Shannon Jacoby
Department of Psychology
The Ohio State University
Title: Assessing linearity via monotonicity and polynomials: A simulation study
Abstract: Selecting an appropriate modeling framework is one of the first tasks researchers face after data collection and cleaning have been completed. After making this choice, typically model diagnostics are run to evaluate adherence to the model assumptions. Across a wide array of content areas, many researchers choose to operate within a linear modeling framework, and more specifically within the regression approach. A central assumption of this approach is linearity of the regression function, and the current diagnostic criterion for this assumption is a visual inspection of a scatter- or residual plot for the absence of systematic nonlinearity. Given that violation of the linearity assumption can lead to biased estimates of parameters and error variances, our current work endeavors to create an additional avenue for examination of the linearity assumption that goes beyond graphical analysis. By borrowing inspiration from the ANOVA tradition, we will apply three different contrast analyses (trend, Helmert, and adjacent) to simulated data in an effort to identify potential inflection points, which will further inform our understanding of the tonic quality of the relationship between the independent and dependent variables. Criteria for the evaluation of this method will be defined and possible limitations will be addressed. Additionally, advantages and drawbacks of a continuous approach to simulating data will be explored.
Discussant: Hanrui Mei