Assessing sensitivity to unmeasured confounding is an important step in observational studies, which typically estimate effects under the assumption that all confounders are measured. In this paper, we develop a sensitivity analysis framework for balancing weights estimators, an increasingly popular approach that solves an optimization problem to…

Empirical studies often demonstrate multiple causal mechanisms potentially involving simultaneous or causally related mediators. However, researchers often use simple mediation models to understand the processes because they do not or cannot measure other theoretically relevant mediators. In such cases, another potentially relevant but unobserved…

Structural equation modeling (SEM) and path analysis using composite-scores are distinct classes of methods for modeling the relationship of theoretical constructs. The two classes of methods are integrated in the partial-least-squares approach to structural equation modeling (PLS-SEM), which systematically generates weighted composites and uses…

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…

Autocorrelation and partial autocorrelation, which provide a mathematical tool to understand repeating patterns in time series data, are often used to facilitate the identification of model orders of time series models (e.g., moving average and autoregressive models). Asymptotic methods for testing autocorrelation and partial autocorrelation such…

Cronbach's coefficient alpha is a widely used reliability measure in social, behavioral, and education sciences. It is reported in nearly every study that involves measuring a construct through multiple items. With non-tau-equivalent items, McDonald's omega has been used as a popular alternative to alpha in the literature. Traditional estimation…

The normal-distribution-based likelihood ratio statistic T[subscript ml] = nF[subscript ml] is widely used for power analysis in structural Equation modeling (SEM). In such an analysis, power and sample size are computed by assuming that T[subscript ml] follows a central chi-square distribution under H[subscript 0] and a noncentral chi-square…

This article suggests two alternative statistical approaches for estimating student growth percentiles (SGP). The first is to estimate percentile ranks of current test scores conditional on past test scores directly, by modeling the conditional cumulative distribution functions, rather than indirectly through quantile regressions. This would…

In a pretest-posttest cluster-randomized trial, one of the methods commonly used to detect an intervention effect involves controlling pre-test scores and other related covariates while estimating an intervention effect at post-test. In many applications in education, the total post-test and pre-test scores that ignores measurement error in the…

Multilevel modeling (MLM) is frequently used to detect group differences, such as an intervention effect in a pre-test--post-test cluster-randomized design. Group differences on the post-test scores are detected by controlling for pre-test scores as a proxy variable for unobserved factors that predict future attributes. The pre-test and post-test…

Regression, weighting and related approaches to estimating a population mean from a sample with nonrandom missing data often rely on the assumption that conditional on covariates, observed samples can be treated as random. Standard methods using this assumption generally will fail to yield consistent estimators when covariates are measured with…

Measurement invariance (MI) is a property of measurement that is often implicitly assumed, but in many cases, not tested. When the assumption of MI is tested, it generally involves determining if the measurement holds longitudinally or cross-culturally. A growing literature shows that other groupings can, and should, be considered as well.…