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WIREs Comp Stat

Response modeling methodology

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Response modeling methodology (RMM) is a general platform for modeling monotone convex relationships. Unique to RMM models is their ‘continuous convexity’ property, which allows the data to ‘select’ the final form of the model via the estimated parameters (analogously with the Box–Cox transformation). This renders RMM a versatile and effective platform for empirical modeling of random variation (‘distribution fitting’) and of systematic variation (‘relational modeling’). In this overview, we detail the motivation that led to the development of RMM, explain RMM core concepts, and introduce RMM basic model and variations. Allied maximum‐likelihood estimation procedures are detailed, separately for models of random variation and for models of systematic variation. Numerical examples demonstrate RMM effectiveness in comparison to other current approaches. Current literature on RMM (about 25 publications), available software, and ongoing research are also addressed. WIREs Comp Stat 2011 3 357–372 DOI: 10.1002/wics.151

Figure 1.

Four common types of monotone convex relationships.

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Figure 2.

Climbing up the ‘ladder’ by introducing two additional parameters, β and κ.

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Figure 3.

(a) Density functions of four positively skewed distributions. (b) Standard‐normal‐based quantile functions of the distributions in (a). Y here represents the standardized X.

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Figure 4.

Data‐based comparison of goodness‐of‐fit of Pearson and Response Modeling Methodology (measured by L2 norm, relating to functional distances of the density functions). ‘Real’ curve refers to fitting the distribution that had generated the data. Each point is an average based on 30 samples.

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Figure 5.

Error plots from approximating the pdf by Generalized Lambda Distribution and Response Modeling Methodology, minimizing the L2 norm (refer to Tables 1 and 2 for parameters' values).

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Figure 6.

(a) Plot of the source model and the fitted RMM3 (Model 1). (b) Error plot for fitting RMM3 to Model 1. RMM, Response Modeling Methodology.

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Figure 7.

(a) Plot of the source model and the fitted RMM3 (Model 2). (b) Error plot for fitting RMM3 to Model 2. RMM, Response Modeling Methodology.

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Figure 8.

(a) Plot of the source model and the fitted RMM3 (Model 3). (b) Error plot for fitting RMM3 to Model 3. RMM, Response Modeling Methodology.

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Figure 9.

(a) Plot of the source model and the fitted RMM3 (Model 4). (b) Error plot for fitting RMM3 to Model 4. RMM, Response Modeling Methodology.

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Computational Intensive Statistical Methods > Density Estimation and Curve Fitting
Modeling and Simulation > Modeling Methods and Algorithms
Machine Learning > Statistical Methodology
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