A procedure that can be used to evaluate the variance inflation factors and tolerance indices in linear regression models is discussed. The method permits both point and interval estimation of these factors and indices associated with explanatory variables considered for inclusion in a regression model. The approach makes use of popular latent variable modeling software to obtain these point and interval estimates. The procedure allows more informed evaluation of these quantities when addressing multicollinearity-related issues in empirical research using regression models. The method is illustrated on an empirical example using the popular software M plus. Results of a simulation study investigating the capabilities of the procedure are also presented.
Survey data in social, behavioral, and health sciences often contain many variables (p). Structural equation modeling (SEM) is commonly used to analyze such data. With a sufficient number of participants (N), SEM enables researchers to easily set up and reliably test hypothetical relationships among theoretical constructs as well as those between the constructs and their observed indicators. However, SEM analyses with small N or large p have been shown to be problematic. This article reviews issues and solutions for SEM with small N, especially when p is large. The topics addressed include methods for parameter estimation, test statistics for overall model evaluation, and reliable standard errors for evaluating the significance of parameter estimates. Previous recommendations on required sample size N are also examined together with more recent developments. In particular, the requirement for N with conventional methods can be a lot more than expected, whereas new advances and developments can reduce the requirement for N substantially. The issues and developments for SEM with many variables described in this article not only let applied researchers be aware of the cutting edge methodology for SEM with big data as characterized by a large p but also highlight the challenges that methodologists need to face in further investigation.
Synthesizing results from multiple studies is a daunting task during which researchers must tackle a variety of challenges. The task is even more demanding when studying developmental processes longitudinally and when different instruments are used to measure constructs. Data integration methodology is an emerging field that enables researchers to pool data drawn from multiple existing studies. To date, these methods are not commonly utilized in the social and behavioral sciences, even though they can be very useful for studying various complex developmental processes. This article illustrates the use of two data integration methods, the and the approaches. The illustration makes use of six longitudinal studies of mathematics ability in children with a goal of examining individual changes in mathematics ability and determining differences in the trajectories based on sex and socioeconomic status. The studies vary in their assessment of mathematics ability and in the timing and number of measurement occasions. The advantages of using a data fusion approach, which can allow for the fitting of more complex growth models that might not otherwise have been possible to fit in a single data set, are emphasized. The article concludes with a discussion of the limitations and benefits of these approaches for research synthesis.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.