MARS is an innovative and flexible modeling tool that automates the building of accurate predictive models for continuous and binary dependent variables. Multivariate Adaptive Regression Splines was developed in the early 1990s by Jerry Friedman, a world-renowned statistician and one of the co-developers of CART. Salford Systems' MARS, based on the original code, has been substantially enhanced with new features and capabilities in exclusive collaboration with Friedman.
MARS excels at finding optimal variable transformations and interactions, the complex data structure that often hides in high dimensional data. In doing so, this new generation approach to data mining uncovers business critical data patterns and relationships that are difficult, if not impossible, for other approaches to uncover.
Given a target variable and a set of candidate predictor variables, MARS automates all aspects of model development, including:
separating relevant from irrelevant predictors
Large numbers of variables are examined using efficient algorithms, and all promising variables are identified.
transforming predictor variables exhibiting a nonlinear relationship with the target variable
Every variable selected for entry into the model is repeatedly checked for non-linear response. Highly non-linear functions can be traced with precision via essentially piecewise regression.
determining interactions between predictor variables
MARS repeatedly searches through the interactions allowed by the analyst. Unlike recursive partitioning schemes, MARS models may be constrained to forbid interactions of certain types, thus allowing some variables to enter only as main effects, while allowing other variables to enter as interactions, but only with a specified subset of other variables.
handling missing values with new nested variable techniques
Certain variables are deemed to be meaningful (possibly non-missing) in the model only if particular conditions are met (e.g., X has a meaningful non-missing value only if categorical variable Y has a value in some range).
conducting extensive self tests to protect against overfitting
The user can choose to reserve a random subset of data for test, or use v-fold cross validation to tune the final model selection parameters.
MARS enables analysts to rapidly search through all possible models and to quickly identify the optimal solution, providing insights that can lead to a definitive competitive advantage. Because the software can be exploited via an easy-to-use GUI, intelligent default settings, and aesthetically appealing output, for the first time analysts at all levels can easily access MARS' innovations.
MARS for Windows also incorporates two alternative control modes that extend the program's features and capabilities. In addition to controlling MARS with the GUI, you can also issue commands at the command prompt or submit a command file.
User-Friendly Graphical User Interface
MARS' easy-to-use GUI allows the user to control the variables and functional forms to be entered into the model and the interactions to be considered or forbidden, while allowing the MARS algorithm to optimize those parts of the model the analyst chooses to leave free. Once the model is selected, the user can easily remove or add terms, instantly see the impact of changes on model fit, review diagnostics that assist in model selection, save the model and apply the model to new data for prediction.
MARS Output
MARS output is an easy-to-deploy regression model that can be automatically applied to new data from within MARS itself or exported as ready-to-run SASŪ and C source code. To facilitate interpretation of the model, the output also includes interpretive summary reports as well as exportable two- and three-dimensional curve and surface plots:
For a detailed technical discussion of the MARS methodology, a PDF version of Friedman's original 1991 article, Multivariate Adaptive Regression Splines published in Annals of Statistics, 19, 1-141 , can be downloaded by clicking here (note: file is 14 MB). For a much shorter and less technical overview, see our white paper on MARS, Overview of the MARS Methodology.