star.nominal: Effect stars for multinomial logit models
In EffectStars: Visualization of Categorical Response Models
Description
Usage
Arguments
Details
Value
Author(s)
References
See Also
Examples
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
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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.
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.
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 e^{γ_{rj}}, r=1,…,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^{γ_{rj}}, r=1,…,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
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
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## 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)
Example output
Loading required package: VGAM
Loading required package: stats4
Loading required package: splines
***
The package EffectStars is not the latest implementation of effect stars,
it is recommended to use EffectStars2 instead!
***
$odds
(Intercept) Age Religioncatholic Religionother religion
CDU 4.0414180 1.3610160 1.4966912 0.6995756
SPD 1.5990015 1.1593572 0.8217861 0.6516310
FDP 0.7082683 0.8949610 1.0941385 1.3833039
Greens 0.3340832 0.6717696 0.8806534 1.3315266
Left Party 0.6539807 1.0541321 0.8437849 1.1909573
Democracynot satisfied Pol.Interestless interested
CDU 0.4647250 1.2235443
SPD 0.6981521 1.4007700
FDP 1.0014337 0.7694186
Greens 1.0089709 1.2356738
Left Party 3.0503736 0.6136870
Unemploymentunemployed Highschoolhighschool Unionmember Westwest
CDU 0.5982192 1.1681635 0.6654958 0.7187891
SPD 1.1349142 0.8022314 1.4926187 1.4746518
FDP 0.5714916 1.0529723 0.6002910 1.0248900
Greens 0.9302358 1.7567339 0.6772513 1.8973255
Left Party 2.7705995 0.5768644 2.4762479 0.4851655
Gendermale
CDU 0.7689529
SPD 0.8261321
FDP 1.2896875
Greens 0.9805111
Left Party 1.2448406
$coefficients
(Intercept) Age Religioncatholic Religionother religion
CDU 1.3965956 0.30823148 0.4032568 -0.3572814
SPD 0.4693794 0.14786569 -0.1962752 -0.4282769
FDP -0.3449323 -0.11097516 0.0899673 0.3244748
Greens -1.0963653 -0.39783981 -0.1270911 0.2863261
Left Party -0.4246775 0.05271779 -0.1698577 0.1747574
Democracynot satisfied Pol.Interestless interested
CDU -0.766309354 0.2017518
SPD -0.359318301 0.3370221
FDP 0.001432664 -0.2621201
Greens 0.008930930 0.2116164
Left Party 1.115264061 -0.4882702
Unemploymentunemployed Highschoolhighschool Unionmember Westwest
CDU -0.51379809 0.15543288 -0.4072230 -0.33018727
SPD 0.12655704 -0.22035813 0.4005321 0.38842192
FDP -0.55950553 0.05161693 -0.5103407 0.02458526
Greens -0.07231714 0.56345632 -0.3897129 0.64044524
Left Party 1.01906373 -0.55014800 0.9067445 -0.72326516
Gendermale
CDU -0.26272555
SPD -0.19100061
FDP 0.25439996
Greens -0.01968127
Left Party 0.21900748
$se
(Intercept) Age Religioncatholic Religionother religion
CDU 0.2241927 0.06883799 0.1629137 0.1675209
SPD 0.2455006 0.07244088 0.1661454 0.1722205
FDP 0.3115509 0.09372309 0.2388794 0.2184724
Greens 0.3272014 0.09663391 0.2339503 0.2129104
Left Party 0.3134423 0.09450515 0.2328685 0.2050096
Democracynot satisfied Pol.Interestless interested
CDU 0.1388867 0.1467924
SPD 0.1475394 0.1596959
FDP 0.1943961 0.1906783
Greens 0.1933167 0.2026824
Left Party 0.2290404 0.1853934
Unemploymentunemployed Highschoolhighschool Unionmember Westwest
CDU 0.3657321 0.1691938 0.2118770 0.1559298
SPD 0.3140084 0.1889271 0.1836195 0.1722526
FDP 0.4982842 0.2177526 0.2891862 0.2070996
Greens 0.4216104 0.2081806 0.2730769 0.2221560
Left Party 0.3014527 0.2426935 0.2164160 0.1942954
Gendermale
CDU 0.1353619
SPD 0.1423126
FDP 0.1874526
Greens 0.1840917
Left Party 0.1806023
$pvalues
(Intercept) Age Religioncatholic Religionother religion
CDU 4.680987e-10 7.547395e-06 0.01331325 0.03294467
SPD 5.588552e-02 4.123181e-02 0.23746528 0.01289003
FDP 2.682310e-01 2.363834e-01 0.70645435 0.13749137
Greens 8.059719e-04 3.838704e-05 0.58696459 0.17868341
Left Party 1.754550e-01 5.769606e-01 0.46574801 0.39397247
Democracynot satisfied Pol.Interestless interested
CDU 3.438249e-08 0.169316829
SPD 1.487511e-02 0.034823994
FDP 9.941198e-01 0.169233235
Greens 9.631521e-01 0.296449019
Left Party 1.119999e-06 0.008446062
Unemploymentunemployed Highschoolhighschool Unionmember
CDU 0.1600664566 0.358269369 5.460851e-02
SPD 0.6869209386 0.243466508 2.916006e-02
FDP 0.2614951256 0.812622691 7.760614e-02
Greens 0.8638102011 0.006798138 1.535459e-01
Left Party 0.0007235162 0.023399826 2.791731e-05
Westwest Gendermale
CDU 0.0342142665 0.05226895
SPD 0.0241360950 0.17955713
FDP 0.9055033181 0.17473587
Greens 0.0039407876 0.91486024
Left Party 0.0001972576 0.22526357
$p_rel
Age Religioncatholic Religionother religion
[1,] 5.625482e-07 0.08015606 0.01694874
Democracynot satisfied Pol.Interestless interested Unemploymentunemployed
[1,] 2.955651e-10 0.01335832 0.01308379
Highschoolhighschool Unionmember Westwest Gendermale
[1,] 0.01862473 3.281531e-05 1.548773e-05 0.1509492
$xlim
[1] 10.50769 57.38814
$ylim
[1] 10.06313 72.58387
$odds
Intercept Age Religionevangelical Religioncatholic
CDU 4.1038303 1.3610160 0.9847917 1.4739290
SPD 1.2984813 1.1593572 1.2314398 1.0119800
FDP 0.8131946 0.8949610 0.8709703 0.9529622
Greens 0.3522948 0.6717696 0.9483057 0.8351287
Left Party 0.6550497 1.0541321 0.9983681 0.8424079
Religionother religion Democracynot satisfied
CDU 0.6889363 0.4647250
SPD 0.8024443 0.6981521
FDP 1.2048167 1.0014337
Greens 1.2626943 1.0089709
Left Party 1.1890138 3.0503736
Pol.Interestless interested Unemploymentunemployed
CDU 1.2235443 0.5982192
SPD 1.4007700 1.1349142
FDP 0.7694186 0.5714916
Greens 1.2356738 0.9302358
Left Party 0.6136870 2.7705995
Highschoolhighschool Unionmember Westwest Gendermale
CDU 1.1681635 0.6654958 0.7187891 0.7689529
SPD 0.8022314 1.4926187 1.4746518 0.8261321
FDP 1.0529723 0.6002910 1.0248900 1.2896875
Greens 1.7567339 0.6772513 1.8973255 0.9805111
Left Party 0.5768644 2.4762479 0.4851655 1.2448406
$coefficients
Intercept Age Religionevangelical Religioncatholic
CDU 1.4119208 0.30823148 -0.015325137 0.38793164
SPD 0.2611953 0.14786569 0.208184031 0.01190884
FDP -0.2067849 -0.11097516 -0.138147356 -0.04818006
Greens -1.0432870 -0.39783981 -0.053078312 -0.18016946
Left Party -0.4230442 0.05271779 -0.001633224 -0.17149096
Religionother religion Democracynot satisfied
CDU -0.3726065 -0.766309354
SPD -0.2200929 -0.359318301
FDP 0.1863274 0.001432664
Greens 0.2332478 0.008930930
Left Party 0.1731242 1.115264061
Pol.Interestless interested Unemploymentunemployed
CDU 0.2017518 -0.51379809
SPD 0.3370221 0.12655704
FDP -0.2621201 -0.55950553
Greens 0.2116164 -0.07231714
Left Party -0.4882702 1.01906373
Highschoolhighschool Unionmember Westwest Gendermale
CDU 0.15543288 -0.4072230 -0.33018727 -0.26272555
SPD -0.22035813 0.4005321 0.38842192 -0.19100061
FDP 0.05161693 -0.5103407 0.02458526 0.25439996
Greens 0.56345632 -0.3897129 0.64044524 -0.01968127
Left Party -0.55014800 0.9067445 -0.72326516 0.21900748
$se
Intercept Age Religionevangelical Religioncatholic
CDU 0.2048591 0.06883799 0.09223425 0.1001700
SPD 0.2302391 0.07244088 0.09354785 0.1038609
FDP 0.2783674 0.09372309 0.13051669 0.1410074
Greens 0.2983715 0.09663391 0.12673305 0.1395573
Left Party 0.2905319 0.09450515 0.12298175 0.1411115
Religionother religion Democracynot satisfied
CDU 0.1026717 0.1388867
SPD 0.1071088 0.1475394
FDP 0.1295069 0.1943961
Greens 0.1278369 0.1933167
Left Party 0.1258816 0.2290404
Pol.Interestless interested Unemploymentunemployed
CDU 0.1467924 0.3657321
SPD 0.1596959 0.3140084
FDP 0.1906783 0.4982842
Greens 0.2026824 0.4216104
Left Party 0.1853934 0.3014527
Highschoolhighschool Unionmember Westwest Gendermale
CDU 0.1691938 0.2118770 0.1559298 0.1353619
SPD 0.1889271 0.1836195 0.1722526 0.1423126
FDP 0.2177526 0.2891862 0.2070996 0.1874526
Greens 0.2081806 0.2730769 0.2221560 0.1840917
Left Party 0.2426935 0.2164160 0.1942954 0.1806023
$pvalues
Intercept Age Religionevangelical Religioncatholic
CDU 5.495382e-12 7.547395e-06 0.8680354 0.0001076213
SPD 2.566048e-01 4.123181e-02 0.0260525 0.9087135202
FDP 4.575732e-01 2.363834e-01 0.2898435 0.7325883134
Greens 4.712200e-04 3.838704e-05 0.6753478 0.1967011577
Left Party 1.453642e-01 5.769606e-01 0.9894042 0.2242566252
Religionother religion Democracynot satisfied
CDU 0.0002844045 3.438249e-08
SPD 0.0398932677 1.487511e-02
FDP 0.1502227182 9.941198e-01
Greens 0.0680653775 9.631521e-01
Left Party 0.1690403259 1.119999e-06
Pol.Interestless interested Unemploymentunemployed
CDU 0.169316829 0.1600664566
SPD 0.034823994 0.6869209386
FDP 0.169233235 0.2614951256
Greens 0.296449019 0.8638102011
Left Party 0.008446062 0.0007235162
Highschoolhighschool Unionmember Westwest Gendermale
CDU 0.358269369 5.460851e-02 0.0342142665 0.05226895
SPD 0.243466508 2.916006e-02 0.0241360950 0.17955713
FDP 0.812622691 7.760614e-02 0.9055033181 0.17473587
Greens 0.006798138 1.535459e-01 0.0039407876 0.91486024
Left Party 0.023399826 2.791731e-05 0.0001972576 0.22526357
$p_rel
Age Religionevangelical Religioncatholic Religionother religion
[1,] 5.625482e-07 0.2626094 0.003582126 0.0005500146
Democracynot satisfied Pol.Interestless interested Unemploymentunemployed
[1,] 2.955651e-10 0.01335832 0.01308379
Highschoolhighschool Unionmember Westwest Gendermale
[1,] 0.01862473 3.281531e-05 1.548773e-05 0.1509492
$xlim
[1] 10.66996 58.27439
$ylim
[1] 10.21854 73.70479
$odds
(Intercept) Age Religioncatholic Religionother religion
CDU 5.7060549 1.5207546 1.3679174 0.5057281
SPD 2.2576210 1.2954276 0.7510805 0.4710685
FDP 1.0000000 1.0000000 1.0000000 1.0000000
Greens 0.4716901 0.7506133 0.8048829 0.9625698
Left Party 0.9233516 1.1778526 0.7711865 0.8609513
Democracynot satisfied Pol.Interestless interested
CDU 0.4640597 1.5902192
SPD 0.6971526 1.8205564
FDP 1.0000000 1.0000000
Greens 1.0075264 1.6059837
Left Party 3.0460065 0.7975983
Unemploymentunemployed Highschoolhighschool Unionmember Westwest
CDU 1.046768 1.1093963 1.108622 0.701333
SPD 1.985881 0.7618733 2.486492 1.438839
FDP 1.000000 1.0000000 1.000000 1.000000
Greens 1.627733 1.6683571 1.128205 1.851248
Left Party 4.848015 0.5478439 4.125079 0.473383
Gendermale
CDU 0.5962319
SPD 0.6405676
FDP 1.0000000
Greens 0.7602703
Left Party 0.9652265
$coefficients
(Intercept) Age Religioncatholic Religionother religion
CDU 1.74152788 0.4192066 0.3132895 -0.68175613
SPD 0.81431162 0.2588408 -0.2862425 -0.75275167
FDP 0.00000000 0.0000000 0.0000000 0.00000000
Greens -0.75143303 -0.2868646 -0.2170584 -0.03814868
Left Party -0.07974521 0.1636929 -0.2598250 -0.14971736
Democracynot satisfied Pol.Interestless interested
CDU -0.767742018 0.4638719
SPD -0.360750965 0.5991421
FDP 0.000000000 0.0000000
Greens 0.007498266 0.4737365
Left Party 1.113831397 -0.2261501
Unemploymentunemployed Highschoolhighschool Unionmember Westwest
CDU 0.04570744 0.1038159 0.1031177 -0.3547725
SPD 0.68606257 -0.2719751 0.9108727 0.3638367
FDP 0.00000000 0.0000000 0.0000000 0.0000000
Greens 0.48718839 0.5118394 0.1206278 0.6158600
Left Party 1.57856926 -0.6017649 1.4170851 -0.7478504
Gendermale
CDU -0.51712552
SPD -0.44540058
FDP 0.00000000
Greens -0.27408124
Left Party -0.03539249
$se
(Intercept) Age Religioncatholic Religionother religion
CDU 0.4220943 0.1284890 0.3203470 0.3074542
SPD 0.4442439 0.1327380 0.3263015 0.3141396
FDP 0.0000000 0.0000000 0.0000000 0.0000000
Greens 0.5159175 0.1543686 0.3848512 0.3480746
Left Party 0.5064943 0.1516619 0.3850721 0.3421935
Democracynot satisfied Pol.Interestless interested
CDU 0.2600591 0.2660984
SPD 0.2699315 0.2800846
FDP 0.0000000 0.0000000
Greens 0.3083076 0.3181562
Left Party 0.3493993 0.3002862
Unemploymentunemployed Highschoolhighschool Unionmember Westwest
CDU 0.7168156 0.3030877 0.4094070 0.2862837
SPD 0.6775748 0.3242459 0.3874875 0.3039475
FDP 0.0000000 0.0000000 0.0000000 0.0000000
Greens 0.7594057 0.3391514 0.4639056 0.3477532
Left Party 0.6641415 0.3728742 0.4108741 0.3211784
Gendermale
CDU 0.2570392
SPD 0.2654878
FDP 0.0000000
Greens 0.3006768
Left Party 0.2982518
$pvalues
(Intercept) Age Religioncatholic Religionother religion
CDU 3.692535e-05 0.001104003 0.3280896 0.02659417
SPD 6.679837e-02 0.051174581 0.3803601 0.01656455
FDP NaN NaN NaN NaN
Greens 1.452549e-01 0.063125017 0.5727499 0.91272727
Left Party 8.748938e-01 0.280441463 0.4998385 0.66173243
Democracynot satisfied Pol.Interestless interested
CDU 0.003155358 0.08129272
SPD 0.181401080 0.03242377
FDP NaN NaN
Greens 0.980596779 0.13648582
Left Party 0.001433366 0.45138068
Unemploymentunemployed Highschoolhighschool Unionmember Westwest
CDU 0.94915769 0.7319538 0.8011408394 0.21525889
SPD 0.31128627 0.4015857 0.0187373783 0.23129186
FDP NaN NaN NaN NaN
Greens 0.52117253 0.1312536 0.7948432433 0.07656597
Left Party 0.01746087 0.1065589 0.0005627659 0.01988781
Gendermale
CDU 0.04423527
SPD 0.09341183
FDP NaN
Greens 0.36200690
Left Party 0.90553959
$p_rel
Age Religioncatholic Religionother religion
[1,] 5.625482e-07 0.08015606 0.01694874
Democracynot satisfied Pol.Interestless interested Unemploymentunemployed
[1,] 2.955651e-10 0.01335832 0.01308379
Highschoolhighschool Unionmember Westwest Gendermale
[1,] 0.01862473 3.281531e-05 1.548773e-05 0.1509492
$xlim
[1] 14.83574 81.02598
$ylim
[1] 14.20808 102.48075
$odds
(Intercept) Age Religioncatholic Religionother religion
CDU 1.0000000 1.0000000 1.0000000 1.0000000
SPD 0.3338381 0.8544309 0.4743828 0.7626943
FDP 0.1579086 0.6940809 0.7918960 1.8993904
Greens 0.1179807 0.5200108 0.5297035 1.1791441
Left Party 0.2026168 0.6936736 0.3420366 0.8549764
Democracynot satisfied Pol.Interestless interested
CDU 1.000000 1.0000000
SPD 1.507947 1.1270586
FDP 2.441964 0.6392326
Greens 1.762012 0.9507445
Left Party 5.465299 0.6643712
Unemploymentunemployed Highschoolhighschool Unionmember Westwest
CDU 1.0000000 1.0000000 1.000000 1.000000
SPD 1.0555968 0.6585272 2.324278 2.834841
FDP 0.9387644 0.9973818 1.153750 1.291316
Greens 0.8301664 1.1021122 1.018120 3.066906
Left Party 1.5027408 0.3607133 3.952546 1.388188
Gendermale
CDU 1.0000000
SPD 0.9556325
FDP 1.3423935
Greens 1.3323552
Left Party 1.7687651
$coefficients
(Intercept) Age Religioncatholic Religionother religion
CDU 0.000000 0.0000000 0.0000000 0.0000000
SPD -1.097099 -0.1573196 -0.7457408 -0.2708979
FDP -1.845739 -0.3651667 -0.2333253 0.6415330
Greens -2.137235 -0.6539058 -0.6354378 0.1647889
Left Party -1.596439 -0.3657537 -1.0728376 -0.1566814
Democracynot satisfied Pol.Interestless interested
CDU 0.0000000 0.00000000
SPD 0.4107491 0.11961119
FDP 0.8928026 -0.44748689
Greens 0.5664564 -0.05050993
Left Party 1.6984188 -0.40891428
Unemploymentunemployed Highschoolhighschool Unionmember Westwest
CDU 0.00000000 0.000000000 0.00000000 0.0000000
SPD 0.05410625 -0.417749460 0.84340928 1.0419859
FDP -0.06319079 -0.002621586 0.14301714 0.2556618
Greens -0.18612916 0.097228544 0.01795783 1.1206694
Left Party 0.40729066 -1.019671745 1.37435987 0.3279992
Gendermale
CDU 0.0000000
SPD -0.0453819
FDP 0.2944542
Greens 0.2869482
Left Party 0.5702816
$se
(Intercept) Age Religioncatholic Religionother religion
CDU 0.0000000 0.0000000 0.0000000 0.0000000
SPD 0.4295907 0.1224415 0.2950486 0.3095479
FDP 0.4710302 0.1375100 0.3459872 0.3332884
Greens 0.5327558 0.1568381 0.3789121 0.3663943
Left Party 0.5707470 0.1709698 0.4186809 0.3889426
Democracynot satisfied Pol.Interestless interested
CDU 0.0000000 0.0000000
SPD 0.2500313 0.2800531
FDP 0.2837937 0.2941212
Greens 0.3129732 0.3451305
Left Party 0.3941989 0.3504066
Unemploymentunemployed Highschoolhighschool Unionmember Westwest
CDU 0.0000000 0.0000000 0.0000000 0.0000000
SPD 0.6187108 0.3252709 0.3783768 0.2992684
FDP 0.7599459 0.3299130 0.4327055 0.3123042
Greens 0.7430884 0.3687666 0.4765291 0.3691915
Left Party 0.6767333 0.4385371 0.4542210 0.3698077
Gendermale
CDU 0.0000000
SPD 0.2476625
FDP 0.2785494
Greens 0.3046967
Left Party 0.3277823
$pvalues
(Intercept) Age Religioncatholic Religionother religion
CDU NaN NaN NaN NaN
SPD 1.065470e-02 1.988427e-01 0.01148720 0.38149748
FDP 8.909618e-05 7.917593e-03 0.50007270 0.05424709
Greens 6.029352e-05 3.055308e-05 0.09354131 0.65288474
Left Party 5.156296e-03 3.241229e-02 0.01039445 0.68706635
Democracynot satisfied Pol.Interestless interested
CDU NaN NaN
SPD 1.004263e-01 0.6693052
FDP 1.655446e-03 0.1281502
Greens 7.030827e-02 0.8836449
Left Party 1.643413e-05 0.2432222
Unemploymentunemployed Highschoolhighschool Unionmember Westwest
CDU NaN NaN NaN NaN
SPD 0.9303138 0.19903266 0.025812622 0.0004980983
FDP 0.9337309 0.99365984 0.741008289 0.4129973117
Greens 0.8022158 0.79204286 0.969939119 0.0024016216
Left Party 0.5472753 0.02006307 0.002480163 0.3751084798
Gendermale
CDU NaN
SPD 0.85460899
FDP 0.29046655
Greens 0.34632055
Left Party 0.08189092
$catspec
Social Immigration Nuclear Left_Right
[1,] -0.1630662 -0.1194577 -0.1848822 -0.6269847
$catspecse
Social Immigration Nuclear Left_Right
[1,] 0.03313544 0.03170079 0.02960555 0.04180896
$p_rel
Social Immigration Nuclear Left_Right Age
[1,] 5.117136e-07 0.0001397863 1.107482e-10 0 0.000175962
Religioncatholic Religionother religion Democracynot satisfied
[1,] 0.0606889 0.1014177 3.01792e-05
Pol.Interestless interested Unemploymentunemployed Highschoolhighschool
[1,] 0.2696232 0.9151604 0.04863854
Unionmember Westwest Gendermale
[1,] 0.002959962 0.001123774 0.2346133
$xlim
[1] 14.20978 77.60724
$ylim
[1] 13.60859 98.15676
EffectStars documentation built on Oct. 30, 2019, 9:39 a.m.
R Package Documentation
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Description Usage Arguments Details Value Author(s) References See Also Examples
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
1 2 3 4 5 6 7 | 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^{γ_{rj}}, r=1,…,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^{γ_{rj}}, r=1,…,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
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 | ## 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)
|
Example output
Loading required package: VGAM
Loading required package: stats4
Loading required package: splines
***
The package EffectStars is not the latest implementation of effect stars,
it is recommended to use EffectStars2 instead!
***
$odds
(Intercept) Age Religioncatholic Religionother religion
CDU 4.0414180 1.3610160 1.4966912 0.6995756
SPD 1.5990015 1.1593572 0.8217861 0.6516310
FDP 0.7082683 0.8949610 1.0941385 1.3833039
Greens 0.3340832 0.6717696 0.8806534 1.3315266
Left Party 0.6539807 1.0541321 0.8437849 1.1909573
Democracynot satisfied Pol.Interestless interested
CDU 0.4647250 1.2235443
SPD 0.6981521 1.4007700
FDP 1.0014337 0.7694186
Greens 1.0089709 1.2356738
Left Party 3.0503736 0.6136870
Unemploymentunemployed Highschoolhighschool Unionmember Westwest
CDU 0.5982192 1.1681635 0.6654958 0.7187891
SPD 1.1349142 0.8022314 1.4926187 1.4746518
FDP 0.5714916 1.0529723 0.6002910 1.0248900
Greens 0.9302358 1.7567339 0.6772513 1.8973255
Left Party 2.7705995 0.5768644 2.4762479 0.4851655
Gendermale
CDU 0.7689529
SPD 0.8261321
FDP 1.2896875
Greens 0.9805111
Left Party 1.2448406
$coefficients
(Intercept) Age Religioncatholic Religionother religion
CDU 1.3965956 0.30823148 0.4032568 -0.3572814
SPD 0.4693794 0.14786569 -0.1962752 -0.4282769
FDP -0.3449323 -0.11097516 0.0899673 0.3244748
Greens -1.0963653 -0.39783981 -0.1270911 0.2863261
Left Party -0.4246775 0.05271779 -0.1698577 0.1747574
Democracynot satisfied Pol.Interestless interested
CDU -0.766309354 0.2017518
SPD -0.359318301 0.3370221
FDP 0.001432664 -0.2621201
Greens 0.008930930 0.2116164
Left Party 1.115264061 -0.4882702
Unemploymentunemployed Highschoolhighschool Unionmember Westwest
CDU -0.51379809 0.15543288 -0.4072230 -0.33018727
SPD 0.12655704 -0.22035813 0.4005321 0.38842192
FDP -0.55950553 0.05161693 -0.5103407 0.02458526
Greens -0.07231714 0.56345632 -0.3897129 0.64044524
Left Party 1.01906373 -0.55014800 0.9067445 -0.72326516
Gendermale
CDU -0.26272555
SPD -0.19100061
FDP 0.25439996
Greens -0.01968127
Left Party 0.21900748
$se
(Intercept) Age Religioncatholic Religionother religion
CDU 0.2241927 0.06883799 0.1629137 0.1675209
SPD 0.2455006 0.07244088 0.1661454 0.1722205
FDP 0.3115509 0.09372309 0.2388794 0.2184724
Greens 0.3272014 0.09663391 0.2339503 0.2129104
Left Party 0.3134423 0.09450515 0.2328685 0.2050096
Democracynot satisfied Pol.Interestless interested
CDU 0.1388867 0.1467924
SPD 0.1475394 0.1596959
FDP 0.1943961 0.1906783
Greens 0.1933167 0.2026824
Left Party 0.2290404 0.1853934
Unemploymentunemployed Highschoolhighschool Unionmember Westwest
CDU 0.3657321 0.1691938 0.2118770 0.1559298
SPD 0.3140084 0.1889271 0.1836195 0.1722526
FDP 0.4982842 0.2177526 0.2891862 0.2070996
Greens 0.4216104 0.2081806 0.2730769 0.2221560
Left Party 0.3014527 0.2426935 0.2164160 0.1942954
Gendermale
CDU 0.1353619
SPD 0.1423126
FDP 0.1874526
Greens 0.1840917
Left Party 0.1806023
$pvalues
(Intercept) Age Religioncatholic Religionother religion
CDU 4.680987e-10 7.547395e-06 0.01331325 0.03294467
SPD 5.588552e-02 4.123181e-02 0.23746528 0.01289003
FDP 2.682310e-01 2.363834e-01 0.70645435 0.13749137
Greens 8.059719e-04 3.838704e-05 0.58696459 0.17868341
Left Party 1.754550e-01 5.769606e-01 0.46574801 0.39397247
Democracynot satisfied Pol.Interestless interested
CDU 3.438249e-08 0.169316829
SPD 1.487511e-02 0.034823994
FDP 9.941198e-01 0.169233235
Greens 9.631521e-01 0.296449019
Left Party 1.119999e-06 0.008446062
Unemploymentunemployed Highschoolhighschool Unionmember
CDU 0.1600664566 0.358269369 5.460851e-02
SPD 0.6869209386 0.243466508 2.916006e-02
FDP 0.2614951256 0.812622691 7.760614e-02
Greens 0.8638102011 0.006798138 1.535459e-01
Left Party 0.0007235162 0.023399826 2.791731e-05
Westwest Gendermale
CDU 0.0342142665 0.05226895
SPD 0.0241360950 0.17955713
FDP 0.9055033181 0.17473587
Greens 0.0039407876 0.91486024
Left Party 0.0001972576 0.22526357
$p_rel
Age Religioncatholic Religionother religion
[1,] 5.625482e-07 0.08015606 0.01694874
Democracynot satisfied Pol.Interestless interested Unemploymentunemployed
[1,] 2.955651e-10 0.01335832 0.01308379
Highschoolhighschool Unionmember Westwest Gendermale
[1,] 0.01862473 3.281531e-05 1.548773e-05 0.1509492
$xlim
[1] 10.50769 57.38814
$ylim
[1] 10.06313 72.58387
$odds
Intercept Age Religionevangelical Religioncatholic
CDU 4.1038303 1.3610160 0.9847917 1.4739290
SPD 1.2984813 1.1593572 1.2314398 1.0119800
FDP 0.8131946 0.8949610 0.8709703 0.9529622
Greens 0.3522948 0.6717696 0.9483057 0.8351287
Left Party 0.6550497 1.0541321 0.9983681 0.8424079
Religionother religion Democracynot satisfied
CDU 0.6889363 0.4647250
SPD 0.8024443 0.6981521
FDP 1.2048167 1.0014337
Greens 1.2626943 1.0089709
Left Party 1.1890138 3.0503736
Pol.Interestless interested Unemploymentunemployed
CDU 1.2235443 0.5982192
SPD 1.4007700 1.1349142
FDP 0.7694186 0.5714916
Greens 1.2356738 0.9302358
Left Party 0.6136870 2.7705995
Highschoolhighschool Unionmember Westwest Gendermale
CDU 1.1681635 0.6654958 0.7187891 0.7689529
SPD 0.8022314 1.4926187 1.4746518 0.8261321
FDP 1.0529723 0.6002910 1.0248900 1.2896875
Greens 1.7567339 0.6772513 1.8973255 0.9805111
Left Party 0.5768644 2.4762479 0.4851655 1.2448406
$coefficients
Intercept Age Religionevangelical Religioncatholic
CDU 1.4119208 0.30823148 -0.015325137 0.38793164
SPD 0.2611953 0.14786569 0.208184031 0.01190884
FDP -0.2067849 -0.11097516 -0.138147356 -0.04818006
Greens -1.0432870 -0.39783981 -0.053078312 -0.18016946
Left Party -0.4230442 0.05271779 -0.001633224 -0.17149096
Religionother religion Democracynot satisfied
CDU -0.3726065 -0.766309354
SPD -0.2200929 -0.359318301
FDP 0.1863274 0.001432664
Greens 0.2332478 0.008930930
Left Party 0.1731242 1.115264061
Pol.Interestless interested Unemploymentunemployed
CDU 0.2017518 -0.51379809
SPD 0.3370221 0.12655704
FDP -0.2621201 -0.55950553
Greens 0.2116164 -0.07231714
Left Party -0.4882702 1.01906373
Highschoolhighschool Unionmember Westwest Gendermale
CDU 0.15543288 -0.4072230 -0.33018727 -0.26272555
SPD -0.22035813 0.4005321 0.38842192 -0.19100061
FDP 0.05161693 -0.5103407 0.02458526 0.25439996
Greens 0.56345632 -0.3897129 0.64044524 -0.01968127
Left Party -0.55014800 0.9067445 -0.72326516 0.21900748
$se
Intercept Age Religionevangelical Religioncatholic
CDU 0.2048591 0.06883799 0.09223425 0.1001700
SPD 0.2302391 0.07244088 0.09354785 0.1038609
FDP 0.2783674 0.09372309 0.13051669 0.1410074
Greens 0.2983715 0.09663391 0.12673305 0.1395573
Left Party 0.2905319 0.09450515 0.12298175 0.1411115
Religionother religion Democracynot satisfied
CDU 0.1026717 0.1388867
SPD 0.1071088 0.1475394
FDP 0.1295069 0.1943961
Greens 0.1278369 0.1933167
Left Party 0.1258816 0.2290404
Pol.Interestless interested Unemploymentunemployed
CDU 0.1467924 0.3657321
SPD 0.1596959 0.3140084
FDP 0.1906783 0.4982842
Greens 0.2026824 0.4216104
Left Party 0.1853934 0.3014527
Highschoolhighschool Unionmember Westwest Gendermale
CDU 0.1691938 0.2118770 0.1559298 0.1353619
SPD 0.1889271 0.1836195 0.1722526 0.1423126
FDP 0.2177526 0.2891862 0.2070996 0.1874526
Greens 0.2081806 0.2730769 0.2221560 0.1840917
Left Party 0.2426935 0.2164160 0.1942954 0.1806023
$pvalues
Intercept Age Religionevangelical Religioncatholic
CDU 5.495382e-12 7.547395e-06 0.8680354 0.0001076213
SPD 2.566048e-01 4.123181e-02 0.0260525 0.9087135202
FDP 4.575732e-01 2.363834e-01 0.2898435 0.7325883134
Greens 4.712200e-04 3.838704e-05 0.6753478 0.1967011577
Left Party 1.453642e-01 5.769606e-01 0.9894042 0.2242566252
Religionother religion Democracynot satisfied
CDU 0.0002844045 3.438249e-08
SPD 0.0398932677 1.487511e-02
FDP 0.1502227182 9.941198e-01
Greens 0.0680653775 9.631521e-01
Left Party 0.1690403259 1.119999e-06
Pol.Interestless interested Unemploymentunemployed
CDU 0.169316829 0.1600664566
SPD 0.034823994 0.6869209386
FDP 0.169233235 0.2614951256
Greens 0.296449019 0.8638102011
Left Party 0.008446062 0.0007235162
Highschoolhighschool Unionmember Westwest Gendermale
CDU 0.358269369 5.460851e-02 0.0342142665 0.05226895
SPD 0.243466508 2.916006e-02 0.0241360950 0.17955713
FDP 0.812622691 7.760614e-02 0.9055033181 0.17473587
Greens 0.006798138 1.535459e-01 0.0039407876 0.91486024
Left Party 0.023399826 2.791731e-05 0.0001972576 0.22526357
$p_rel
Age Religionevangelical Religioncatholic Religionother religion
[1,] 5.625482e-07 0.2626094 0.003582126 0.0005500146
Democracynot satisfied Pol.Interestless interested Unemploymentunemployed
[1,] 2.955651e-10 0.01335832 0.01308379
Highschoolhighschool Unionmember Westwest Gendermale
[1,] 0.01862473 3.281531e-05 1.548773e-05 0.1509492
$xlim
[1] 10.66996 58.27439
$ylim
[1] 10.21854 73.70479
$odds
(Intercept) Age Religioncatholic Religionother religion
CDU 5.7060549 1.5207546 1.3679174 0.5057281
SPD 2.2576210 1.2954276 0.7510805 0.4710685
FDP 1.0000000 1.0000000 1.0000000 1.0000000
Greens 0.4716901 0.7506133 0.8048829 0.9625698
Left Party 0.9233516 1.1778526 0.7711865 0.8609513
Democracynot satisfied Pol.Interestless interested
CDU 0.4640597 1.5902192
SPD 0.6971526 1.8205564
FDP 1.0000000 1.0000000
Greens 1.0075264 1.6059837
Left Party 3.0460065 0.7975983
Unemploymentunemployed Highschoolhighschool Unionmember Westwest
CDU 1.046768 1.1093963 1.108622 0.701333
SPD 1.985881 0.7618733 2.486492 1.438839
FDP 1.000000 1.0000000 1.000000 1.000000
Greens 1.627733 1.6683571 1.128205 1.851248
Left Party 4.848015 0.5478439 4.125079 0.473383
Gendermale
CDU 0.5962319
SPD 0.6405676
FDP 1.0000000
Greens 0.7602703
Left Party 0.9652265
$coefficients
(Intercept) Age Religioncatholic Religionother religion
CDU 1.74152788 0.4192066 0.3132895 -0.68175613
SPD 0.81431162 0.2588408 -0.2862425 -0.75275167
FDP 0.00000000 0.0000000 0.0000000 0.00000000
Greens -0.75143303 -0.2868646 -0.2170584 -0.03814868
Left Party -0.07974521 0.1636929 -0.2598250 -0.14971736
Democracynot satisfied Pol.Interestless interested
CDU -0.767742018 0.4638719
SPD -0.360750965 0.5991421
FDP 0.000000000 0.0000000
Greens 0.007498266 0.4737365
Left Party 1.113831397 -0.2261501
Unemploymentunemployed Highschoolhighschool Unionmember Westwest
CDU 0.04570744 0.1038159 0.1031177 -0.3547725
SPD 0.68606257 -0.2719751 0.9108727 0.3638367
FDP 0.00000000 0.0000000 0.0000000 0.0000000
Greens 0.48718839 0.5118394 0.1206278 0.6158600
Left Party 1.57856926 -0.6017649 1.4170851 -0.7478504
Gendermale
CDU -0.51712552
SPD -0.44540058
FDP 0.00000000
Greens -0.27408124
Left Party -0.03539249
$se
(Intercept) Age Religioncatholic Religionother religion
CDU 0.4220943 0.1284890 0.3203470 0.3074542
SPD 0.4442439 0.1327380 0.3263015 0.3141396
FDP 0.0000000 0.0000000 0.0000000 0.0000000
Greens 0.5159175 0.1543686 0.3848512 0.3480746
Left Party 0.5064943 0.1516619 0.3850721 0.3421935
Democracynot satisfied Pol.Interestless interested
CDU 0.2600591 0.2660984
SPD 0.2699315 0.2800846
FDP 0.0000000 0.0000000
Greens 0.3083076 0.3181562
Left Party 0.3493993 0.3002862
Unemploymentunemployed Highschoolhighschool Unionmember Westwest
CDU 0.7168156 0.3030877 0.4094070 0.2862837
SPD 0.6775748 0.3242459 0.3874875 0.3039475
FDP 0.0000000 0.0000000 0.0000000 0.0000000
Greens 0.7594057 0.3391514 0.4639056 0.3477532
Left Party 0.6641415 0.3728742 0.4108741 0.3211784
Gendermale
CDU 0.2570392
SPD 0.2654878
FDP 0.0000000
Greens 0.3006768
Left Party 0.2982518
$pvalues
(Intercept) Age Religioncatholic Religionother religion
CDU 3.692535e-05 0.001104003 0.3280896 0.02659417
SPD 6.679837e-02 0.051174581 0.3803601 0.01656455
FDP NaN NaN NaN NaN
Greens 1.452549e-01 0.063125017 0.5727499 0.91272727
Left Party 8.748938e-01 0.280441463 0.4998385 0.66173243
Democracynot satisfied Pol.Interestless interested
CDU 0.003155358 0.08129272
SPD 0.181401080 0.03242377
FDP NaN NaN
Greens 0.980596779 0.13648582
Left Party 0.001433366 0.45138068
Unemploymentunemployed Highschoolhighschool Unionmember Westwest
CDU 0.94915769 0.7319538 0.8011408394 0.21525889
SPD 0.31128627 0.4015857 0.0187373783 0.23129186
FDP NaN NaN NaN NaN
Greens 0.52117253 0.1312536 0.7948432433 0.07656597
Left Party 0.01746087 0.1065589 0.0005627659 0.01988781
Gendermale
CDU 0.04423527
SPD 0.09341183
FDP NaN
Greens 0.36200690
Left Party 0.90553959
$p_rel
Age Religioncatholic Religionother religion
[1,] 5.625482e-07 0.08015606 0.01694874
Democracynot satisfied Pol.Interestless interested Unemploymentunemployed
[1,] 2.955651e-10 0.01335832 0.01308379
Highschoolhighschool Unionmember Westwest Gendermale
[1,] 0.01862473 3.281531e-05 1.548773e-05 0.1509492
$xlim
[1] 14.83574 81.02598
$ylim
[1] 14.20808 102.48075
$odds
(Intercept) Age Religioncatholic Religionother religion
CDU 1.0000000 1.0000000 1.0000000 1.0000000
SPD 0.3338381 0.8544309 0.4743828 0.7626943
FDP 0.1579086 0.6940809 0.7918960 1.8993904
Greens 0.1179807 0.5200108 0.5297035 1.1791441
Left Party 0.2026168 0.6936736 0.3420366 0.8549764
Democracynot satisfied Pol.Interestless interested
CDU 1.000000 1.0000000
SPD 1.507947 1.1270586
FDP 2.441964 0.6392326
Greens 1.762012 0.9507445
Left Party 5.465299 0.6643712
Unemploymentunemployed Highschoolhighschool Unionmember Westwest
CDU 1.0000000 1.0000000 1.000000 1.000000
SPD 1.0555968 0.6585272 2.324278 2.834841
FDP 0.9387644 0.9973818 1.153750 1.291316
Greens 0.8301664 1.1021122 1.018120 3.066906
Left Party 1.5027408 0.3607133 3.952546 1.388188
Gendermale
CDU 1.0000000
SPD 0.9556325
FDP 1.3423935
Greens 1.3323552
Left Party 1.7687651
$coefficients
(Intercept) Age Religioncatholic Religionother religion
CDU 0.000000 0.0000000 0.0000000 0.0000000
SPD -1.097099 -0.1573196 -0.7457408 -0.2708979
FDP -1.845739 -0.3651667 -0.2333253 0.6415330
Greens -2.137235 -0.6539058 -0.6354378 0.1647889
Left Party -1.596439 -0.3657537 -1.0728376 -0.1566814
Democracynot satisfied Pol.Interestless interested
CDU 0.0000000 0.00000000
SPD 0.4107491 0.11961119
FDP 0.8928026 -0.44748689
Greens 0.5664564 -0.05050993
Left Party 1.6984188 -0.40891428
Unemploymentunemployed Highschoolhighschool Unionmember Westwest
CDU 0.00000000 0.000000000 0.00000000 0.0000000
SPD 0.05410625 -0.417749460 0.84340928 1.0419859
FDP -0.06319079 -0.002621586 0.14301714 0.2556618
Greens -0.18612916 0.097228544 0.01795783 1.1206694
Left Party 0.40729066 -1.019671745 1.37435987 0.3279992
Gendermale
CDU 0.0000000
SPD -0.0453819
FDP 0.2944542
Greens 0.2869482
Left Party 0.5702816
$se
(Intercept) Age Religioncatholic Religionother religion
CDU 0.0000000 0.0000000 0.0000000 0.0000000
SPD 0.4295907 0.1224415 0.2950486 0.3095479
FDP 0.4710302 0.1375100 0.3459872 0.3332884
Greens 0.5327558 0.1568381 0.3789121 0.3663943
Left Party 0.5707470 0.1709698 0.4186809 0.3889426
Democracynot satisfied Pol.Interestless interested
CDU 0.0000000 0.0000000
SPD 0.2500313 0.2800531
FDP 0.2837937 0.2941212
Greens 0.3129732 0.3451305
Left Party 0.3941989 0.3504066
Unemploymentunemployed Highschoolhighschool Unionmember Westwest
CDU 0.0000000 0.0000000 0.0000000 0.0000000
SPD 0.6187108 0.3252709 0.3783768 0.2992684
FDP 0.7599459 0.3299130 0.4327055 0.3123042
Greens 0.7430884 0.3687666 0.4765291 0.3691915
Left Party 0.6767333 0.4385371 0.4542210 0.3698077
Gendermale
CDU 0.0000000
SPD 0.2476625
FDP 0.2785494
Greens 0.3046967
Left Party 0.3277823
$pvalues
(Intercept) Age Religioncatholic Religionother religion
CDU NaN NaN NaN NaN
SPD 1.065470e-02 1.988427e-01 0.01148720 0.38149748
FDP 8.909618e-05 7.917593e-03 0.50007270 0.05424709
Greens 6.029352e-05 3.055308e-05 0.09354131 0.65288474
Left Party 5.156296e-03 3.241229e-02 0.01039445 0.68706635
Democracynot satisfied Pol.Interestless interested
CDU NaN NaN
SPD 1.004263e-01 0.6693052
FDP 1.655446e-03 0.1281502
Greens 7.030827e-02 0.8836449
Left Party 1.643413e-05 0.2432222
Unemploymentunemployed Highschoolhighschool Unionmember Westwest
CDU NaN NaN NaN NaN
SPD 0.9303138 0.19903266 0.025812622 0.0004980983
FDP 0.9337309 0.99365984 0.741008289 0.4129973117
Greens 0.8022158 0.79204286 0.969939119 0.0024016216
Left Party 0.5472753 0.02006307 0.002480163 0.3751084798
Gendermale
CDU NaN
SPD 0.85460899
FDP 0.29046655
Greens 0.34632055
Left Party 0.08189092
$catspec
Social Immigration Nuclear Left_Right
[1,] -0.1630662 -0.1194577 -0.1848822 -0.6269847
$catspecse
Social Immigration Nuclear Left_Right
[1,] 0.03313544 0.03170079 0.02960555 0.04180896
$p_rel
Social Immigration Nuclear Left_Right Age
[1,] 5.117136e-07 0.0001397863 1.107482e-10 0 0.000175962
Religioncatholic Religionother religion Democracynot satisfied
[1,] 0.0606889 0.1014177 3.01792e-05
Pol.Interestless interested Unemploymentunemployed Highschoolhighschool
[1,] 0.2696232 0.9151604 0.04863854
Unionmember Westwest Gendermale
[1,] 0.002959962 0.001123774 0.2346133
$xlim
[1] 14.20978 77.60724
$ylim
[1] 13.60859 98.15676
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