity which investigates what we mean by bias, how we can identify bias, and how we can use it to our advantage!

The well-known recency effect in immediate free recall reverses when subjects attempt to recall items studied and tested on a series of prior lists, as in the final-free-recall procedure (Craik, 1970). In this case, the last few items on each list are actually remembered less well than are the midlist items. Because dual-store theories of recall…

Several statistical models have been developed in educational measurement to determine and track the performance of students in longitudinal studies. An example of a model designed for such purpose is the latent transition analysis (LTA) model. The LTA model (Graham, Collins, Wugalter, Chung, & Hansen 1991) is a type of autoregressive model…

Undergraduate students tend to struggle with probability in their introductory statistics course. Probability problem solving requires several steps. First, students must make sense of the probability scenario, then determine the appropriate probability rules, and finally, execute the procedures to solve the problem. With no previous exposure to…

A Machine Learning framework for predicting enrollment is proposed. The framework consists of Amazon Web Services SageMaker together with standard Python tools for data analytics, including Pandas, NumPy, MatPlotLib, and ScikitLearn. The tools are deployed with Jupyter Notebooks running on AWS SageMaker. Based on three years of enrollment history,…

The transition from vocational education and training to regular employment is an important step in the occupational biography of apprenticeship graduates. In the last decade, the retention rate of apprenticeship completers has remained stable at a high level, and graduates face good job opportunities in Germany. Despite these positive…

This study investigated the extent to which class-specific parameter estimates are biased by the within-class normality assumption in nonnormal growth mixture modeling (GMM). Monte Carlo simulations for nonnormal GMM were conducted to analyze and compare two strategies for obtaining unbiased parameter estimates: relaxing the within-class normality…

Interpreting phenomena under uncertainty stands as a substantial cognitive activity in our daily life. Furthermore, in probability education research, there is a need for developing a unified model that involves several probabilistic conceptions. From this aspect, a central inquiry has been raised through this study: how do preservice mathematics…

The article analyses the effect of gender in professors' career advancement using data on the entire population of professors in the Italian university system, data on the National Scientific Qualification (NSQ) accreditation scheme, and data on scientific productivity (SciVal) for bibliometric scientific sectors. As NSQ accreditation is a…

There is increasing attention on the retention of international students, with many stakeholders desiring to keep international students for long-term economic growth. This study examined the factors affecting international students choosing to stay in Finland 5 years after initial enrollment, with particular focus on the role graduation plays in…

We estimate the relationship between exclusionary discipline given in eighth-grade and the probability of ninth-grade retention. We use a rich 7-year, student-level, panel data set from Arkansas. We use a novel approach by limiting our sample to students who switch schools between eighth and ninth grades. This movement gives each student a fresh…

When we read, errors in oculomotor programming can cause the eyes to land and fixate on different words from what the mind intended. Previous work suggests that these "mislocated fixations" form 10-30% of first-pass fixations in reading eye movement data, which presents theoretical and analytic issues for eyetracking-while-reading…

This paper investigates two specific probabilistic biases which middle graders usually exhibit when reasoning about probability and randomness on assessment items. We discuss how students' reasoning about key probability concepts undergirds statistics literacy related to randomness, independence, and the likelihood of future events based on past…