Visualization of Categorical Response Models: From Data Glyphs to Parameter Glyphs

Abstract

The multinomial logit model is the most widely used model for nominal multi-category responses. One problem with the model is that many parameters are involved, another that interpretation of parameters is much harder than for linear models because the model is non-linear. Both problems can profit from graphical representations. We propose to visualize the effect strengths by star plots, where one star collects all the parameters connected to one term in the linear predictor. In simple models one star refers to one explanatory variable. In contrast to conventional star plots, which are used to represent data, the plots represent parameters and are considered as parameter glyphs. The set of stars for a fitted model makes the main features of the effects of explanatory variables on the response variable easily accessible. The method is extended to ordinal models and illustrated by several data sets.

Modeling electoral choices in multiparty systems with high-dimensional data: A regularized selection of parameters using the lasso approach

“…To summarize the main effects model from Table 1 in a concise and easy-to-read fashion, we suggest the use of so-called effect stars (Tutz and Schauberger, 2013). depicts these effect stars for each covariate.…”

Cumulative and CUB Models for Rating Data: A Comparative Analysis

“…Thus, although uncertainty is just a proportional displacement in the probability distribution, the bias of the location parameter is proportional to its weight, and it reduces for almost symmetric distributions. Because researchers are not a priori sure about the size of uncertainty, a suggestion may be to let data speak for themselves : this strategy is automatically accomplished by CUB models. Visual representation of estimated POM is pursued by the inspection of the distribution and/or the probability mass functions for varying covariates as in Figure ; the proposal put forward by Tutz & Schauberger () has been also previously discussed. The search of effective synthesis of the results of cumulative models is pursued by Agresti & Kateri () who list several measures to make the interpretations of the estimated models easier to practitioners.…”

“…Visual representation of estimated POM is pursued by the inspection of the distribution and/or the probability mass functions for varying covariates as in Figure 13; the proposal put forward by Tutz & Schauberger (2010) has been also previously discussed. The search of effective synthesis of the results of cumulative models is pursued by Agresti & Kateri (2017) who list several measures to make the interpretations of the estimated models easier to practitioners.…”

“…The shape of these representations depends on the nature of the explanatory variables, which can be continuous and/or categorical (some examples are in Section 4.2). Tutz & Schauberger () have proposed to visualise the estimates of cumulative models by exploiting the proportional odds property of POM in order to give a graphical interpretation of the effect of a covariate X on the ordinal response ceteris paribus . If the odds of preferring the first j categories of the response Y over the higher scores are modified by the factor if covariate X is increased by one unit.…”

KATIE HARRON, HARVEY GOLDSTEIN, AND CHRIS DIBBEN, eds, Methodological Developments in Data Linkage. New York: Wiley.

“…Some models also seem to merit more attention, such as baseline-category logit models with qualitative predictors, for which the large number of parameters can be intimidating. See Tutz and Schauberger (2013) for recent work on using star plots for effects in multinomial logit models. However, I think that this book is an important contribution and a strong addition to the existing discrete-data texts.…”