Showing papers on "Scatterplot smoothing published in 2005"
TL;DR: In this article, an analytically solvable regression model and a fully Bayesian approach that uses Gibbs sampling are presented for making simultaneous inferences about the features in the data.
Abstract: A rather common problem of data analysis is to find interesting features, such as local minima, maxima, and trends in a scatterplot. Variance in the data can then be a problem and inferences about features must be made at some selected level of significance. The recently introduced SiZer technique uses a family of nonparametric smooths of the data to uncover features in a whole range of scales. To aid the analysis, a color map is generated that visualizes the inferences made about the significance of the features. The purpose of this article is to present Bayesian versions of SiZer methodology. Both an analytically solvable regression model and a fully Bayesian approach that uses Gibbs sampling are presented. The prior distributions of the smooths are based on a roughness penalty. Simulation based algorithms are proposed for making simultaneous inferences about the features in the data.
65 citations
TL;DR: The software aims to provide a picture of the relation between a response variable and each of several continuous predictors simultaneously, which may be a valuable tool in exploratory data analysis, before constructing a more formal multiple regression model.
Abstract: We present an extension of Sasieni, Royston, and Cox’s bivariate
smoother running to the multivariable context. The software aims to provide a
picture of the relation between a response variable and each of several continuous
predictors simultaneously. This may be a valuable tool in exploratory data
analysis, before constructing a more formal multiple regression model.
38 citations
TL;DR: Applications of SiZerSS to mode, linearity, quadraticity and monotonicity tests, and some small scale simulations are presented to demonstrate that the SiZers often give similar performance in exploring data structure but they can not replace each other completely.
Abstract: Smoothing splines are an attractive method for scatterplot smoothing. The SiZer approach to statistical inference is adapted to this smoothing method, named SiZerSS. This allows quick and sure inference as to “which features in the smooth are really there” as opposed to “which are due to sampling artifacts”, when using smoothing splines for data analysis. Applications of SiZerSS to mode, linearity, quadraticity and monotonicity tests are illustrated using a real data example. Some small scale simulations are presented to demonstrate that the SiZerSS and the SiZerLL (the original local linear version of SiZer) often give similar performance in exploring data structure but they can not replace each other completely.
32 citations
TL;DR: In this article, the idea of double, diagonal and polar smoothing is revisited with various examples from environmental datasets, and it is implemented by regression on a series of sine and cosine terms.
Abstract: Identifying patterns in bivariate data on a scatterplot remains a ba- sic statistical problem, with special avor when both variables are on the same footing. Ideas of double, diagonal, and polar smoothing inspired by Cleveland and McGill's 1984 paper in the Journal of the American Statistical Association are revisited with various examples from environmental datasets. Double smooth- ing means smoothing both y given x and x given y. Diagonal smoothing means smoothing based on the sum and dierence of y and x that treats the two variables symmetrically, possibly under standardization. Polar smoothing is based on the transformation from Cartesian to polar coordinates followed by smoothing and then reverse transformation; here the smoothing is implemented by regression on a series of sine and cosine terms. These methods thus oer exploratory tools for determining the broad structure of bivariate data.
20 citations
Journal Article•
3 citations
15 Oct 2005
TL;DR: In this paper, a three-dimensional scatterplot is used to display the relationship between three continuous variables at one time, where the data are represented as a cloud of points within the 3D space formed by the three axes of the plot.
Abstract: A three-dimensional scatterplot displays the relationship between three continuous variables at once. The data are represented as a cloud of points within the three-dimensional space formed by the three axes of the plot. Such plots can be difficult to interpret and other methods of representing the third variable are generally more effective.
Keywords:
association;
bubble plot;
regression;
scatterplot matrix
1 citations
15 Oct 2005
TL;DR: In this paper, generalized additive models (GAM) provide an extension to generalized linear models by allowing the explanatory variables in the model to be represented by smoothed functions, for example, locally weighted regression fits suggested by the empirical relationship between the response and each explanatory variable.
Abstract: Generalized additive models (GAM) provide an extension to generalized linear models by allowing the explanatory variables in the model to be represented by smoothed functions, for example, locally weighted regression fits suggested by the empirical relationship between the response and each explanatory variable.
Keywords:
smoothed functions;
locally weighted regression;
scatterplot smoothers
1 citations