Type: | Package |
Title: | Visualization of Categorical Response Models |
Version: | 1.9-1 |
Date: | 2019-10-22 |
Depends: | VGAM |
Author: | Gunther Schauberger |
Maintainer: | Gunther Schauberger <gunther.schauberger@tum.de> |
Description: | Notice: The package EffectStars2 provides a more up-to-date implementation of effect stars! EffectStars provides functions to visualize regression models with categorical response as proposed by Tutz and Schauberger (2013) <doi:10.1080/10618600.2012.701379>. The effects of the variables are plotted with star plots in order to allow for an optical impression of the fitted model. |
License: | GPL-2 |
LazyLoad: | yes |
NeedsCompilation: | no |
Packaged: | 2019-10-22 08:01:48 UTC; ge29weh |
Repository: | CRAN |
Date/Publication: | 2019-10-22 09:40:05 UTC |
Visualization of Categorical Response Models
Description
The package EffectStars2 provides a more up-to-date implementation of effect stars!
The package provides functions that visualize categorical regression models.
Included models are the multinomial logit model, the sequential logit model and the
cumulative logit model.
The exponentials of the effects of the predictors are plotted as star plots showing the strengths of the effects.
In addition p-values for the effect of predictors are given.
Various data sets and examples are provided.
The plots should in general be exported to file formats like pdf, ps or png to recieve the optimal display. Plotting in R devices may not provide the optimal results.
For further details see star.nominal
, star.sequential
and star.cumulative
.
Author(s)
Gunther Schauberger
gunther.schauberger@tum.de
https://www.sg.tum.de/epidemiologie/team/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
See Also
star.nominal
, star.sequential
, star.cumulative
British Election Panel Study
Description
These data are drawn from the 1997-2001 British Election Panel Study (BEPS).
Usage
data(BEPS)
Format
A data frame with 1525 observations on the following 10 variables.
Europe
An 11-point scale that measures respondents' attitudes toward European integration. High scores represent eurosceptic sentiment
Leader_Cons
Assessment of the Conservative leader Hague, 1 to 5
Leader_Labour
Assessment of the Labour leader Blair, 1 to 5
Leader_Liberals
Assessment of the Liberals leader Kennedy, 1 to 5
Vote
Party Choice with levels
Conservative
,Labour
andLiberal Democrat
Age
Age in years
Gender
Gender with levels
female
andmale
Political_Knowledge
Knowledge of parties' positions on European integration, 0 to 3
National_Economy
Assessment of current national economic conditions, 1 to 5
Household
Assessment of current household economic conditions, 1 to 5
Source
R package carData: BEPS
References
British Election Panel Study (BEPS)
J. Fox and R. Andersen (2006): Effect displays for multinomial and proportional-odds logit models. Sociological Methodology 36, 225–255
Examples
## Not run:
data(BEPS)
BEPS$Europe<-scale(BEPS$Europe)
BEPS$Age<-scale(BEPS$Age)
BEPS$Leader_Labour<-BEPS$Leader_Labour-BEPS$Leader_Cons
BEPS$Leader<-BEPS$Leader_Labour
BEPS$Leader_Liberals<-BEPS$Leader_Liberals-BEPS$Leader_Cons
star.nominal(Vote ~ Age + Household + National_Economy + Household + Leader +
Europe + Political_Knowledge + Gender, data = BEPS,
xij = list(Leader~Leader_Labour+Leader_Liberals), catstar = FALSE, symmetric = FALSE)
## End(Not run)
Party Identification
Description
Subset of the 1996 American National Election Study.
Usage
data(election)
Format
A data frame with 944 observations on the following 6 variables.
TVnews
Days in the past week spent watching news on TV
PID
Party identification with levels
Democrat
,Independent
andRepublican
Income
Income
Education
Educational level with levels
low
(no college) andhigh
(at least college)Age
Age in years
Population
Population of respondent's location in 1000s of people
Source
R package faraway: nes96
Examples
## Not run:
data(PID)
PID$TVnews <- scale(PID$TVnews)
PID$Income <- scale(PID$Income)
PID$Age <- scale(PID$Age)
PID$Population <- scale(PID$Population)
star.nominal(PID ~ TVnews + Income + Population + Age + Education, data = PID)
## End(Not run)
Alligator Food
Description
The data describe the food choice of alligators, they originate from a study of the Florida Game and Fresh Water Commission.
Usage
data(alligator)
Format
A data frame with 219 observations on the following 4 variables.
Food
Food type with levels
bird
,fish
,invert
,other
andrep
Size
Size of the alligator with levels
<2.3
and>2.3
Gender
Gender with levels
female
andmale
Lake
Name of the lake with levels
George
,Hancock
,Oklawaha
andTrafford
Source
http://www.stat.ufl.edu/~aa/cda/sas/sas.html
References
Agresti (2002): Categorical Data Analysis, Wiley.
Examples
## Not run:
data(alligator)
star.nominal(Food ~ Size + Lake + Gender, data = alligator, nlines = 2)
## End(Not run)
Coffee Brands
Description
The data frame is part of a long-term panel about the choice of coffee brands in 2111 households. The explanatory variables either refer to the household as a whole or to the head of the household.
Usage
data(coffee)
Format
A data frame with 2111 observations on the following 8 variables.
Education
Educational level with levels
no Highschool
andHighschool
PriceSensitivity
Price sensitivity with levels
not sensitive
andsensitive
Income
Income with levels
< 2499
and>= 2500
SocialLevel
Social level with levels
high
andlow
Age
Age with levels
< 49
and>= 50
Brand
Coffee Brand with levels
Jacobs
,JacobsSpecial
,Aldi
,AldiSpecial
,Eduscho
,EduschoSpecial
,Tchibo
,TchiboSpecial
andOthers
Amount
Amount of packs with levels
1
and>= 2
Persons
Number of persons in household
References
Gesellschaft für Konsumforschung (GfK)
Examples
## Not run:
data(coffee)
star.nominal(Brand ~ Amount + Age + SocialLevel + Income + Persons +
PriceSensitivity + Education, coffee, cex.cat = 0.5, cex.labels = 0.8)
## End(Not run)
Election Data
Description
The data set contains data from the German Longitudinal Election Study. The Response Categories refer to the five dominant parties in Germany. The explanatory variables refer to the declarations of single voters.
Usage
data(election)
Format
A data frame with 816 observations on the following 30 variables.
Age
Standardized age of the voter
AgeOrig
Unstandardized age of the voter
Partychoice
Party Choice with levels
CDU
,SPD
,FDP
,Greens
andLeft Party
Gender
Gender with levels
female
andmale
West
Regional provenance (West-Germany or East-Germany) with levels
east
andwest
Union
Member of a Union with levels
no member
andmember
Highschool
Educational level with levels
no highschool
andhighschool
Unemployment
Unemployment with levels
not unemployed
andunemployed
Pol.Interest
Political Interest with levels
very interested
andless interested
Democracy
Satisfaction with the functioning of democracy with levels
satisfied
andnot satisfied
Religion
Religion with levels
evangelical
,catholic
andother religion
Social_CDU
Difference in attitude towards the socioeconomic dimension of politics between respondent and CDU
Social_SPD
Difference in attitude towards the socioeconomic dimension of politics between respondent and SPD
Social_FDP
Difference in attitude towards the socioeconomic dimension of politics between respondent and FDP
Social_Greens
Difference in attitude towards the socioeconomic dimension of politics between respondent and the Greens
Social_Left
Difference in attitude towards the socioeconomic dimension of politics between respondent and the Left party
Immigration_CDU
Difference in attitude towards immigration of foreigners between respondent and CDU
Immigration_SPD
Difference in attitude towards immigration of foreigners between respondent and SPD
Immigration_FDP
Difference in attitude towards immigration of foreigners between respondent and FDP
Immigration_Greens
Difference in attitude towards immigration of foreigners between respondent and the Greens
Immigration_Left
Difference in attitude towards immigration of foreigners between respondent and the Left party
Nuclear_CDU
Difference in attitude towards nuclear energy between respondent and CDU
Nuclear_SPD
Difference in attitude towards nuclear energy between respondent and SPD
Nuclear_FDP
Difference in attitude towards nuclear energy between respondent and FDP
Nuclear_Greens
Difference in attitude towards nuclear energy between respondent and the Greens
Nuclear_Left
Difference in attitude towards nuclear energy between respondent and the Left party
Left_Right_CDU
Difference in attitude towards the positioning on a political left-right scale between respondent and CDU
Left_Right_SPD
Difference in attitude towards the positioning on a political left-right scale between respondent and SPD
Left_Right_FDP
Difference in attitude towards the positioning on a political left-right scale between respondent and FDP
Left_Right_Greens
Difference in attitude towards the positioning on a political left-right scale between respondent and the Greens
Left_Right_Left
Difference in attitude towards the positioning on a political left-right scale between respondent and the Left party
References
German Longitudinal Election Study (GLES)
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)
Insolvency data
Description
The data set originates from the Munich founder study. The data were collected on business founders who registered their new companies at the local chambers of commerce in Munich and surrounding administrative districts. The focus was on survival of firms measured in 7 categories, the first six represent failure in intervals of six months, the last category represents survival time beyond 36 months.
Usage
data(insolvency)
Format
A data frame with 1224 observations on the following 16 variables.
Insolvency
Survival of firms in ordered categories with levels
1
<2
<3
<4
<5
<6
<7
Sector
Economic Sector with levels
industry
,commerce
andservice industry
Legal
Legal form with levels
small trade
,one man business
,GmBH
andGbR, KG, OHG
Location
Location with levels
residential area
andbusiness area
New_Foundation
New Foundation or take-over with levels
new foundation
andtake-over
Pecuniary_Reward
Pecuniary reward with levels
main
andadditional
Seed_Capital
Seed capital with levels
< 25000
and> 25000
Equity_Capital
Equity capital with levels
no
andyes
Debt_Capital
Debt capital with levels
no
andyes
Market
Market with levels
local
andnational
Clientele
Clientele with levels
wide spread
andsmall
Degree
Educational level with levels
no A-levels
andA-Levels
Gender
Gender with levels
female
andmale
Experience
Professional experience with levels
< 10 years
and> 10 years
Employees
Number of employees with levels
0 or 1
and> 2
Age
Age of the founder at formation of the company
Source
Münchner Gründer Studie
References
Brüderl, J. and Preisendörfer, P. and Ziegler, R. (1996): Der Erfolg neugegründeter Betriebe: eine empirische Studie zu den Chancen und Risiken von Unternehmensgründungen, Duncker & Humblot.
Examples
## 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)
star.cumulative(Insolvency ~ Sector + Employees, insolvency, select = 2:4)
## End(Not run)
Chilean Plebiscite
Description
The data origin from a survey refering to the plebiscite in Chile 1988. The chilean people had to decide, wether Augusto Pinochet would remain president for another ten years (voting yes) or if there would be presidential elections in 1989 (voting no).
Usage
data(plebiscite)
Format
A data frame with 2431 observations on the following 7 variables.
Gender
Gender with levels
female
andmale
Education
Educational level with levels
low
andhigh
SantiagoCity
Respondent from Santiago City with levels
no
andyes
Income
Monthly Income in Pesos
Population
Population size of respondent's community
Age
Age in years
Vote
Response with levels
Abstention
,No
,Undecided
andYes
Source
R package carData: Chile
References
Personal communication from FLACSO/Chile.
Fox, J. (2008): Applied Regression Analysis and Generalized Linear Models, Second Edition.
Examples
## Not run:
data(plebiscite)
plebiscite$Population <- scale(plebiscite$Population)
plebiscite$Age <- scale(plebiscite$Age)
plebiscite$Income <- scale(plebiscite$Income)
star.nominal(Vote ~ SantiagoCity + Population + Gender + Age + Education +
Income, data = plebiscite)
## End(Not run)
Effect stars for cumulative logit models
Description
The package EffectStars2 provides a more up-to-date 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
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 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 |
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 |
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 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 |
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^{\gamma_{rj}}, r=1,\ldots,k-1
represents the multiplicative effect of the covariate j on the cumulative odds \frac{P(Y\leq 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 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 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
.
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 category-specific covariate, so-called
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 p-values refer to the various submodels.
For partial=TRUE
, the p-values p-rel
and p-global
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
P-values 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 |
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 |
|
ylim |
|
Author(s)
Gunther Schauberger
gunther.schauberger@tum.de
https://www.sg.tum.de/epidemiologie/team/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
See Also
Examples
## Not run:
data(insolvency)
star.cumulative(Insolvency ~ Sector + Employees, insolvency, select = 2:4)
## End(Not run)
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)
Arguments
formula |
An object of class “formula”. Formula for the multinomial logit model to be fitted and visualized. |
data |
An object of class “data.frame” containing the covariates used in |
xij |
An object of class list, used if category-specific covariates are to be inlcuded. Every element is a formula referring to one of the category-specific covariates. For details see help for |
conf.int |
If |
symmetric |
Which side constraint for the coefficients in the multinomial logit model shall be used for the plot?
Default |
pred.coding |
Which coding for categorical predictors with more than two categories is to be used?
Default |
printpvalues |
If |
test.rel |
Provides a Likelihood-Ratio-Test to test the relevance of the explanatory covariates.
The corresponding p-values will be printed behind the covariates labels. |
refLevel |
Reference category for multinomial logit model. Ignored if |
maxit |
Maximal number of iterations to fit the multinomial 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. |
catstar |
A logical argument to specify if all category-specific effects in the model should be visualized with an additional star. Ignored if |
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 |
main |
An overall title for the plot. See also |
lwd.stars |
Line width of the stars. 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 |
lty.conf |
Line type of confidence intervals. Ignored, if |
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 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 |
|
ylim |
|
Author(s)
Gunther Schauberger
gunther.schauberger@tum.de
https://www.sg.tum.de/epidemiologie/team/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
See Also
star.sequential
, star.cumulative
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)
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
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 |
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 |
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 |
globcircle |
If |
maxit |
Maximal number of iterations to fit the sequential 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 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 |
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 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^{\gamma_{rj}}, r=1,\ldots,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 |
|
ylim |
|
Author(s)
Gunther Schauberger
gunther.schauberger@tum.de
https://www.sg.tum.de/epidemiologie/team/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
See Also
Examples
## 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)
Canadian Women's Labour-Force Participation
Description
The data are from a 1977 survey of the Canadian population.
Usage
data(womenlabour)
Format
A data frame with 263 observations on the following 4 variables.
Participation
Labour force participation with levels
fulltime
,not.work
andparttime
IncomeHusband
Husband's income in 1000 $
Children
Presence od children in household with levels
absent
andpresent
Region
Region with levels
Atlantic
,BC
,Ontario
,Prairie
andQuebec
Source
R package carData: Womenlf
References
Social Change in Canada Project. York Institute for Social Research.
Fox, J. (2008): Applied Regression Analysis and Generalized Linear Models, Second Edition.
Examples
## Not run:
data(womenlabour)
womenlabour$IncomeHusband <- scale(womenlabour$IncomeHusband)
star.nominal(Participation ~ IncomeHusband + Children + Region, womenlabour)
## End(Not run)