Monotone fitting for developmental variables |
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Authors: | Valentin Rousson |
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Institution: | Department of Biostatistics, Institute for Social and Preventive Medicine , University of Zürich , Hirschengraben, Zürich, Switzerland |
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Abstract: | In order to study developmental variables, for example, neuromotor development of children and adolescents, monotone fitting is typically needed. Most methods, to estimate a monotone regression function non-parametrically, however, are not straightforward to implement, a difficult issue being the choice of smoothing parameters. In this paper, a convenient implementation of the monotone B-spline estimates of Ramsay Monotone regression splines in action (with discussion), Stat. Sci. 3 (1988), pp. 425–461] and Kelly and Rice Montone smoothing with application to dose-response curves and the assessment of synergism, Biometrics 46 (1990), pp. 1071–1085] is proposed and applied to neuromotor data. Knots are selected adaptively using ideas found in Friedman and Silverman Flexible parsimonous smoothing and additive modelling (with discussion), Technometrics 31 (1989), pp. 3–39] yielding a flexible algorithm to automatically and accurately estimate a monotone regression function. Using splines also simultaneously allows to include other aspects in the estimation problem, such as modeling a constant difference between two groups or a known jump in the regression function. Finally, an estimate which is not only monotone but also has a ‘levelling-off’ (i.e. becomes constant after some point) is derived. This is useful when the developmental variable is known to attain a maximum/minimum within the interval of observation. |
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Keywords: | B-spline smoothing F-tests knots selection leveling-off monotone regression non-negative least squares selection of variables |
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