Datos nominales y ordinales

Datos nominales y ordinales
23 de septiembre de 2015
Datos:
carros<-read.csv(’carros.csv’)
Modelo logistico nominal:
library(VGAM)
## Loading required package: stats4
## Loading required package: splines
carros_mod<-read.csv(’carros_mod.csv’)
modelo1<-vglm(cbind(y1,y2,y3)~sex+age,family = multinomial,data = carros_mod)
summary(modelo1)
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Call:
vglm(formula = cbind(y1, y2, y3) ~ sex + age, family = multinomial,
data = carros_mod)
Pearson residuals:
log(mu[,1]/mu[,3]) log(mu[,2]/mu[,3])
1
0.7377
-0.077667
2
-0.3497
0.835541
3
-0.4440
-0.583338
4
-0.6930
-0.009047
5
0.2174
-0.875593
6
0.4829
0.700820
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept):1 -1.0647
0.3496 -3.045 0.002327 **
(Intercept):2 -0.4559
0.2878 -1.584 0.113253
sexwomen:1
-0.8130
0.3210 -2.532 0.011326 *
sexwomen:2
-0.4249
0.3006 -1.414 0.157473
age18-23:1
2.9168
0.4229
6.897 5.32e-12 ***
age18-23:2
1.3290
0.3925
3.386 0.000709 ***
age24-40:1
1.4386
0.4158
3.460 0.000541 ***
age24-40:2
0.9792
0.3424
2.860 0.004241 **
--Signif. codes: 0 ’***’ 0.001 ’**’ 0.01 ’*’ 0.05 ’.’ 0.1 ’ ’ 1
Number of linear predictors:
2
Names of linear predictors: log(mu[,1]/mu[,3]), log(mu[,2]/mu[,3])
Dispersion Parameter for multinomial family:
1
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## Residual deviance: 3.9387 on 4 degrees of freedom
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## Log-likelihood: -25.3704 on 4 degrees of freedom
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## Number of iterations: 3
Modelo logistico nominal (con otra codificación):
modelo1<-vglm(cbind(y1,y2,y3)~sex+age,family = multinomial(refLevel = 1),data = carros_mod,
contrasts = list(sex=contr.treatment(2,2),age=contr.treatment(3,2)))
summary(modelo1)
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Call:
vglm(formula = cbind(y1, y2, y3) ~ sex + age, family = multinomial(refLevel = 1),
data = carros_mod, contrasts = list(sex = contr.treatment(2,
2), age = contr.treatment(3, 2)))
Pearson residuals:
log(mu[,2]/mu[,1]) log(mu[,3]/mu[,1])
1
-0.4396
-0.5975
2
0.8953
-0.1375
3
-0.2575
0.6864
4
0.3559
0.5946
5
-0.8602
0.2718
6
0.3519
-0.7749
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept):1 -0.5908
0.2840 -2.080 0.037484 *
(Intercept):2 -1.0391
0.3305 -3.144 0.001667 **
sex1:1
-0.3881
0.3005 -1.292 0.196510
sex1:2
-0.8130
0.3210 -2.532 0.011326 *
age1:1
1.5877
0.4029
3.941 8.12e-05 ***
age1:2
2.9168
0.4229
6.897 5.32e-12 ***
age3:1
1.1283
0.3416
3.302 0.000958 ***
age3:2
1.4781
0.4009
3.687 0.000227 ***
--Signif. codes: 0 ’***’ 0.001 ’**’ 0.01 ’*’ 0.05 ’.’ 0.1 ’ ’ 1
Number of linear predictors:
2
Names of linear predictors: log(mu[,2]/mu[,1]), log(mu[,3]/mu[,1])
Dispersion Parameter for multinomial family:
1
Residual deviance: 3.9387 on 4 degrees of freedom
Log-likelihood: -25.3704 on 4 degrees of freedom
Number of iterations: 3
Modelo reducido 1:
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modelo1a<-vglm(cbind(y1,y2,y3)~sex,family = multinomial(refLevel = 1),data = carros_mod,
contrasts = list(sex=contr.treatment(2,2)))
DeltaDa<-deviance(modelo1a)-deviance(modelo1)
pchisq(DeltaDa,df = 8-4,lower.tail = F)
## [1] 1.94304e-13
Modelo reducido 2:
modelo1b<-vglm(cbind(y1,y2,y3)~age,family = multinomial(refLevel = 1),data = carros_mod,
contrasts = list(age=contr.treatment(3,2)))
DeltaDb<-deviance(modelo1b)-deviance(modelo1)
pchisq(DeltaDb,df = 6-4,lower.tail = F)
## [1] 0.03867396
Comparación modelo completo-modelo nulo
modelo1_r<-vglm(cbind(y1,y2,y3)~1,family = multinomial(refLevel = 1),data = carros_mod)
DeltaDc<-deviance(modelo1_r)-deviance(modelo1)
pchisq(DeltaDc,df = 10-4,lower.tail = F)
## [1] 9.965531e-15
Seudo-R2
R2<-(deviance(modelo1_r)-deviance(modelo1))/deviance(modelo1_r)
R2
## [1] 0.951838
Bondad de ajuste:
pchisq(deviance(modelo1),df = 4,lower.tail = F)
## [1] 0.4143637
Modelos no agrupados. Convertir a una tabla tipo Tidy:
library(dplyr)
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## Attaching package: ’dplyr’
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## The following object is masked from ’package:stats’:
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filter
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## The following objects are masked from ’package:base’:
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intersect, setdiff, setequal, union
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library(tidyr)
colnames(carros_mod)[3:5]<-c(’No’,’Importante’,’MuyImp’)
carros_temp<-carros_mod%>%gather(respuesta,frecuencia,-sex,-age)
Ncarros_temp<-dim(carros_temp)[1]
carros_ind<-NULL
for(i in 1:Ncarros_temp){
carros_ind<-rbind(carros_ind,carros_temp[rep(i,carros_temp[i,4]),]
)
}
carros_ind<-carros_ind[,-4]
Modelo completo individual:
modelo_ind<-vglm(respuesta~sex+age,family = multinomial(refLevel = 1),data = carros_ind,
contrasts = list(sex=contr.treatment(2,2),age=contr.treatment(3,2)))
Modelo nulo individual:
modelo_ind_null<-vglm(respuesta~1,family = multinomial(refLevel = 1),data = carros_ind)
R2_ind<-(deviance(modelo_ind_null)-deviance(modelo_ind))/deviance(modelo_ind_null)
R2_ind
## [1] 0.118203
DeltaD_ind<-deviance(modelo_ind_null)-deviance(modelo_ind)
pchisq(DeltaDc,df = 598-592,lower.tail = F)
## [1] 9.965531e-15
Predicciones:
predicciones_ind<-predict(modelo_ind,se.fit=T)
Datos ordinales
Modelo acumulativo:
modelo_acum1<-vglm(cbind(No,Importante,MuyImp)~sex+age,family = cumulative(),data = carros_mod,
contrasts = list(sex=contr.treatment(2,2),age=contr.treatment(3,2)))
summary(modelo_acum1)
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## Call:
## vglm(formula = cbind(No, Importante, MuyImp) ~ sex + age, family = cumulative(),
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data = carros_mod, contrasts = list(sex = contr.treatment(2,
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2), age = contr.treatment(3, 2)))
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## Pearson residuals:
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logit(P[Y<=1]) logit(P[Y<=2])
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0.7937
-0.6680
-0.3285
-0.6911
0.5733
0.3400
0.2375
0.5315
-0.6280
-0.2243
-0.6273
0.7308
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept):1 0.06428
0.24864
0.259 0.79601
(Intercept):2 1.52613
0.30782
4.958 7.13e-07 ***
sex1:1
0.59071
0.26736
2.209 0.02714 *
sex1:2
0.57225
0.26851
2.131 0.03307 *
age1:1
-2.25992
0.35864 -6.301 2.95e-10 ***
age1:2
-2.10268
0.34508 -6.093 1.11e-09 ***
age3:1
-1.24641
0.30572 -4.077 4.56e-05 ***
age3:2
-0.94903
0.36284 -2.616 0.00891 **
--Signif. codes: 0 ’***’ 0.001 ’**’ 0.01 ’*’ 0.05 ’.’ 0.1 ’ ’ 1
Number of linear predictors:
2
Names of linear predictors: logit(P[Y<=1]), logit(P[Y<=2])
Dispersion Parameter for cumulative family:
1
Residual deviance: 3.8306 on 4 degrees of freedom
Log-likelihood: -25.3164 on 4 degrees of freedom
Number of iterations: 5
Modelo acumulativo con paralelismo (odds proporcionales):
modelo_acum2<-vglm(cbind(No,Importante,MuyImp)~sex+age,family = cumulative(parallel = T),data = carros_m
contrasts = list(sex=contr.treatment(2,2),age=contr.treatment(3,2)))
summary(modelo_acum2)
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Call:
vglm(formula = cbind(No, Importante, MuyImp) ~ sex + age, family = cumulative(parallel = T),
data = carros_mod, contrasts = list(sex = contr.treatment(2,
2), age = contr.treatment(3, 2)))
Pearson residuals:
logit(P[Y<=1]) logit(P[Y<=2])
1
0.9579
-0.09868
2
-0.9674
0.84653
3
-0.3441
-0.61980
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-0.4223
-0.64680
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0.3105
-0.38184
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0.3644
0.71420
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Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept):1 0.04354
0.23030
0.189
0.8501
(Intercept):2 1.65498
0.25360
6.526 6.76e-11 ***
sex1
0.57622
0.22611
2.548
0.0108 *
age1
-2.23246
0.29042 -7.687 1.50e-14 ***
age3
-1.14710
0.27727 -4.137 3.52e-05 ***
--Signif. codes: 0 ’***’ 0.001 ’**’ 0.01 ’*’ 0.05 ’.’ 0.1 ’ ’ 1
Number of linear predictors:
2
Names of linear predictors: logit(P[Y<=1]), logit(P[Y<=2])
Dispersion Parameter for cumulative family:
1
Residual deviance: 4.5321 on 7 degrees of freedom
Log-likelihood: -25.6671 on 7 degrees of freedom
Number of iterations: 4
Prueba de paralelismo:
DeltaDd<-deviance(modelo_acum2)-deviance(modelo_acum1)
pchisq(DeltaDd,df = 3,lower.tail = F)
## [1] 0.8728591
Modelo con categorías adyacentes:
modelo_acat1<-vglm(cbind(No,Importante,MuyImp)~sex+age,family = acat(),data = carros_mod,
contrasts = list(sex=contr.treatment(2,2),age=contr.treatment(3,2)))
summary(modelo_acat1)
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Call:
vglm(formula = cbind(No, Importante, MuyImp) ~ sex + age, family = acat(),
data = carros_mod, contrasts = list(sex = contr.treatment(2,
2), age = contr.treatment(3, 2)))
Pearson residuals:
loge(P[Y=2]/P[Y=1]) loge(P[Y=3]/P[Y=2])
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-0.6601
-0.3383
2
0.6975
-0.5778
3
0.1826
0.7100
4
0.5629
0.4043
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-0.6334
0.6424
6
-0.1280
-0.8414
Coefficients:
Estimate Std. Error z value Pr(>|z|)
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(Intercept):1
(Intercept):2
sex1:1
sex1:2
age1:1
age1:2
age3:1
age3:2
--Signif. codes:
-0.5908
-0.4483
-0.3881
-0.4249
1.5877
1.3290
1.1283
0.3498
0.2840
0.3509
0.3005
0.3006
0.4029
0.3925
0.3416
0.4089
-2.080
-1.278
-1.292
-1.414
3.941
3.386
3.302
0.856
0.037484
0.201400
0.196510
0.157473
8.12e-05
0.000709
0.000958
0.392198
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0 ’***’ 0.001 ’**’ 0.01 ’*’ 0.05 ’.’ 0.1 ’ ’ 1
Number of linear predictors:
2
Names of linear predictors: loge(P[Y=2]/P[Y=1]), loge(P[Y=3]/P[Y=2])
Dispersion Parameter for acat family:
1
Residual deviance: 3.9387 on 4 degrees of freedom
Log-likelihood: -25.3704 on 4 degrees of freedom
Number of iterations: 3
Modelo con categorías adyacentes con paralelismo:
modelo_acat2<-vglm(cbind(No,Importante,MuyImp)~sex+age,family = acat(parallel = T),data = carros_mod,
contrasts = list(sex=contr.treatment(2,2),age=contr.treatment(3,2)))
summary(modelo_acat2)
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Call:
vglm(formula = cbind(No, Importante, MuyImp) ~ sex + age, family = acat(parallel = T),
data = carros_mod, contrasts = list(sex = contr.treatment(2,
2), age = contr.treatment(3, 2)))
Pearson residuals:
loge(P[Y=2]/P[Y=1]) loge(P[Y=3]/P[Y=2])
1
-0.95852
0.1011
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1.13048
-1.0878
3
0.05493
0.8325
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0.22502
0.8662
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-0.11790
0.1985
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-0.25845
-0.7854
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept):1 -0.4446
0.1935 -2.298 0.02158 *
(Intercept):2 -0.6868
0.2280 -3.012 0.00259 **
sex1
-0.4065
0.1605 -2.532 0.01134 *
age1
1.5196
0.2113
7.193 6.36e-13 ***
age3
0.7845
0.1956
4.012 6.03e-05 ***
--Signif. codes: 0 ’***’ 0.001 ’**’ 0.01 ’*’ 0.05 ’.’ 0.1 ’ ’ 1
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Number of linear predictors:
2
Names of linear predictors: loge(P[Y=2]/P[Y=1]), loge(P[Y=3]/P[Y=2])
Dispersion Parameter for acat family:
1
Residual deviance: 5.5031 on 7 degrees of freedom
Log-likelihood: -26.1526 on 7 degrees of freedom
Number of iterations: 3
Prueba de paralelismo:
DeltaDe<-deviance(modelo_acat2)-deviance(modelo_acat1)
pchisq(DeltaDe,df = 3,lower.tail = F)
## [1] 0.6674897
Modelo de cociente de continuación con logits:
log
π1 + · · · + πj−1
πj
modelo_cratio1<-vglm(cbind(No,Importante,MuyImp)~sex+age,family = cratio(reverse = T),data = carros_mod,
contrasts = list(sex=contr.treatment(2,2),age=contr.treatment(3,2)))
summary(modelo_cratio1)
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Call:
vglm(formula = cbind(No, Importante, MuyImp) ~ sex + age, family = cratio(reverse = T),
data = carros_mod, contrasts = list(sex = contr.treatment(2,
2), age = contr.treatment(3, 2)))
Pearson residuals:
logit(P[Y<2|Y<=2]) logit(P[Y<3|Y<=3])
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0.61389
0.4017
2
-0.73799
0.4357
3
0.05089
-0.6570
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-0.53274
-0.4138
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0.65777
-0.4960
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-0.04758
0.7617
Coefficients:
(Intercept):1
(Intercept):2
sex1:1
sex1:2
age1:1
Estimate Std. Error z value Pr(>|z|)
0.5623
0.2838
1.981 0.04754 *
1.5266
0.3087
4.945 7.60e-07 ***
0.4489
0.3050
1.472 0.14109
0.5930
0.2710
2.189 0.02862 *
-1.6201
0.4051 -3.999 6.36e-05 ***
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age1:2
-2.1137
0.3462
age3:1
-1.1235
0.3424
age3:2
-0.9711
0.3638
--Signif. codes: 0 ’***’ 0.001 ’**’
Number of linear predictors:
-6.105 1.03e-09 ***
-3.282 0.00103 **
-2.670 0.00760 **
0.01 ’*’ 0.05 ’.’ 0.1 ’ ’ 1
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Names of linear predictors: logit(P[Y<2|Y<=2]), logit(P[Y<3|Y<=3])
Dispersion Parameter for cratio family:
1
Residual deviance: 3.4306 on 4 degrees of freedom
Log-likelihood: -25.1164 on 4 degrees of freedom
Number of iterations: 4
con paralelismo:
modelo_cratio2<-vglm(cbind(No,Importante,MuyImp)~sex+age,family = cratio(reverse = T,parallel = T),data
contrasts = list(sex=contr.treatment(2,2),age=contr.treatment(3,2)))
DeltaDf<-deviance(modelo_cratio2)-deviance(modelo_cratio1)
pchisq(DeltaDf,df = 3,lower.tail = F)
## [1] 0.640452
Bondad de ajuste en el modelo con paralelismo:
pchisq(deviance(modelo_cratio2),df = 7,lower.tail = F)
## [1] 0.6459577
pchisq(sum(residuals(modelo_cratio2,type=’pearson’)^2),df = 7,lower.tail = F)
## [1] 0.6478282
Análisis de residuos y outliers. . .
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