Contemporary Precalculus through Applications

The first edition of Contemporary Precalculus through Applications was published in 1993, well before the widespread use of computers in the classroom. Collaborating with students and teachers across the state, faculty from the North Carolina School of Science and Mathematics (NCSSM) have steadily developed, reviewed, and tested the textbook in the years since. It is the sole textbook used in NCSSM precalculus courses. This third edition contains extensively updated data, graphics, and material attuned to contemporary technology while keeping what made the book so revolutionary when it was first published—a focus on real-world problem solving and student discovery. This edition will prepare students to learn mathematics in the following major areas: · Data analysis and linear regression · Functions: linear, polynomial, rational, exponential, logarithmic, parametric, and trigonometric · Modifying functions through transformations and compositions · Recursive systems and sequences · Modeling real-world phenomenon and applications An open access edition of this book is available at cpta.ncssm.edu, along with supplementary materials and other information.

Mediation analysis in recursive systems of distributed-lag linear regressions

Recursive systems of linear regressions is a consolidated methodology for mediation analysis, allowing to determine causal effects of interest in a closed form based on the regression coefficients. In a dynamic perspective, distributed-lags can be added to each regression in order to represent causal effects persisting over several periods. However, mediation analysis in the dynamic case is challenging, because causal effects depend on the time lag, and a general procedure to compute their lag distribution based on the regression coefficients is currently missing. In this paper, we formalize the rules to perform mediation analysis in recursive systems of distributed-lag linear regressions, here called Distributed-lag Linear Recursive Models (DLRMs). Firstly, mediation analysis is based on the Directed Acyclic Graph (DAG) representation of the DLRM, then a DAG-free algorithm is proposed to improve computational efficiency. Our DAG-free algorithm is applied to a DLRM representing the impact pathways of agricultural research expenditure towards poverty reduction in rural areas.

Multilevel Multiprocess Modeling with Gsem

Multilevel multiprocess models are simultaneous equation systems that include multilevel hazard equations with correlated random effects. Demographers routinely use these models to adjust estimates for endogeneity and sample selection. In this article, I demonstrate how multilevel multiprocess models can be fit with the gsem command. I distinguish between two classes of multilevel multiprocess models: nonrecursive systems of hazard equations without observed endogenous variables and recursive systems that include a hazard equation with observed endogenous qualitative variables. I illustrate the estimation of both classes of models using sample datasets shipped with the statistical software aML. I pay special attention to identifying structural coefficients in nonrecursive simultaneous systems.