Previous research explicates ordinal and disordinal interactions through the concept of the "crossover point." This point is determined via simple regression models of a focal predictor at specific moderator values and signifies the intersection of these models. An interaction effect is labeled as disordinal (or ordinal) when the…

Suppression effects in multiple linear regression are one of the most elusive phenomena in the educational and psychological measurement literature. The question is, How can including a variable, which is completely unrelated to the criterion variable, in regression models significantly increase the predictive power of the regression models? In…

Treatments in randomized studies are often targeted to key mediating variables. Researchers want to know if the treatment is effective and how the mediators affect the outcome. The data are often analyzed using structural equation models (SEMs), and model coefficients are interpreted as effects. However, only assignment to treatment groups is…

This article addresses three questions: Does reduced class size cause higher academic achievement in reading, mathematics, listening, and word recognition skills? If it does, how large are these effects? Does the magnitude of such effects vary significantly across schools? The authors analyze data from Tennessee's Student/Teacher Achievement Ratio…

The topic of "truncation by death" in randomized experiments arises in many fields, such as medicine, economics and education. Traditional approaches addressing this issue ignore the fact that the outcome after the truncation is neither "censored" nor "missing," but should be treated as being defined on an extended sample space. Using an…

An analytical approach was employed to compare sensitivity of causal effect estimates with different assumptions on treatment noncompliance and non-response behaviors. The core of this approach is to fully clarify bias mechanisms of considered models and to connect these models based on common parameters. Focusing on intention-to-treat analysis,…

In this article the authors develop a model that employs a factor analysis structure at Level 2 of a two-level hierarchical linear model (HLM). The model (HLM2F) imposes a structure on a deficient rank Level 2 covariance matrix [tau], and facilitates estimation of a relatively large [tau] matrix. Maximum likelihood estimators are derived via the…

Inference for causal effects is a critical activity in many branches of science and public policy. The field of statistics is the one field most suited to address such problems, whether from designed experiments or observational studies. Consequently, it is arguably essential that departments of statistics teach courses in causal inference to both…

The use of hierarchical models in social science research is discussed, with emphasis on causal inference and consideration of the limitations of hierarchical models. The increased use of Gibbs sampling and other Markov-chain Monte Carlo methods in the application of hierarchical models is recommended. (SLD)