Residual-Based Shadings for Visualizing (Conditional) Independence

Abstract

Residual-based shadings for enhancing mosaic and association plots to visualize independence models for contingency tables are extended in two directions: (a) perceptually uniform Hue-Chroma-Luminance (HCL) colors are used and (b) the result of an associated significance test is coded by the appearance of color in the visualization. For obtaining (a), a general strategy for deriving diverging palettes in the perceptually-based HCL space is suggested. As for (b), cut offs that control the appearance of color are computed in a data-driven way based on the conditional permutation distribution of maximum-type test statistics. The shadings are first established for the case of independence in 2-way tables and then extended to more general independence models for multi-way tables, including in particular conditional independence models.

The Strucplot Framework: Visualizing Multi-way Contingency Tables withvcd

“…The idea is to visualize at least sign and absolute size of the residuals, but some shadings, additionally, indicate overall significance. One particular shading, the maximum shading (Meyer et al 2003;Zeileis et al 2005), even allows to identify the cells that cause the rejection of the null hypothesis. Conceptually, the strucplot framework offers three alternatives to add residual-based shading to plots:…”

“…shading_hsv() and shading_hcl() provide the same conceptual tools, but use different color spaces: the Hue-Saturation-Value (HSV) and the Hue-Chroma-Luminance (HCL) scheme, respectively. We will first expose the basic concept of these shading functions using HSV space, and then briefly explain the differences to HCL space (a detailed discussion can be found in Zeileis et al 2005). Color palettes in HCL space are preferable to palettes derived from HSV space from a perceptual point of view.…”

“…In addition to the defaults of the HSV shading, it uses the border color and line type to redundantly code the residuals' sign. The following example again uses the Bundesliga data from above, this time using the Friendly scheme and, in addition, an alternative legend (see A more "advanced" function building upon shading_hcl() is shading_max(), using the maximum statistic both to conduct the independence test and to visualize significant cells causing the rejection of the independence hypothesis (Meyer et al 2003;Zeileis et al 2005). The level argument of shading_max() then can be used to specify several confidence levels from which the corresponding cut-off points are computed.…”

“…Using residual-based shadings to visualize log-linear models (Friendly 1994(Friendly , 2000 and significance of statistical tests (Meyer, Zeileis, and Hornik 2003;Zeileis, Meyer, and Hornik 2005).…”

Growth of hartweg’s pine (<em>Pinus hartwegii</em>) parasitized by two dwarf mistletoe species (<em>Arceuthobium</em> spp.)

“…Thereafter, we verified trough Pearson residuals whose categories were significant. All analyses were performed using the stats package, except for Pearson residual analysis, which was performed using the vcd package (Meyer et al, 2006(Meyer et al, , 2012Zeileis et al, 2007) both of the R software (R Development Core Team, 2012).…”