Using generalized additive (mixed) models to analyze single case designs

This article shows how to apply generalized additive models and generalized additive mixed models to single-case design data. These models excel at detecting the functional form between two variables (often called trend), that is, whether trend exists, and if it does, what its shape is (e.g., linear and nonlinear). In many respects, however, these models are also an ideal vehicle for analyzing single-case designs because they can consider level, trend, variability, overlap, immediacy of effect, and phase consistency that single-case design researchers examine when interpreting a functional relation. We show how these models can be implemented in a wide variety of ways to test whether treatment is effective, whether cases differ from each other, whether treatment effects vary over cases, and whether trend varies over cases. We illustrate diagnostic statistics and graphs, and we discuss overdispersion of data in detail, with examples of quasibinomial models for overdispersed data, including how to compute dispersion and quasi-AIC fit indices in generalized additive models. We show how generalized additive mixed models can be used to estimate autoregressive models and random effects and discuss the limitations of the mixed models compared to generalized additive models. We provide extensive annotated syntax for doing all these analyses in the free computer program R.     

Nonlinearity in the relationship between political skill and work outcomes: Convergent evidence from three studies

The current investigation examined the form and magnitude of the relationship between political skill and two intrapersonal worker reactions—job satisfaction and job tension. Political skill was hypothesized to demonstrate an inverted U-shaped nonlinear relationship with job satisfaction and a U-shaped relationship with job tension. Data from three separate studies supported the hypothesized relationships. Specifically, moderate levels of political skill were associated with higher levels of job satisfaction (Studies 1-3) and lower levels of job tension (Studies 1 and 2). Conversely, in comparison to more moderate levels, higher and lower levels of political skill were adversely related to these outcomes. Implications, strengths and limitations, and directions for future research are discussed.     

Nonlinear change processes and the emergence of suicidal behavior: A conceptual model based on the fluid vulnerability theory of suicide

Although ideation-to-action theories of suicide aim to explain the emergence of suicidal behaviors, researchers have primarily focused on the content of underlying mechanisms (i.e., who dies by suicide). Much less attention has focused on the temporal dynamics of suicide risk (i.e., when suicide occurs). The fluid vulnerability theory conceptualizes suicide as an inherently dynamic construct that follows a nonlinear time course. Newer research implicates the existence of multiple nonlinear change processes among suicidal individuals, some of which appear to be associated with the emergence of suicidal behavior. The cusp catastrophe model provides a useful model for conceptualizing these change processes and provides a foundation for explaining a number of poorly understood phenomena including sudden emergence of suicidal behavior without prior suicidal planning. The implications of temporal dynamics for suicide-focused theory, practice, and research are discussed.