Probing Interactions in Differential Susceptibility ResearchThe purpose of this application is to facilitate the investigation of differential susceptibility hypotheses in developmental and clinical research. Go to the version of the application for a continuous moderator (e.g., age) Go to the version of the application for a binary or two-level categorical moderator (e.g., sex) Go to the version of the application for continuous or binary moderators Conceptual Overview of Differential Susceptibility
One of the goals of research on development, psychopathology, and individual differences is to understand the protective factors that moderate the impact of environmental stressors on development (Luthar, Cicchetti, & Becker, 2000; Masten, 2001). The dominant theoretical model of risk and adaptation is the diathesis-stress or dual-risk model (Heim & Nemeroff, 1999). The diathesis-stress model suggests that poor developmental experiences (e.g., low quality parenting) are most likely to impact the development of individuals who carry vulnerability factors—-latent diatheses that when 'triggered' by poor experience result in maladaptation. Many potential diatheses have been the focus of empirical inquiry, including temperamental traits, such as difficulty (Belsky, Hsieh, & Crnic, 1998), as well as specific molecular genetic polymorphisms, such as the short allele of the serotonin transporter gene (Caspi et al., 2003). A common theme in this research is that such moderators are 'vulnerability factors' that inhibit successful adaptation in the face of adversity. Thus, one of the more important developments in the last decade is the theory of differential susceptibility—-an evolutionary inspired theory which assumes that these factors are not diatheses, but are plasticity agents instead (Belsky, 1997). More specifically, differential susceptibility theory posits that many putative sources of vulnerability (e.g., difficult temperament) are more accurately conceptualized as plasticity factors because they not only amplify risk for maladaptation given poor caregiving experiences (as in the diathesis-stress account), but also increase the probability of positive adaptation given high-quality caregiving experiences (Belsky & Pluess, 2009). In short, the theory assumes that some individuals vary in their susceptibility to environmental factors both 'for worse' and 'for better' (Belsky, Bakermans-Kranenburg, & van IJzendoorn, 2007). Both diathesis-stress and differential susceptibility models are often tested by examining the interaction term in a multiple regression equation that models Y, a developmental outcome (e.g., social adjustment), as a function of an environmental factor, X (e.g., quality of parenting), the vulnerability/plasticity factor, Z (e.g., difficult temperament), and the interaction between X and Z. One of the challenges of research on risk and development, however, is that there are no conventions in place for evaluating whether data are more compatible with differential susceptibility or diathesis-stress accounts. The primary method for making the distinction is based on examining and plotting simple slopes (i.e., the regression of Y on X separately for people high on the vulnerability/plasticity factor and people low on the vulnerability/plasticity factor). Although this method can be useful, it also can be whimsical. Namely, whether investigators conclude in favor of diathesis-stress or differential susceptibility often becomes a function of their theoretical biases, the range of X values under examination, and the range of Y and Z values sampled. Overview of this Application
The purpose of this application is to help solve the problems described above by providing a number of tools that investigators can use to probe interactions in multiple regression and to better understand their implications for alternative models of risk and adaptation. Although the application was developed originally to explore questions concerning differential susceptibility, the application can be used for the general analysis of interaction terms in multiple regression. This application provides a number of tools that can be helpful for evaluating evidence for differential susceptibility, including: **Graphs**. This application can be used to plot the regression of Y on X for various values of Z. Such graphs can be used to better understand the form of the interaction in question. Moreover, these graphs can be imported into PowerPoint or word processing programs for the purposes of making publication-quality figures.**Regions of significance (RoS) with respect to X**. These values indicate the values of X for which the regression of Y on Z is statistically significant. When the differential susceptibility account is warranted, the association between Y and Z should be significant both for low values of X and high values of X. Importantly, however, these associations should be significant for regions of X that fall within the range of interest (i.e., 2 SDs above and below the mean of X).**Regions of significance (RoS) with respect to Z**. These values indicate the values of Z for which the regression of Y on X is statistically significant. When the differential susceptibility account is warranted, the association between Y and X should be significant for values of Z that fall within the range of interest (i.e., within 2 SDs of the mean of Z). There is no range on Z that necessarily differentiates differential susceptibility from diathesis-stress, however.**Simple slopes with respect to X and Z**. The program can be configured to evaluate the simple slopes for any value of the moderator. It is also possible to evaluate the simple slopes for the regression of Y on Z at any value of X.**Proportion of the Interaction (PoI)**. The PoI provides a way to express the proportion of the total interaction that is represented on the right side of the crossover point for the interaction. In differential susceptibility theory, this represents the area for which the effect of X on Y is 'for better' if, in fact, a positive association represents a gain rather than a cost. In a prototypical differential susceptibility account, this value will be 50%. In a prototypical diathesis-stress account, this value will be 0% or 100%, depending on the variables in question and whether they represent potential risks or gains.**Proportion Affected (PA)**. The PA value provides a way to express the proportion of cases that are differentially affected by X. In differential susceptibility theory, this represents the proportion of individuals for whom the effect of X on Y is 'for better'. In a prototypical differential susceptibility account, this value should include a non-trivial proportion of people (e.g., 50%). In a prototypical diathesis-stress account, this value will be closer to 0% (or 100%, depending on how the variables are coded).
Details on How to Use this Application
This application is designed to be self-explanatory. Nonetheless, additional information is provided here to clarify the details. This application takes as input two basic kinds of parameters. First, in the Regression parameters section, enter the estimated regression coefficients for the Intercept/Constant, the predictor X, the moderator Z, and the interaction between X and Z. Second, in the section labeled Parameter variance/covariance matrix, you will need to enter some of the estimated variances of and covariances between the parameter estimates. This kind of information is not returned by default by most statistical packages. Nonetheless, it can be obtained by selecting the appropriate options within those programs. These estimates are typically contained in what is sometimes called the asymptotic variance-covariance matrix. To learn more about how to acquire these values from various statistical packages, please see Kris Preacher's excellent discussion. If you're only interested in plotting the interaction and not in the various statistics the application returns (e.g., RoS X), you can simply leave the default values in the input boxes for the "parameter variance/covariance matrix" section.You should also enter the degrees of freedom for the analysis, which should be computed as N - k - 1, where N is your sample size and k is the number of predictors in the regression equation (3, in most cases). The degrees of freedom are used for the simple slopes t-tests. The df is not used for the RoS X/Z analyses. Again, you can leave the default value in place if you're only interested in producing graphs and do not need computations for simple slope tests.Many of the other input boxes are optional. You can choose, for example, to label the variables to make the output easier to interpret. Moreover, you can adjust some of the plotting dimensions. You can also adjust the default values that are used to test simple slopes for both X and Z. (Simply enter a positive value. The app will automatically examine that value and the same value multiplied by -1.) You can also toggle off the detailed explanations for the output by unchecking the box labeled Provide detailed explanations.
To create a graph and perform the analyses, simply press the Create graph button.Details on Graphing and Saving the Graph
The default graphing parameters assume that the predictor variables are standardized. If you are using unstandardized coefficients or unstandardized variables, you will need to adjust the min/max values for X and Y in the 'optional parameters' section. The graph is generated dynamically and combines javascript, canvas, and HTML elements. As such, it cannot be copied and pasted like a traditional image file. To save the graph (e.g., for the purposes of a presentation or manuscript), I recommend taking a screen shot by using the Print Screen key on Windows systems and then pasting the contents of your clipboard into a PowerPoint slide. From there, you can trim/crop away the elements that are not needed or further annotate it in ways that seem useful. Details on Binary Moderators
If you have a binary moderator (e.g., sex, short/short vs. long/short allele), please select the version of the application that designed for binary moderators. You will need to enter a label for both groups (e.g., "male" and "female") and you will need to chose numeric values for the two groups for the purpose of plotting the regression lines and calculating the various statistics. If the regression parameters you used were based on unstandardized variables, use the natural numeric codes you used for your binary variable in your original analysis (e.g., 0 and 1). If you standardized your variables before analysis, it will be necessary to use the z-scored version of those binary variables (e.g., -1 and 1 or -.66 and .33--depending on the baserates of your binary variable). (If you're unsure exactly what to do, I encourage you to analyze the data without standardizing the predictors and entering unstandardized coefficients into the parameter boxes of the application and using codes of 0 and 1 to represent your two moderator groups.) About
This application was designed by R. Chris Fraley. It is a supplement to Roisman, G. I., Newman, D. A., Fraley, R. C., Haltigan, J. D., Groh, A. M., & Haydon, K. C. (2012). Distinguishing differential susceptibility from diathesis-stress: Recommendations for evaluating interaction effects. Development and Psychopathology, 24, 389-409. Go to the version of the application for a continuous moderator (e.g., age) Go to the version of the application for a binary or two-level categorical moderator (e.g., sex) Go to the version of the application that can accomodate continuous moderators or binary moderators. |