Bridging Advanced Quantitative Methods and Applied Research in the Behavioral, Social and Health Sciences



We currently offer workshops on Multilevel Modeling, Structural Equation Modeling, Structural Equation Models for Longitudinal Data, Mixture Models and Cluster Analysis, and Network Analysis. We also provide individually tailored instruction to groups with specific data analytic needs.


We provide consulting services on each phase of the research process, from study design to the application and interpretation of quantitative methods. We offer several modes of consulting to suit a variety of needs.


We seek to provide you with the information you need to be a knowledgeable user of quantitative methods, including updates on ongoing developments in the field, discussion of common data analytic concerns, and tutorials on commonly used techniques.


How can I define nonlinear trajectories in a growth curve model?

February 6, 2019

Growth curve models, whether estimated as a multilevel model (MLM) or a structural equation model (SEM), have become widely used in many areas of behavioral, health, and education sciences. The most common type of growth model defines a linear trajectory in which the time scores defining the slopes increment evenly for equally spaced repeated measures (e.g., values representing time are set to 0, 1, 2, 3, etc.). These values can be modified to allow for unequally spaced time assessments or to place the zero value at the beginning, middle, or end of the series, but the slope of the line always implies an equal change in the outcome per-unit change in time.

However, many constructs we study do not change linearly over time. Instead of equal change per-unit time, there is often differential change with respect to time. So there might be greater change earlier in time that then systematically slows (e.g., reading ability in young children), or the rate of change might increase positively but accelerate with the passage of time (e.g., substance use in adolescence), or the construct might slowly increase, peak, and then slowly decrease (e.g., heavy drinking in young adults). Regardless of particular form, it is critical that an appropriate nonlinear function be incorporated into the growth model to protect against making biased inferences about the nature of change over time. Fortunately, there are many options available to capture nonlinear change over time in growth models.