Peña et al. Respond

The Results sections of empirical research articles summarize findings of data using descriptive and inferential statistical analyses. In his letter, Moulton seems to imply that the use of line graphs of model-estimated relationships is a graphical “faux pas” or violation of conventional norms. We disagree and contend that such graphs are useful and conventional tools for displaying inferential statistical results of logistic regression models.

While the results of a logistic regression can be summarized numerically with odds ratios, these numbers are limited. This is especially true for model-estimated relationships involving an independent variable with a metric that is not interpretable (e.g., a latent factor or index variable). For example, simply reporting the estimated odds ratio (in this case odds ratio = 1.14; 95% confidence interval = 1.07, 1.21) has little contextual meaning beyond the sign and statistical significance. This is why statistical textbooks recommend the use of graphical depictions for regression models with categorical outcomes as in, “The most direct approach for interpretation is to examine the predicted probabilities of an event for different values of the independent variables.”^1(p64) Indeed, our plot communicates the practical significance of the model results by showing estimated probabilities of suicide attempts and how these estimates double across the range of observed factor scores (Figures 1 and 2).² Line graphs are commonly used for this purpose.

Moulton also objects to the labeling of model-estimated probabilities along the range of predictor values. We included these labels because it is visually challenging to know where the plotted line crosses the y- and x-axes. Moreover, we write in our article that we operationalized suicide attempt as a binary (0/1) outcome and that the figures are based on logistic regression models. In the same way that Moulton was able to comprehend the figures, we felt that the Journal readers would understand that the plotted values are model-estimated probabilities. However, while we include the term “propensity to attempt suicide” within the caption of both figures, an elaborated figure caption stating the plotted relationship is a model-estimated relationship based on a logistic regression model would reduce the risk of figures being misconstrued for those not consulting the article’s text itself.

In summary, far from being a “faux pas” or violation of convention, the use of graphs depicting model-estimated relationships is an effective, efficient, and conventional means for communicating research findings and for enabling readers to make their own evaluation of the meaning of those findings.