Package ‘EffectStars’ September 2, 2016 Type Package Title Visualization of Categorical Response Models Version 1.7 Date 2016-09-01 Depends VGAM Author Gunther Schauberger Maintainer Gunther Schauberger <[email protected]> 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. 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 Repository CRAN Date/Publication 2016-09-02 14:59:07 R topics documented: alligator . . . . BEPS . . . . . coffee . . . . . EffectStars . . . election . . . . insolvency . . . PID . . . . . . plebiscite . . . star.cumulative star.nominal . . star.sequential . womenlabour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 3 4 5 6 8 9 10 11 15 19 23 24 1 2 alligator alligator 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 and rep Size Size of the alligator with levels <2.3 and >2.3 Gender Gender with levels female and male Lake Name of the lake with levels George, Hancock, Oklawaha and Trafford 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) BEPS BEPS 3 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 and Liberal Democrat Age Age in years Gender Gender with levels female and male 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 effects: 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$Leader_Labour 4 coffee BEPS$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) coffee 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 and Highschool PriceSensitivity Price sensitivity with levels not sensitive and sensitive Income Income with levels < 2499 and >= 2500 SocialLevel Social level with levels high and low Age Age with levels < 49 and >= 50 Brand Coffee Brand with levels Jacobs, JacobsSpecial, Aldi, AldiSpecial, Eduscho, EduschoSpecial, Tchibo, TchiboSpecial and Others Amount Amount of packs with levels 1 and >= 2 Persons Number of persons in household Source http://www.stat.uni-muenchen.de/service/datenarchiv/ References Gesellschaft für Konsumforschung (GfK) EffectStars 5 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) EffectStars 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 <[email protected]> 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 See Also star.nominal, star.sequential, star.cumulative 6 election election 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 and Left Party Gender Gender with levels female and male West Regional provenance (West-Germany or East-Germany) with levels east and west Union Member of a Union with levels no member and member Highschool Educational level with levels no highschool and highschool Unemployment Unemployment with levels not unemployed and unemployed Pol.Interest Political Interest with levels very interested and less interested Democracy Satisfaction with the functioning of democracy with levels satisfied and not satisfied Religion Religion with levels evangelical, catholic and other 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 election 7 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 8 insolvency election[,13:16] election[,18:21] election[,23:26] election[,28:31] <<<<- election[,13:16] election[,18:21] election[,23:26] election[,28:31] - election[,12] election[,17] election[,22] 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 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 and service industry Legal Legal form with levels small trade, one man business, GmBH and GbR, KG, OHG Location Location with levels residential area and business area New_Foundation New Foundation or take-over with levels new foundation and take-over Pecuniary_Reward Pecuniary reward with levels main and additional Seed_Capital Seed capital with levels < 25000 and > 25000 PID 9 Equity_Capital Equity capital with levels no and yes Debt_Capital Debt capital with levels no and yes Market Market with levels local and national Clientele Clientele with levels wide spread and small Degree Educational level with levels no A-levels and A-Levels Gender Gender with levels female and male 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) PID Party Identification Description Subset of the 1996 American National Election Study. Usage data(election) 10 plebiscite 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 and Republican Income Income Education Educational level with levels low (no college) and high (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) plebiscite 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) star.cumulative 11 Format A data frame with 2431 observations on the following 7 variables. Gender Gender with levels female and male Education Educational level with levels low and high SantiagoCity Respondent from Santiago City with levels no and yes Income Monthly Income in Pesos Population Population size of respondent’s community Age Age in years Vote Response with levels Abstention, No, Undecided and Yes Source R package car: 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) star.cumulative 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. 12 star.cumulative 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 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. See also Details. 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 pvalues will be printed as p-global. test.glob=FALSE and globcircle=FALSE might save a lot of time. See also Details. partial If partial=TRUE, partial proportional odds models with only one categoryspecific covariate are fitted. The resulting effects of the (sub)models are plotted. For further information see Details. 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 cumulative 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. star.cumulative 13 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 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 eγrj , r = 1, . . . , k−1 P (Y ≤r|x) represents the multiplicative effect of the covariate j on the cumulative odds P (Y >r|x) if xj 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, 14 star.cumulative 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 coefficients se p_rel p_global xlim ylim Odds or exponential coefficients of the cumulative logit model Coefficients of the cumulative logit model Standard errors of the coefficients P-values of Likelihood-Ratio-Tests for the relevance of the explanatory covariates P-values of Likelihood-Ratio-Tests wether the covariates need to be included category-specific xlim values that were automatically produced. May be helpfull if you want to specify your own xlim ylim values that were automatically produced. May be helpfull if you want to specify your own ylim Author(s) Gunther Schauberger <[email protected]> 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 See Also star.sequential, star.nominal star.nominal 15 Examples ## Not run: data(insolvency) star.cumulative(Insolvency ~ Sector + Employees, insolvency, select = 2:4) ## End(Not run) star.nominal 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 formula. 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 xij in vglm.control and the details below. conf.int If TRUE, confidence intervals are drawn. symmetric Which side constraint for the coefficients in the multinomial logit model shall be used for the plot? Default TRUE uses symmetric side constraints, FALSE uses the reference category specified by refLevel. If category-specific covariates are specified using xij, automatically symmetric = FALSE is set. Symmetric side constraints are not possible in the case of category-specific covariates. 16 star.nominal pred.coding Which coding for categorical predictors with more than two categories is to be used? Default pred.coding="reference" uses the first category as reference category, the alternative pred.coding="effect" uses effect coding equivalent to symmetric side constraints. For pred.coding="effect" a star for every category is plotted, for pred.coding="reference" no star for the reference category is plotted. printpvalues If TRUE, p-values for the respective coefficients are printed besides the category labels. P-values are recieved by a Wald test. 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. test.rel=FALSE might save a lot of time. refLevel Reference category for multinomial logit model. Ignored if symmetric=TRUE. See also multinomial. maxit Maximal number of iterations to fit the multinomial 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. catstar A logical argument to specify if all category-specific effects in the model should be visualized with an additional star. Ignored if xij=NULL. 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. lwd.stars Line width of the stars. See also lwd in par. 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. star.nominal 17 lty.circle Line type of the circle. See also lty in par. lty.conf Line type of confidence intervals. Ignored, if conf.int=FALSE. See also lty in par. 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 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 eγrj , r = 1, . . . , k represents the multiplicative effect of the covari(Y =r|x) ate j on the odds PGM (x) if xj increases by one unit and GM (x) is the median response. For the model with reference category k, the exponential eγrj , r = 1, . . . , k−1 represents the multiplicative (Y =r|x) effect of the covariate j on the odds PP (Y =k|x) if xj 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 18 star.nominal 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 Author(s) Gunther Schauberger <[email protected]> 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 See Also star.sequential, star.cumulative star.sequential 19 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) star.sequential 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. 20 star.sequential 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 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 pvalues 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. star.sequential 21 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 eγrj , r = 1, . . . , k−1 P (Y =r|x) represents the multiplicative effect of the covariate j on the continuation ratio odds P (Y >r|x) if xj 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. 22 star.sequential 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 <[email protected]> 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 See Also star.nominal, star.cumulative 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) womenlabour womenlabour 23 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 and parttime IncomeHusband Husband’s income in 1000 $ Children Presence od children in household with levels absent and present Region Region with levels Atlantic, BC, Ontario, Prairie and Quebec Source R package car: 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) Index ∗Topic categorical data EffectStars, 5 ∗Topic cumulative logit model EffectStars, 5 star.cumulative, 11 ∗Topic datasets alligator, 2 BEPS, 3 coffee, 4 election, 6 insolvency, 8 PID, 9 plebiscite, 10 womenlabour, 23 ∗Topic multinomial logit model EffectStars, 5 star.nominal, 15 ∗Topic multinomial response alligator, 2 BEPS, 3 coffee, 4 EffectStars, 5 election, 6 PID, 9 plebiscite, 10 star.nominal, 15 womenlabour, 23 ∗Topic ordinal response EffectStars, 5 insolvency, 8 star.cumulative, 11 star.sequential, 19 ∗Topic package EffectStars, 5 ∗Topic sequential logit model EffectStars, 5 star.sequential, 19 ∗Topic star plot star.cumulative, 11 star.nominal, 15 star.sequential, 19 alligator, 2 BEPS, 3, 3 Chile, 11 coffee, 4 EffectStars, 5 EffectStars-package (EffectStars), 5 election, 6 insolvency, 8 multinomial, 16 nes96, 10 par, 13, 16, 17, 21 PID, 9 plebiscite, 10 plot, 13, 16, 21 plot.window, 13, 17, 21 star.cumulative, 5, 11, 18, 22 star.nominal, 5, 14, 15, 22 star.sequential, 5, 14, 18, 19 stars, 11, 15, 19 vglm, 13, 17, 21 vglm.control, 12, 15–17, 20 womenlabour, 23 Womenlf, 23 24

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