plot3logit: Ternary Plots for Interpreting Trinomial Regression Models

Flavio Santi, Maria Michela Dickson, Giuseppe Espa, Diego Giuliani

Main Article Content


This paper presents the R package plot3logit which enables the covariate effects of trinomial regression models to be represented graphically by means of a ternary plot. The aim of the plot is helping the interpretation of regression coefficients in terms of the effects that a change in values of regressors has on the probability distribution of the dependent variable. Such changes may involve either a single regressor, or a group of them (composite changes), and the package permits both cases to be handled in a user-friendly way. Moreover, plot3logit can compute and draw confidence regions of the effects of covariate changes and enables multiple changes and profiles to be represented and compared jointly. Upstream and downstream compatibility makes the package able to work with other R packages or applications other than R.

Article Details

Article Sidebar


Agresti A (2013). Categorical Data Analysis. 3 edition. John Wiley & Sons.

Armstrong D (2020). DAMisc: Dave Armstrong’s Miscellaneous Functions. R package version 1.6.1, URL

Bancroft WD (1897). “A Triangular Diagram.” Journal of Physical Chemistry, 1, 403–10.

Christensen RHB (2019). ordinal — Regression Models for Ordinal Data. R package version 2019.12-10, URL

Croissant Y (2020). mlogit: Multinomial Logit Models. R package version 1.1-0, URL

Democracy Fund Voter Study Group (2017). “Views of the Electorate Research Survey, December 2016.” URL

Fox J (2003). “Effect Displays in R for Generalised Linear Models.” Journal of Statistical Software, 8(15), 1–27. URL

Fox J, Hong J (2009). “Effect Displays in R for Multinomial and Proportional-Odds Logit Models: Extensions to the effects Package.” Journal of Statistical Software, 32(1), 1–24. URL

Fox J, Weisberg S (2018). “Visualizing Fit and Lack of Fit in Complex Regression Models with Predictor Effect Plots and Partial Residuals.” Journal of Statistical Software, 87(9), 1–27. doi:10.18637/jss.v087.i09. URL

Fox J, Weisberg S (2019). An R Companion to Applied Regression. 3rd edition. Sage, Thousand Oaks CA. URL

Hamilton NE, Ferry M (2018). “ggtern: Ternary Diagrams Using ggplot2.” Journal of Statistical Software, Code Snippets, 87(3), 1–17. doi:10.18637/jss.v087.c03.

Howarth RJ (1996). “Sources for a History of the Ternary Diagram.” The British Journal for the History of Science, 29(3), 337–356. doi:10.1017/S000708740003449X.

Johnson NL, Kemp AW, Kotz S (2005). Univariate Discrete Distributions. 3 edition. John Wiley & Sons.

Lee AJ, Nyangoma SO, Seber GAF (2002). “Confidence Regions for Multinomial Parameters.” Computational Statistics & Data Analysis, 39, 329–342.

Lehmann EL, Casella G (1998). Theory of Point Estimation. 2 edition. Springer-Verlag.

Lenth RV (2016). “Least-Squares Means: The R Package lsmeans.” Journal of Statistical Software, 69(1), 1–33. doi:10.18637/jss.v069.i01.

Lenth RV (2020). emmeans: Estimated Marginal Means, aka Least-Squares Means. R package version 1.5.0, URL

Müller K, Wickham H (2020). tibble: Simple Data Frames. R package version 3.0.1, URL

Neumann M (2020). MNLpred – Simulated Predicted Probabilities for Multinomial Logit Models. R version 0.0.4, URL

R Core Team (2020). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. URL

Robinson D, Hayes A (2020). broom: Convert Statistical Analysis Objects into Tidy Tibbles. R package version 0.5.6, URL

Santi F, Dickson MM, Espa G (2019). “A Graphical Tool for Interpreting Regression Coefficients of Trinomial Logit Models.” The American Statistician, 73(2), 200–207. doi: 10.1080/00031305.2018.1442368.

Santi F, Dickson MM, Espa G, Giuliani D (2021). plot3logit: Ternary Plots for Trinomial Regression Models. R package version 3.1.0, URL

Schauberger G (2019). EffectStars2: Effect Stars. R package version 0.1-3, URL

Severini TA (2000). Likelihood Methods in Statistics. Oxford University Press. ISBN 978-0-19-850650-8.

Smith MR (2017). “Ternary: An R Package for Creating Ternary Plots.” Zenodo.

Tutz G, Schauberger G (2013). “Visualization of Categorical Response Models: From Data Glyphs to Parameter Glyphs.” Journal of Computational and Graphical Statistics, 22(1), 156–177. doi:10.1080/10618600.2012.701379.

Venables WN, Ripley BD (2002). Modern Applied Statistics with S. Fourth edition. Springer-Verlag, New York. ISBN 0-387-95457-0, URL

Wickham H (2016). ggplot2: Elegant Graphics for Data Analysis. Springer-Verlag. ISBN 978-3-319-24277-4.

Wickham H, Grolemund G (2016). R for Data Science: Import, Tidy, Transform, Visualize, and Model Data. O’Reilly. ISBN 978-1-491-91039-9.

Wilkinson L (2005). The Grammar of Graphics. Statistics and Computing, 2 edition. Springer-Verlag.

Wooldridge JM (2010). Econometric Analysis of Cross Section and Panel Data. 2 edition. The MIT Press. ISBN 978-0-262-23258-6.

Yee TW (2010). “The VGAM Package for Categorical Data Analysis.” Journal of Statistical Software, Articles, 32(10), 1–34. doi:10.18637/jss.v032.i10.