![]() ![]() The resulting equally spaced bins are used to compute the density regions. The default bandwidth for determining the smoothness of the HDR regions is computed as follows: The HDR regions are based on a nonparametric density estimated by applying a Gaussian kernel to the data after the points have been interpolated to a grid. You can adjust the smoothness of the regions using the Smoothness option. If you remove points from the plot, the points that remain represent outliers relative to the 99% probability region. ![]() (Note that the regions can be noncontiguous and may not contain exactly 50% or 99% of the input data.) The density mode within the 50% probability region is represented by a line (univariate data) or an asterisk (bivariate data). The lighter shaded region represents the 99% probability region the darker shaded region represents the 50% probability region. For more information about Bagplots, see Rousseeuw ( 1999).ĭraws highest density region rectangles for univariate and contours for bivariate data. Points that lie outside the fence are designated outliers, and are shown as points on the plot. The outer polygon is the convex hull of all points contained within the fence. Not shown in the plot is the fence, which is the bag polygon inflated three times relative to the median point. The inner polygon is the bag, which contains at most 50% of the data points. The median point is the average of all points at maximum depth, which is plotted as an asterisk. All computations are based on first computing the Tukey depth (bivariate depth) of each point in the data. A Bagplot consists of two polygons, a set of outlier points, and a median point. (Available only for bivariate plots.) A smooth bivariate nonparametric density surface.ĭraws a Bagplot, also known as a bivariate box plot. In these cases, if points are stretched in one dimension and not the other, Delaunay triangulation tries to minimize long, skinny triangles, which can obscure some features. This option might be desirable in cases where the X and Y units are very different. This causes both the X and Y values to be scaled to before computing the Delaunay triangulation. (Available only when you have a Color variable.) Transforms the triangulation to use a normalized scale for X and Y by selecting Range Normalized. The original data are interpolated to a grid, and then a Gaussian smoother is applied. This value can be interpreted as a smoothing kernel radius. The smoothness value is normalized between -1 and 1. (Not available for Bagplots.) Smooths the boundaries of the contour plots. Increasing alpha can eliminate some of the long, skinny, or large triangles where interpolation might be undesirable. (Available only when you have a Color variable.) Controls the hull of value contours. (Available only when you have a Color variable.) Adds a line around the outside boundary of the contour. The number can be between, the default is 4 contours. (Available for Nonpar Density.) For density contours, specifies the number of contours that appear. (Not available for Bagplots.) Adds lines around the contours. (Not available for Bagplots.) Fills in the contours. Contour Optionsįigure 3.29 Contour Options for a Contour Plot or a Violin Plot You can select an option (Transform) to show a plot where the X and Y ranges have been normalized. ![]() ![]() The value contours are computed using Delaunay triangulation. If you add a Color variable to a contour plot, the plot shows value contours that reflect the levels of the Color variable.Alternatively, you can select High Density Region (HDR) contours. The violin plot is similar to a box plot with symmetric kernel densities replacing the box and whiskers. The kernel density estimates the probability density function at each point, providing a continuous analog of the histogram. A violin plot illustrates the density of the data by plotting symmetric kernel densities around a common vertical axis. ğor only one continuous variable, a violin plot appears instead of a contour plot.Alternatively, you can select a Bagplot or High Density Region (HDR) contours. You can specify the number of contour levels to display. These contours are 100%, 75%, 50%, and 25% density contours. ğor two continuous variables, four contours are plotted by default.The nonparametric density surface estimates the bivariate probability density function at each point, providing a continuous analog of a bivariate histogram. The default is a smooth bivariate nonparametric density surface that is fit to reflect the density of the data points. Density contours are useful when you have a scatterplot with many points where the mass of points makes it difficult to see patterns in density. In Graph Builder, the Contour element shows regions of density (or value contours when used with a Color variable). ![]()
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