"We have so consistently inveighed against the use of areas to illustrate quantities that the reader will indeed be surprised at some coming retractions. [...] But the fact is that we now propose to turn to advantage the very feature of areas which has previously been their greatest fault. [...] We now come to data in which we wish to show simultaneously three ratios or sets of ratios, one of which is always the product of the other two. In other words, we wish to show two factors or sets of factors and their product." (Karl Karsten, "Charts and Graphs", 1925)
"A contingency table specifies the joint distribution of a number of discrete variables. The numbers in a contingency table are represented by rectangles of areas proportional to the numbers, with shape and position chosen to expose deviations from independence models. The collection of rectangles for the contingency table is called a mosaic." (John A Hartigan & B Kleiner, "Mosaics for Contingency Tables", 1981)
"Mosaic displays represent the counts in a contingency table by tiles whose size is proportional to the cell count. This graphical display for categorical data generalizes readily to multiway tables." (Michael Friendly, "Mosaic Displays for Loglinear Models", Proceedings of the Statistical Graphics, 1992)
"Although the basic mosaic display shows the data in any contingency table, it does not in general provide a visual representation of the fit of the data to a specified model. In the two-way case independence is shown when the tiles in each row align vertically, but visual assessment of other models is more difficult." (Michael Friendly, "Mosaic Displays for Loglinear Models", Proceedings of the Statistical Graphics, 1992)
"Categorical data are most often modeled using loglinear models. For certain loglinear models, mosaic plots have unique shapes that do not depend on the actual data being modeled. These shapes reflect the structure of a model, defined by the presence and absence of particular model coefficients. Displaying the expected values of a loglinear model allows one to incorporate the residuals of the model graphically and to visually judge the adequacy of the loglinear fit. This procedure leads to stepwise interactive graphical modeling of loglinear models. We show that it often results in a deeper understanding of the structure of the data. Linking mosaic plots to other inter- active displays offers additional power that allows the investigation of more complex dependence models than provided by static displays." (Martin Theus & Stephan R W Lauer, "Visualizing Loglinear Models", Journal of Computational and Graphical Statistics Vol. 8 (3), 1999)
"The scatterplot matrix shows all pairwise (bivariate marginal) views of a set of variables in a coherent display. One analog for categorical data is a matrix of mosaic displays showing some aspect of the bivariate relation between all pairs of variables. The simplest case shows the bivariate marginal relation for each pair of variables. Another case shows the conditional relation between each pair, with all other variables partialled out. For quantitative data this represents (a) a visualization of the conditional independence relations studied by graphical models, and (b) a generalization of partial residual plots. The conditioning plot, or coplot, shows a collection of partial views of several quantitative variables, conditioned by the values of one or more other variables. A direct analog of the coplot for categorical data is an array of mosaic plots of the dependence among two or more variables, stratified by the values of one or more given variables. Each such panel then shows the partial associations among the foreground variables; the collection of such plots shows how these associations change as the given variables vary." (Michael Friendly, "Extending Mosaic Displays: Marginal, Conditional, and Partial Views of Categorical Data", 199)
"A graphical display of a p-dimensional contingency table, the empirical distribution of p categorical variables, is a mosaic plot. Each tile (or bin) corresponds to one cell of the contingency table, its size to the number of the cell's entries. The shape of a tile is calculated during the (strictly hierarchical) construction." (Heike Hoffmann, "Generalized Odds Ratios for Visual Modeling", Journal of Computational and Graphical Statistics Vol. 10 (4), 2001)
"Mosaics are space-filling designs composed of contiguous shapes ('tiles')." (Michael Friendly, "A Brief History of the Mosaic Display", Journal of Computational and Graphical Statistics, Vol. 11 (1), 2002)
"The principal graphical ideas [of mosaic plots] are: (*) using area = height x width, to represent a quantity which depends on a product of two other variables, each of interest; (*) using recursive subsdivision to show any number of variables; (*) using shading to display some other attribute of the data; (*) purely multiplicative relations (e.g., Pij = Pi+P+j) produce equal subdivisions; (*) for two or more variables, the levels of subdivision are spaced with larger gaps at the earlier levels, to allow easier perception of the groupings at various levels, and to provide for empty cells." (Michael Friendly, "A Brief History of the Mosaic Display", Journal of Computational and Graphical Statistics, Vol. 11 (1), 2002)
"Due to their recursive definition, switching the order of variables in a mosaic plot has a strong impact on what can be read from the plot. For instance, exchanging the two variables in a two-dimensional mosaic plot results in a completely new plot rather than in a mere graphically transposed version of the original plot." (Martin Theus & Simon Urbanek, "Interactive Graphics for Data Analysis: Principles and Examples", 2009)
"Mosaic plots are defined recursively, i.e., each variable that is introduced in a mosaic plot is plotted conditioned on the groups already established in the plot. As with barcharts, the area of bars or tiles is proportional to the number of observations (or the sum of the observation weights of a class). The direction along which bars are divided by a newly introduced variable is usually alternating, starting with the x-direction." (Martin Theus & Simon Urbanek, "Interactive Graphics for Data Analysis: Principles and Examples", 2009)
"Mosaic plots become more difficult to read for variables with more than two or three categories. One way out is to assign a constant space for all possible crossings of categories. This way, the data from the r×c table are plotted in a table-like layout. Whereas this regular layout makes it much easier to compare values across rows and columns, the plot space is used less efficiently than in a mosaic plot." (Martin Theus & Simon Urbanek, "Interactive Graphics for Data Analysis: Principles and Examples", 2009)
"Conceptually, mosaic plots for s + 1 factors in strength s designs can be used for any s; in practice, the idea is limited by space constraints, especially for accommodating labels for the factor levels. All four margins are used for four-factor projections; with the next dimension, one margin has to be used for two factors. In practice, one will rarely consider mosaic plots for more factors than four at a time." (Ulrike Grömping, "Mosaic Plots are Useful for Visualizing Low-Order Projections of Factorial Designs", The American Statistician Vol. 68 (2), 2014)
"Mosaic plots are particularly useful for design and analysis of orthogonal main effect plans. [...] mosaic plots do not reflect geometric properties relevant for designs in quantitative factors. Nevertheless, mosaic plots can also be used to visualize founding severity for designs with quantitative factors [...]" (Ulrike Grömping, "Mosaic Plots are Useful for Visualizing Low-Order Projections of Factorial Designs", The American Statistician Vol. 68 (2), 2014)
"Mosaic plots can get quite messy when increasing the number of variables, which is presumably the reason many commercial software products offer them for two variables only." (Ulrike Grömping, "Mosaic Plots are Useful for Visualizing Low-Order Projections of Factorial Designs", The American Statistician Vol. 68 (2), 2014)
"The way that the model differs from the data gives us clues about how we can improve our model. We can use mosaic displays to find the specific ways in which the model is different from the data, since mosaics show the residuals (or differences) of the cells with respect to the model. Looking at these differences, we can observe patterns in the deviation that will help us in our search." (Forrest W Young et al, "Visual Statistics: Seeing data with dynamic interactive graphics", 2016)
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