Oregon State University

Learn how to analyze data with complex interactions using Non-parametric Multiplicative Regression (NPMR) and the HyperNiche software package.

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NPMR compared to other techniques:

NPMR outperformed the following regression and classification techniques for tests that involved non-linear, simulated data: linear regression, logistic regression, General Additive Models (GAM), Classification and Regression Trees (CART), and Random Forest (McCune 2006, Lintz et al. 2011). Additionally, recent tests with MaxEnt against NPMR demonstrated that NPMR had the highest mean externally-validated prediction accuracy compared to MaxEnt for 48 different shapes of simulated data structures (Yost and Lintz 2011, unpublished data).

About NPMR:

NPMR is a form of kernel regression. NPMR optimizes kernel width or tolerance to maximize cross-validated model fit. NPMR can automatically accommodate complex interactions in multi-factor predictor space. NPMR assumes that factors can interact multiplicatively or additively.

See the original paper describing the algorithm here.

See a paper comparing NPMR to CART and Random Forest here. (This paper also develops an index to measure threshold strength from response surfaces.)

References Cited:

Lintz., H., McCune, B., Gray, A., and McCulloh, K. 2011. Quantifying ecological thresholds from response surfaces. Ecological Modelling 222: 427-436.

McCune, B., 2006. Non-parametric habitat models with automatic interactions. Journal of Vegetation Science 17: 819-830.

Yost, A., Lintz, H.E. 2011. A Comparison of the Prediction Accuracy between MaxEnt and Non-parametric Multiplicative Regression (NPMR). Unpublished data analysis; in preparation for submission.