# Effect stars for sequential logit models

### Description

The package EffectStars2 provides a more up-to-date implementation of effect stars!

The function computes and visualizes sequential 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.sequential(formula, data, global = NULL, test.rel = TRUE, test.glob = 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 sequential logit model to be fitted an visualized. data An object of class “data.frame” containing the covariates used in formula. global Numeric vector to choose a subset of predictors to be included with global coefficients. Default is to include all coefficients category-specific. Numbers refer to total amount of predictors, including intercept and dummy variables. test.rel Provides a Likelihood-Ratio-Test to test the relevance of the explanatory covariates. The corresponding p-values will be printed as p-rel. test.rel=FALSE might save a lot of time. test.glob Provides a Likelihood-Ratio-Test to test if a covariate has to be included as a category-specific covariate (in contrast to being global). The corresponding p-values will be printed as p-global. test.glob=FALSE and globcircle=FALSE might save a lot of time. globcircle If TRUE, additional circles that represent the global effects of the covariates are plotted. test.glob=FALSE and globcircle=FALSE might save a lot of time. maxit Maximal number of iterations to fit the sequential logit model. See also vglm.control. scale If TRUE, the stars are scaled to equal maximal ray length. nlines If specified, nlines gives the number of lines in which the effect stars are plotted. 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 x-axis. 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 y-axis. 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 FALSE, all plotting is clipped to the plot region, if TRUE, all plotting is clipped to the figure region, and if NA, all plotting is clipped to the device region. See also par. main An overall title for the plot. See also plot. col.fill Color of background of the circle. See also col in par. col.circle Color of margin of the circle. See also col in par. lwd.circle Line width of the circle. See also lwd in par. lty.circle Line type of the circle. See also lty in par. col.global Color of margin of the global effects circle. See also col in par. Ignored, if globcircle = FALSE. lwd.global Line width of the global effects circle. See also lwd in par. Ignored, if globcircle = FALSE. lty.global Line type of the global effects circle. See also lty in par. Ignored, if globcircle = FALSE. cex.labels Size of labels for covariates placed above the corresponding star. See also cex in par. cex.cat Size of labels for categories placed around the corresponding star. See also cex in par. xlim Optional specification of the x coordinates ranges. See also xlim in plot.window ylim Optional specification of the y coordinates ranges. See also ylim in plot.window

### Details

The underlying models are fitted with the function vglm from the package VGAM. The family argument for vglm is sratio(parallel=FALSE).

The stars show the exponentials of the estimated coefficients. In sequential logit models the exponential coefficients can be interpreted as odds. More precisely, the exponential e^{γ_{rj}}, r=1,…,k-1 represents the multiplicative effect of the covariate j on the continuation ratio odds \frac{P(Y=r|x)}{P(Y>r|x)} 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 no-effects case where all the coefficients are zero. Now the circles can be used to compare different stars based on their respective circles radii. The p-values 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 appearance 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 category-specific but globally. Therefore, the distance between this circle and the star as a whole corresponds to the p-value p-global that is given if test.glob=TRUE.

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

P-values are only available if the corresponding option is set TRUE.

 odds Odds or exponential coefficients of the sequential logit model coefficients Coefficients of the sequential logit model se Standard errors of the coefficients p_rel P-values of Likelihood-Ratio-Tests for the relevance of the explanatory covariates p_global P-values of Likelihood-Ratio-Tests wether the covariates need to be included category-specific xlim xlim values that were automatically produced. May be helpfull if you want to specify your own xlim ylim ylim values that were automatically produced. May be helpfull if you want to specify your own ylim

### Author(s)

Gunther Schauberger
gunther@stat.uni-muenchen.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), 156-177.

Gerhard Tutz (2012): Regression for Categorical Data, Cambridge University Press

star.nominal, star.cumulative
 1 2 3 4 5 6 7 ## Not run: data(insolvency) star.sequential(Insolvency ~ Sector + Legal + Pecuniary_Reward + Seed_Capital + Debt_Capital + Employees, insolvency, test.glob = FALSE, globcircle = TRUE, dist.x = 1.3) ## End(Not run)