Effect stars for cumulative logit models
Description
The package EffectStars2 provides a more uptodate implementation of effect stars!
The function computes and visualizes cumulative logit models. The computation is done with help of
the package VGAM. The visualization is based on the function stars
from the package graphics.
Usage
1 2 3 4 5 6 7  star.cumulative(formula, data, global = NULL, test.rel = TRUE, test.glob = FALSE,
partial = FALSE, globcircle = FALSE, maxit = 100, scale = TRUE,
nlines = NULL, select = NULL, dist.x = 1, dist.y = 1, dist.cov = 1,
dist.cat = 1, xpd = TRUE, main = "", col.fill = "gray90",
col.circle = "black", lwd.circle = 1, lty.circle = "longdash",
col.global = "black", lwd.global = 1, lty.global = "dotdash", cex.labels = 1,
cex.cat = 0.8, xlim = NULL, ylim = NULL)

Arguments
formula 
An object of class “formula”. Formula for the cumulative logit model to be fitted and visualized. 
data 
An object of class “data.frame” containing the covariates used in 
global 
Numeric vector to choose a subset of predictors to be included with global coefficients. Default is to include all coefficients categoryspecific. Numbers refer to total amount of predictors, including intercept and dummy variables. 
test.rel 
Provides a LikelihoodRatioTest to test the relevance of the explanatory covariates.
The corresponding pvalues will be printed as 
test.glob 
Provides a LikelihoodRatioTest to test if a covariate has to be included as a categoryspecific covariate (in contrast to being global). The corresponding pvalues will be printed as 
partial 
If 
globcircle 
If 
maxit 
Maximal number of iterations to fit the cumulative logit model. See also

scale 
If 
nlines 
If specified, 
select 
Numeric vector to choose only a subset of the stars to be plotted. Default is to plot all stars. Numbers refer to total amount of predictors, including intercept and dummy variables. 
dist.x 
Optional factor to increase/decrease distances between the centers of the stars on the xaxis. Values greater than 1 increase, values smaller than 1 decrease the distances. 
dist.y 
Optional factor to increase/decrease distances between the centers of the stars on the yaxis. Values greater than 1 increase, values smaller than 1 decrease the distances. 
dist.cov 
Optional factor to increase/decrease distances between the stars and the covariates labels above the stars. Values greater than 1 increase, values smaller than 1 decrease the distances. 
dist.cat 
Optional factor to increase/decrease distances between the stars and the category labels around the stars. Values greater than 1 increase, values smaller than 1 decrease the distances. 
xpd 
If 
main 
An overall title for the plot. See also 
col.fill 
Color of background of the circle. See also 
col.circle 
Color of margin of the circle. See also 
lwd.circle 
Line width of the circle. See also 
lty.circle 
Line type of the circle. See also 
col.global 
Color of margin of the global effects circle. See also 
lwd.global 
Line width of the global effects circle. See also 
lty.global 
Line type of the global effects circle. See also 
cex.labels 
Size of labels for covariates placed above the corresponding star. See also 
cex.cat 
Size of labels for categories placed around the corresponding star. See also 
xlim 
Optional specification of the x coordinates ranges. See also 
ylim 
Optional specification of the y coordinates ranges. See also 
Details
The underlying models are fitted with the function vglm
from the package VGAM. The family argument
for vglm
is cumulative(parallel=FALSE)
.
The stars show the exponentials of the estimated coefficients. In cumulative logit models the exponential coefficients can
be interpreted as odds. More precisely, the exponential e^{γ_{rj}}, r=1,…,k1 represents the multiplicative effect of the covariate j on the cumulative odds \frac{P(Y≤q rx)}{P(Y>rx)} if x_j increases by one unit.
In addition to the stars, we plot a cirlce that refers to the case where the coefficients of the corresponding star are zero. Therefore, the radii of these circles are always exp(0)=1. If scale=TRUE
, the stars are scaled so that they all have the same maximal ray length. In this case, the actual appearances of the circles differ, but they still refer to the noeffects case where all the coefficients are zero. Now the circles can be used to compare different stars based on their respective circles radii. The pvalues beneath the covariate labels, which are given out if test.rel=TRUE
, correspond to the distance between the circle and the star as a whole. They refer to a likelihood ratio test if all the coefficients from one covariate are zero (i.e. the variable is left out completely) and thus would lie exactly upon the cirlce.
The form of the circles can be modified by col.circle
, lwd.circle
and lty.circle
.
By setting globcircle=TRUE
, an addictional circle can be drawn. The radii now correspond to a model, where the respective covariate is not included categoryspecific but globally. Therefore, the distance between this circle and the star as a whole corresponds to the pvalue pglobal that is given if test.glob=TRUE
.
Please note:
Regular fitting of cumulative logit models may fail because of the restrictions in the parameter space that have to be
considered. If partial=TRUE
, (sub)models with only one categoryspecific covariate, socalled
partial proportional odds models, are fitted. Then at least estimates for every coefficient should be available. If partial=TRUE
, the resulting effects of these (sub)models are plotted.
It should be noted that in this case no coherent model is visualized. Also the pvalues refer to the various submodels.
For partial=TRUE
, the pvalues prel
and pglobal
refer to tests of the corresponding partial proportial odds models against the proportional odds model.
It is strongly recommended to standardize metric covariates, display of effect stars can benefit greatly as in general differences between the coefficients are increased.
Value
Pvalues are only available if the corresponding option is set TRUE
.
odds 
Odds or exponential coefficients of the cumulative logit model 
coefficients 
Coefficients of the cumulative logit model 
se 
Standard errors of the coefficients 
p_rel 
Pvalues of LikelihoodRatioTests for the relevance of the explanatory covariates 
p_global 
Pvalues of LikelihoodRatioTests wether the covariates need to be included categoryspecific 
xlim 

ylim 

Author(s)
Gunther Schauberger
gunther@stat.unimuenchen.de
http://www.statistik.lmu.de/~schauberger/
References
Tutz, G. and Schauberger, G. (2012): Visualization of Categorical Response Models 
from Data Glyphs to Parameter Glyphs, Journal of Computational and Graphical Statistics 22(1), 156177.
Gerhard Tutz (2012): Regression for Categorical Data, Cambridge University Press
See Also
star.sequential
, star.nominal
Examples
1 2 3 4 5 6  ## Not run:
data(insolvency)
star.cumulative(Insolvency ~ Sector + Employees, insolvency, select = 2:4)
## End(Not run)
