star.nominal {EffectStars} R Documentation

## Effect stars for multinomial logit models

### Description

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

The function computes and visualizes multinomial 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

star.nominal(formula, data, xij = NULL, conf.int = FALSE, symmetric = TRUE,
pred.coding = "reference", printpvalues = TRUE, test.rel = TRUE, refLevel = 1,
maxit = 100, scale = TRUE, nlines = NULL, select = NULL, catstar = TRUE,
dist.x = 1, dist.y = 1, dist.cov = 1, dist.cat = 1, xpd = TRUE, main = "",
lwd.stars = 1, col.fill = "gray90", col.circle = "black", lwd.circle = 1,
lty.circle = "longdash", lty.conf = "dotted", cex.labels = 1, cex.cat = 0.8,
xlim = NULL, ylim = NULL)

### Details

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

The stars show the exponentials of the estimated coefficients. In multinomial logit models the exponential coefficients can be interpreted as odds. More precisely, for the model with symmetric side constraints, the exponential e^{\gamma_{rj}}, r=1,\ldots,k represents the multiplicative effect of the covariate j on the odds \frac{P(Y=r|x)}{GM(x)} if x_j increases by one unit and GM(x) is the median response. For the model with reference category k, the exponential e^{\gamma_{rj}}, r=1,\ldots,k-1 represents the multiplicative effect of the covariate j on the odds \frac{P(Y=r|x)}{P(Y=k|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 distances between the rays of a star and the cirlce correspond to the p-values that are printed beneath the category levels if printpvalues=TRUE. The closer a star ray lies to the no–effects circle, the more the p-value is increased.
The p-values beneath the covariate labels, which are given 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.

The argument xij is important because it has to be used to include category-specific covariates. If its default xij=NULL is kept, an ordinary multinomial logit model without category-specific covariates is fitted. If category-specific covariates are to be included, attention has to be paid to the exact usage of xij. Our xij argument is identical to the xij argument used in the embedded vglm function. For details see also vglm.control. The data are thought to be present in a wide format, i.e. a category-specific covariate consists of k columns. Before calling star.nominal, the values for the reference category (defined by refLevel) have to be subtracted from the values of the further categories. Additionally, the resulting variable for the first response category (but not the reference category) has to be duplicated. This duplicate should be denoted by an appropriate name for the category-specific variable, independent from the different response categories. It will be used as an assignment variable for the corresponding coefficient of the covariate and has to be included in to the formula. For every category-specific covariate, a formula has to be specified in the xij argument. On the left hand side of that formula, the assignment variable has to be placed. On the right hand side, the variables containing the differences from the values for the reference category are written. So the left hand side of the formula contains k-1 terms. The order of these terms has to be chosen according to the order of the response categories, ignoring the reference category. Examples for effect stars for models with category-specific covariates are recieved by typing vignette("election") or vignette("plebiscite").

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.
catspec and catspecse are only available if xij is specified.

 odds Odds or exponential coefficients of the multinomial logit model coefficients Coefficients of the multinomial logit model se Standard errors of the coefficients pvalues P-values of Wald tests for the respective coefficients catspec Coefficients for the category-specific covariates catspecse Standard errors for the coefficients for the category-specific covariates p_rel P-values of Likelihood-Ratio-Tests for the relevance of the explanatory covariates 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

### 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

### Examples

## Not run:
data(election)

# simple multinomial logit model
star.nominal(Partychoice ~ Age + Religion + Democracy + Pol.Interest +
Unemployment + Highschool + Union + West + Gender, election)

# Use effect coding for the categorical predictor religion
star.nominal(Partychoice ~ Age + Religion + Democracy + Pol.Interest +
Unemployment + Highschool + Union + West + Gender, election,
pred.coding = "effect")

# Use reference category "FDP" instead of symmetric side constraints
star.nominal(Partychoice ~ Age + Religion + Democracy + Pol.Interest +
Unemployment + Highschool + Union + West + Gender, election,
refLevel = 3, symmetric = FALSE)

# Use category-specific covariates, subtract values for reference
# category CDU
election[,13:16] <- election[,13:16] - election[,12]
election[,18:21] <- election[,18:21] - election[,17]
election[,23:26] <- election[,23:26] - election[,22]
election[,28:31] <- election[,28:31] - election[,27]

election$Social <- election$Social_SPD
election$Immigration <- election$Immigration_SPD
election$Nuclear <- election$Nuclear_SPD
election$Left_Right <- election$Left_Right_SPD

star.nominal(Partychoice ~ Social + Immigration + Nuclear + Left_Right + Age +
Religion + Democracy + Pol.Interest + Unemployment + Highschool + Union + West +
Gender, data = election,
xij = list(Social ~ Social_SPD + Social_FDP + Social_Greens + Social_Left,
Immigration ~ Immigration_SPD + Immigration_FDP + Immigration_Greens + Immigration_Left,
Nuclear ~ Nuclear_SPD + Nuclear_FDP + Nuclear_Greens + Nuclear_Left,
Left_Right ~ Left_Right_SPD + Left_Right_FDP + Left_Right_Greens + Left_Right_Left),
symmetric = FALSE)

## End(Not run)

[Package EffectStars version 1.9-1 Index]