CC BY-NC-ND 3.0
[glims]
(d’après The R Book)Lorsque la variance n’est pas constante, et/ou que les erreurs ne sont pas distribuées selon une loi Normale.
C’est souvent le cas pour des réponses comme :
Si les erreurs ne suivaient pas une loi Normale, nous avions recours à une transformation. Avec les GLM nous pouvons spécifier le type de distribution des erreurs :
Pour spécifier le type de distribution des erreurs, on utilise l’argument family
.
La variable explicative peut être quantitative continue (analyse de régression), ou qualitative (catégories / facteurs ; analyse de type ANOVA).
Pour expliquer \(y\), nous utilisons une composante déterministe qui nous permet de voir quels sont les prédicteurs (\(\beta0+\beta_1x_1+...+\beta_px_p\)). Cette combinaison linéaire est appelée prédicteur linéaire et s’exprime avec \(\eta\) (eta) :
\[\eta_i=\sum_{j=1}^{p}x_{ij}\beta_j\]
La qualité de l’ajustement des GLM se fait en évaluant le prédicteur linéaire pour chaque valeur de la variable de réponse et le compare à une valeur transformée de y au moyen d’une fonction de lien.
Cette fonction de lien est à définir pour chaque cas (minimiser la déviance résiduelle). Pour une première approche on pourra laisser les fonctions de lein par défaut.
Loi de Poisson de paramètre lambda (\(\lambda\)) :
Surdispersion si residual deviance
> degrees of freedom
y <- rpois(n = 1000, lambda = 5)
x <- 1:1000
modSum <- summary(glm(y ~ x, family = "poisson"))
phiEst <- modSum$null.deviance / modSum$df[2]
print(phiEst) # > 1 ?
## [1] 0.9754727
Les principales cause des surdispersions sont :
- une corrélation entre les réponses,
- l’absence d’une variable explicative importante,
- un sur-représentation des valeurs zéro par rapport à ce qui est attendue selon la distribution de Poissson de paramètre Lambda.
En cas de surdispersion, il est nécessaire d’utiliser d’autres structures d’erreur, telles que les structures ‘quasi Poisson’ ou ‘négative binomiale’. C. Della Vedova
Ici : absence d’une variable explicative importante
# comptage de lynx en fonction des tâches solaires
suns <- as.vector(ts.intersect(lynx, sunspot.year)[,"sunspot.year"])
lynx <- as.vector(ts.intersect(lynx, sunspot.year)[,"lynx"])
modSum <- summary(glm(lynx ~ suns, family = "poisson"))
print(modSum)
##
## Call:
## glm(formula = lynx ~ suns, family = "poisson")
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -51.14 -37.31 -19.95 22.79 101.57
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 7.264e+00 4.016e-03 1808.81 <2e-16 ***
## suns 1.654e-03 7.055e-05 23.44 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for poisson family taken to be 1)
##
## Null deviance: 168370 on 113 degrees of freedom
## Residual deviance: 167827 on 112 degrees of freedom
## AIC: 168803
##
## Number of Fisher Scoring iterations: 5
Indépendance : oui (sous l’hypothèse que les lynx tués une année n’influencent pas les populations des années suivantes - en tout cas à la fin du XIXème - … )
Distribution de Poisson :
## [1] 1538.018
Distribution de Poisson : non
Sudispersion : oui
## [1] 1503.3
##
## Call:
## glm(formula = lynx ~ suns, family = "quasipoisson")
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -51.14 -37.31 -19.95 22.79 101.57
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.264107 0.163136 44.528 <2e-16 ***
## suns 0.001654 0.002866 0.577 0.565
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for quasipoisson family taken to be 1650.133)
##
## Null deviance: 168370 on 113 degrees of freedom
## Residual deviance: 167827 on 112 degrees of freedom
## AIC: NA
##
## Number of Fisher Scoring iterations: 5
## Acre Alagoas Amapa Amazonas
## 18452 4644 21831 30636
## Bahia Ceara Distrito Federal Espirito Santo
## 44718 30415 3561 6546
## Goias Maranhao Mato Grosso Minas Gerais
## 37677 25082 96178 37453
## Pará Paraiba Pernambuco Piau
## 24459 52432 24498 37777
## Rio Rondonia Roraima Santa Catarina
## 45160 20259 24384 24359
## Sao Paulo Sergipe Tocantins
## 51118 3237 33675
## $Sergipe
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.00 0.00 3.00 13.54 18.00 198.00
##
## $`Distrito Federal`
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0 0.0 2.0 14.9 17.5 196.0
##
## $Alagoas
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.00 1.00 10.00 19.35 29.00 162.00
##
## $`Espirito Santo`
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.00 4.50 13.00 27.39 36.00 307.00
##
## $Acre
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0 0.0 2.0 77.2 35.0 960.0
##
## $Rondonia
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.00 3.00 11.00 84.77 72.50 969.00
##
## $Amapa
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.00 0.00 2.00 91.34 70.00 969.00
##
## $`Santa Catarina`
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0 14.0 34.0 101.9 79.0 765.0
##
## $Roraima
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0 4 35 102 137 820
##
## $Pará
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0 4.0 10.0 102.3 63.5 982.0
##
## $Pernambuco
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0 5.0 27.0 102.5 158.5 859.0
##
## $Maranhao
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0 2.0 8.0 104.9 93.5 972.0
##
## $Ceara
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0 2.0 16.0 127.3 143.5 995.0
##
## $Amazonas
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0 4.0 23.0 128.2 128.0 998.0
##
## $Tocantins
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0 3.0 29.0 140.9 146.5 989.0
##
## $`Minas Gerais`
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0 16.0 81.0 156.7 179.5 959.0
##
## $Goias
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0 12.5 60.0 157.6 187.5 943.0
##
## $Piau
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0 3.0 35.0 158.1 200.5 943.0
##
## $Bahia
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0 8.0 140.0 187.1 259.0 995.0
##
## $Rio
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.00 6.00 24.00 62.98 70.00 885.00
##
## $`Sao Paulo`
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0 52.0 104.0 213.9 290.0 981.0
##
## $Paraiba
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0 6.0 46.0 109.7 125.0 987.0
##
## $`Mato Grosso`
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.00 5.25 100.00 201.21 305.50 979.00
##
## Call: glm(formula = feux$number ~ feux$state, family = "poisson")
##
## Coefficients:
## (Intercept) feux$stateDistrito Federal
## 2.60594 0.09539
## feux$stateAlagoas feux$stateEspirito Santo
## 0.35675 0.70421
## feux$stateAcre feux$stateRondonia
## 1.74053 1.83395
## feux$stateAmapa feux$stateSanta Catarina
## 1.90868 2.01825
## feux$stateRoraima feux$statePará
## 2.01928 2.02235
## feux$statePernambuco feux$stateMaranhao
## 2.02394 2.04750
## feux$stateCeara feux$stateAmazonas
## 2.24029 2.24753
## feux$stateTocantins feux$stateMinas Gerais
## 2.34211 2.44844
## feux$stateGoias feux$statePiau
## 2.45440 2.45705
## feux$stateBahia feux$stateRio
## 2.62573 1.53695
## feux$stateSao Paulo feux$stateParaiba
## 2.75949 2.09172
## feux$stateMato Grosso
## 2.69841
##
## Degrees of Freedom: 6453 Total (i.e. Null); 6431 Residual
## Null Deviance: 1464000
## Residual Deviance: 1255000 AIC: 1285000
##
## Call:
## glm(formula = feux$number ~ feux$state, family = "poisson")
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -20.682 -12.572 -6.331 1.396 55.441
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 2.60594 0.01758 148.264 < 2e-16 ***
## feux$stateDistrito Federal 0.09539 0.02428 3.928 8.56e-05 ***
## feux$stateAlagoas 0.35675 0.02290 15.581 < 2e-16 ***
## feux$stateEspirito Santo 0.70421 0.02149 32.774 < 2e-16 ***
## feux$stateAcre 1.74053 0.01906 91.341 < 2e-16 ***
## feux$stateRondonia 1.83395 0.01893 96.889 < 2e-16 ***
## feux$stateAmapa 1.90868 0.01883 101.341 < 2e-16 ***
## feux$stateSanta Catarina 2.01825 0.01871 107.883 < 2e-16 ***
## feux$stateRoraima 2.01928 0.01871 107.945 < 2e-16 ***
## feux$statePará 2.02235 0.01870 108.128 < 2e-16 ***
## feux$statePernambuco 2.02394 0.01870 108.223 < 2e-16 ***
## feux$stateMaranhao 2.04750 0.01868 109.632 < 2e-16 ***
## feux$stateCeara 2.24029 0.01849 121.175 < 2e-16 ***
## feux$stateAmazonas 2.24753 0.01848 121.609 < 2e-16 ***
## feux$stateTocantins 2.34211 0.01840 127.277 < 2e-16 ***
## feux$stateMinas Gerais 2.44844 0.01832 133.647 < 2e-16 ***
## feux$stateGoias 2.45440 0.01832 134.005 < 2e-16 ***
## feux$statePiau 2.45705 0.01831 134.163 < 2e-16 ***
## feux$stateBahia 2.62573 0.01820 144.260 < 2e-16 ***
## feux$stateRio 1.53695 0.01820 84.469 < 2e-16 ***
## feux$stateSao Paulo 2.75949 0.01812 152.254 < 2e-16 ***
## feux$stateParaiba 2.09172 0.01811 115.496 < 2e-16 ***
## feux$stateMato Grosso 2.69841 0.01787 151.005 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for poisson family taken to be 1)
##
## Null deviance: 1463651 on 6453 degrees of freedom
## Residual deviance: 1254755 on 6431 degrees of freedom
## AIC: 1285112
##
## Number of Fisher Scoring iterations: 6
Le ratio residual deviance / ddl est égal à 1254755 / 6431 = 195. Beaucoup de surdispersion ! Il est nécessaire d’utiliser une autre structure d’erreur.
##
## Call:
## glm(formula = feux$number ~ feux$state, family = "quasipoisson")
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -20.682 -12.572 -6.331 1.396 55.441
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.60594 0.29133 8.945 < 2e-16 ***
## feux$stateDistrito Federal 0.09539 0.40251 0.237 0.813
## feux$stateAlagoas 0.35675 0.37951 0.940 0.347
## feux$stateEspirito Santo 0.70421 0.35614 1.977 0.048 *
## feux$stateAcre 1.74053 0.31584 5.511 3.71e-08 ***
## feux$stateRondonia 1.83395 0.31374 5.846 5.30e-09 ***
## feux$stateAmapa 1.90868 0.31218 6.114 1.03e-09 ***
## feux$stateSanta Catarina 2.01825 0.31008 6.509 8.14e-11 ***
## feux$stateRoraima 2.01928 0.31006 6.513 7.95e-11 ***
## feux$statePará 2.02235 0.31000 6.524 7.38e-11 ***
## feux$statePernambuco 2.02394 0.30997 6.529 7.11e-11 ***
## feux$stateMaranhao 2.04750 0.30955 6.614 4.03e-11 ***
## feux$stateCeara 2.24029 0.30644 7.311 2.98e-13 ***
## feux$stateAmazonas 2.24753 0.30633 7.337 2.45e-13 ***
## feux$stateTocantins 2.34211 0.30501 7.679 1.84e-14 ***
## feux$stateMinas Gerais 2.44844 0.30365 8.063 8.79e-16 ***
## feux$stateGoias 2.45440 0.30358 8.085 7.38e-16 ***
## feux$statePiau 2.45705 0.30355 8.094 6.83e-16 ***
## feux$stateBahia 2.62573 0.30168 8.704 < 2e-16 ***
## feux$stateRio 1.53695 0.30159 5.096 3.56e-07 ***
## feux$stateSao Paulo 2.75949 0.30041 9.186 < 2e-16 ***
## feux$stateParaiba 2.09172 0.30018 6.968 3.53e-12 ***
## feux$stateMato Grosso 2.69841 0.29619 9.110 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for quasipoisson family taken to be 274.7254)
##
## Null deviance: 1463651 on 6453 degrees of freedom
## Residual deviance: 1254755 on 6431 degrees of freedom
## AIC: NA
##
## Number of Fisher Scoring iterations: 6
Table de variance (cas surdispersion avec Fisher) :
## Warning: package 'car' was built under R version 3.6.1
## Loading required package: carData
## Analysis of Deviance Table (Type II tests)
##
## Response: feux$number
## Error estimate based on Pearson residuals
##
## Sum Sq Df F value Pr(>F)
## feux$state 208896 22 34.564 < 2.2e-16 ***
## Residuals 1766701 6431
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
library(multcomp)
modL <- glm(number ~ state, family = "quasipoisson", data = feux)
tuk <- glht(modL, linfct = mcp(state = "Tukey"))
summary(tuk)
##
## Simultaneous Tests for General Linear Hypotheses
##
## Multiple Comparisons of Means: Tukey Contrasts
##
##
## Fit: glm(formula = number ~ state, family = "quasipoisson", data = feux)
##
## Linear Hypotheses:
## Estimate Std. Error z value
## Distrito Federal - Sergipe == 0 0.095394 0.402514 0.237
## Alagoas - Sergipe == 0 0.356754 0.379509 0.940
## Espirito Santo - Sergipe == 0 0.704207 0.356144 1.977
## Acre - Sergipe == 0 1.740526 0.315837 5.511
## Rondonia - Sergipe == 0 1.833952 0.313737 5.846
## Amapa - Sergipe == 0 1.908684 0.312175 6.114
## Santa Catarina - Sergipe == 0 2.018254 0.310078 6.509
## Roraima - Sergipe == 0 2.019280 0.310060 6.513
## Pará - Sergipe == 0 2.022351 0.310003 6.524
## Pernambuco - Sergipe == 0 2.023945 0.309975 6.529
## Maranhao - Sergipe == 0 2.047503 0.309553 6.614
## Ceara - Sergipe == 0 2.240289 0.306436 7.311
## Amazonas - Sergipe == 0 2.247529 0.306329 7.337
## Tocantins - Sergipe == 0 2.342109 0.305006 7.679
## Minas Gerais - Sergipe == 0 2.448440 0.303654 8.063
## Goias - Sergipe == 0 2.454403 0.303582 8.085
## Piau - Sergipe == 0 2.457053 0.303550 8.094
## Bahia - Sergipe == 0 2.625729 0.301685 8.704
## Rio - Sergipe == 0 1.536952 0.301585 5.096
## Sao Paulo - Sergipe == 0 2.759490 0.300407 9.186
## Paraiba - Sergipe == 0 2.091723 0.300183 6.968
## Mato Grosso - Sergipe == 0 2.698406 0.296187 9.110
## Alagoas - Distrito Federal == 0 0.261359 0.369194 0.708
## Espirito Santo - Distrito Federal == 0 0.608813 0.345131 1.764
## Acre - Distrito Federal == 0 1.645131 0.303364 5.423
## Rondonia - Distrito Federal == 0 1.738558 0.301177 5.773
## Amapa - Distrito Federal == 0 1.813290 0.299550 6.053
## Santa Catarina - Distrito Federal == 0 1.922860 0.297364 6.466
## Roraima - Distrito Federal == 0 1.923886 0.297345 6.470
## Pará - Distrito Federal == 0 1.926957 0.297286 6.482
## Pernambuco - Distrito Federal == 0 1.928550 0.297256 6.488
## Maranhao - Distrito Federal == 0 1.952109 0.296817 6.577
## Ceara - Distrito Federal == 0 2.144895 0.293564 7.306
## Amazonas - Distrito Federal == 0 2.152134 0.293453 7.334
## Tocantins - Distrito Federal == 0 2.246714 0.292071 7.692
## Minas Gerais - Distrito Federal == 0 2.353045 0.290659 8.096
## Goias - Distrito Federal == 0 2.359008 0.290584 8.118
## Piau - Distrito Federal == 0 2.361659 0.290550 8.128
## Bahia - Distrito Federal == 0 2.530335 0.288601 8.768
## Rio - Distrito Federal == 0 1.441558 0.288497 4.997
## Sao Paulo - Distrito Federal == 0 2.664095 0.287266 9.274
## Paraiba - Distrito Federal == 0 1.996329 0.287031 6.955
## Mato Grosso - Distrito Federal == 0 2.603012 0.282849 9.203
## Espirito Santo - Alagoas == 0 0.347453 0.318002 1.093
## Acre - Alagoas == 0 1.383772 0.272103 5.085
## Rondonia - Alagoas == 0 1.477198 0.269662 5.478
## Amapa - Alagoas == 0 1.551930 0.267843 5.794
## Santa Catarina - Alagoas == 0 1.661501 0.265396 6.260
## Roraima - Alagoas == 0 1.662526 0.265375 6.265
## Pará - Alagoas == 0 1.665598 0.265309 6.278
## Pernambuco - Alagoas == 0 1.667191 0.265276 6.285
## Maranhao - Alagoas == 0 1.690750 0.264783 6.385
## Ceara - Alagoas == 0 1.883535 0.261131 7.213
## Amazonas - Alagoas == 0 1.890775 0.261007 7.244
## Tocantins - Alagoas == 0 1.985355 0.259452 7.652
## Minas Gerais - Alagoas == 0 2.091686 0.257861 8.112
## Goias - Alagoas == 0 2.097649 0.257776 8.137
## Piau - Alagoas == 0 2.100300 0.257739 8.149
## Bahia - Alagoas == 0 2.268975 0.255540 8.879
## Rio - Alagoas == 0 1.180199 0.255422 4.621
## Sao Paulo - Alagoas == 0 2.402736 0.254030 9.458
## Paraiba - Alagoas == 0 1.734969 0.253765 6.837
## Mato Grosso - Alagoas == 0 2.341653 0.249025 9.403
## Acre - Espirito Santo == 0 1.036319 0.238435 4.346
## Rondonia - Espirito Santo == 0 1.129745 0.235645 4.794
## Amapa - Espirito Santo == 0 1.204477 0.233562 5.157
## Santa Catarina - Espirito Santo == 0 1.314047 0.230752 5.695
## Roraima - Espirito Santo == 0 1.315073 0.230727 5.700
## Pará - Espirito Santo == 0 1.318144 0.230652 5.715
## Pernambuco - Espirito Santo == 0 1.319737 0.230614 5.723
## Maranhao - Espirito Santo == 0 1.343296 0.230046 5.839
## Ceara - Espirito Santo == 0 1.536082 0.225834 6.802
## Amazonas - Espirito Santo == 0 1.543322 0.225690 6.838
## Tocantins - Espirito Santo == 0 1.637902 0.223890 7.316
## Minas Gerais - Espirito Santo == 0 1.744233 0.222044 7.855
## Goias - Espirito Santo == 0 1.750196 0.221946 7.886
## Piau - Espirito Santo == 0 1.752846 0.221903 7.899
## Bahia - Espirito Santo == 0 1.921522 0.219344 8.760
## Rio - Espirito Santo == 0 0.832745 0.219207 3.799
## Sao Paulo - Espirito Santo == 0 2.055283 0.217584 9.446
## Paraiba - Espirito Santo == 0 1.387516 0.217274 6.386
## Mato Grosso - Espirito Santo == 0 1.994199 0.211719 9.419
## Rondonia - Acre == 0 0.093426 0.168651 0.554
## Amapa - Acre == 0 0.168158 0.165728 1.015
## Santa Catarina - Acre == 0 0.277729 0.161744 1.717
## Roraima - Acre == 0 0.278754 0.161708 1.724
## Pará - Acre == 0 0.281825 0.161600 1.744
## Pernambuco - Acre == 0 0.283419 0.161546 1.754
## Maranhao - Acre == 0 0.306978 0.160735 1.910
## Ceara - Acre == 0 0.499763 0.154646 3.232
## Amazonas - Acre == 0 0.507003 0.154435 3.283
## Tocantins - Acre == 0 0.601583 0.151792 3.963
## Minas Gerais - Acre == 0 0.707914 0.149057 4.749
## Goias - Acre == 0 0.713877 0.148911 4.794
## Piau - Acre == 0 0.716528 0.148846 4.814
## Bahia - Acre == 0 0.885203 0.145004 6.105
## Rio - Acre == 0 -0.203573 0.144797 -1.406
## Sao Paulo - Acre == 0 1.018964 0.142328 7.159
## Paraiba - Acre == 0 0.351197 0.141854 2.476
## Mato Grosso - Acre == 0 0.957881 0.133189 7.192
## Amapa - Rondonia == 0 0.074732 0.161689 0.462
## Santa Catarina - Rondonia == 0 0.184302 0.157602 1.169
## Roraima - Rondonia == 0 0.185328 0.157566 1.176
## Pará - Rondonia == 0 0.188399 0.157455 1.197
## Pernambuco - Rondonia == 0 0.189992 0.157399 1.207
## Maranhao - Rondonia == 0 0.213551 0.156567 1.364
## Ceara - Rondonia == 0 0.406337 0.150309 2.703
## Amazonas - Rondonia == 0 0.413577 0.150092 2.755
## Tocantins - Rondonia == 0 0.508157 0.147372 3.448
## Minas Gerais - Rondonia == 0 0.614488 0.144553 4.251
## Goias - Rondonia == 0 0.620451 0.144402 4.297
## Piau - Rondonia == 0 0.623101 0.144335 4.317
## Bahia - Rondonia == 0 0.791777 0.140370 5.641
## Rio - Rondonia == 0 -0.297000 0.140156 -2.119
## Sao Paulo - Rondonia == 0 0.925538 0.137603 6.726
## Paraiba - Rondonia == 0 0.257771 0.137113 1.880
## Mato Grosso - Rondonia == 0 0.864454 0.128128 6.747
## Santa Catarina - Amapa == 0 0.109570 0.154471 0.709
## Roraima - Amapa == 0 0.110596 0.154433 0.716
## Pará - Amapa == 0 0.113667 0.154320 0.737
## Pernambuco - Amapa == 0 0.115260 0.154263 0.747
## Maranhao - Amapa == 0 0.138819 0.153414 0.905
## Ceara - Amapa == 0 0.331605 0.147022 2.255
## Amazonas - Amapa == 0 0.338845 0.146800 2.308
## Tocantins - Amapa == 0 0.433425 0.144018 3.010
## Minas Gerais - Amapa == 0 0.539756 0.141132 3.824
## Goias - Amapa == 0 0.545719 0.140977 3.871
## Piau - Amapa == 0 0.548369 0.140909 3.892
## Bahia - Amapa == 0 0.717045 0.136845 5.240
## Rio - Amapa == 0 -0.371732 0.136625 -2.721
## Sao Paulo - Amapa == 0 0.850806 0.134005 6.349
## Paraiba - Amapa == 0 0.183039 0.133501 1.371
## Mato Grosso - Amapa == 0 0.789722 0.124255 6.356
## Roraima - Santa Catarina == 0 0.001026 0.150149 0.007
## Pará - Santa Catarina == 0 0.004097 0.150033 0.027
## Pernambuco - Santa Catarina == 0 0.005690 0.149975 0.038
## Maranhao - Santa Catarina == 0 0.029249 0.149101 0.196
## Ceara - Santa Catarina == 0 0.222035 0.142516 1.558
## Amazonas - Santa Catarina == 0 0.229274 0.142287 1.611
## Tocantins - Santa Catarina == 0 0.323854 0.139414 2.323
## Minas Gerais - Santa Catarina == 0 0.430185 0.136431 3.153
## Goias - Santa Catarina == 0 0.436148 0.136271 3.201
## Piau - Santa Catarina == 0 0.438799 0.136200 3.222
## Bahia - Santa Catarina == 0 0.607475 0.131991 4.602
## Rio - Santa Catarina == 0 -0.481302 0.131763 -3.653
## Sao Paulo - Santa Catarina == 0 0.741235 0.129045 5.744
## Paraiba - Santa Catarina == 0 0.073469 0.128522 0.572
## Mato Grosso - Santa Catarina == 0 0.680152 0.118889 5.721
## Pará - Roraima == 0 0.003071 0.149995 0.020
## Pernambuco - Roraima == 0 0.004664 0.149936 0.031
## Maranhao - Roraima == 0 0.028223 0.149062 0.189
## Ceara - Roraima == 0 0.221009 0.142475 1.551
## Amazonas - Roraima == 0 0.228249 0.142246 1.605
## Tocantins - Roraima == 0 0.322829 0.139373 2.316
## Minas Gerais - Roraima == 0 0.429160 0.136389 3.147
## Goias - Roraima == 0 0.435123 0.136229 3.194
## Piau - Roraima == 0 0.437773 0.136158 3.215
## Bahia - Roraima == 0 0.606449 0.131947 4.596
## Rio - Roraima == 0 -0.482328 0.131719 -3.662
## Sao Paulo - Roraima == 0 0.740210 0.129000 5.738
## Paraiba - Roraima == 0 0.072443 0.128477 0.564
## Mato Grosso - Roraima == 0 0.679126 0.118840 5.715
## Pernambuco - Pará == 0 0.001593 0.149820 0.011
## Maranhao - Pará == 0 0.025152 0.148945 0.169
## Ceara - Pará == 0 0.217938 0.142353 1.531
## Amazonas - Pará == 0 0.225178 0.142124 1.584
## Tocantins - Pará == 0 0.319757 0.139247 2.296
## Minas Gerais - Pará == 0 0.426089 0.136261 3.127
## Goias - Pará == 0 0.432052 0.136100 3.175
## Piau - Pará == 0 0.434702 0.136029 3.196
## Bahia - Pará == 0 0.603378 0.131815 4.577
## Rio - Pará == 0 -0.485399 0.131587 -3.689
## Sao Paulo - Pará == 0 0.737138 0.128865 5.720
## Paraiba - Pará == 0 0.069372 0.128341 0.541
## Mato Grosso - Pará == 0 0.676055 0.118694 5.696
## Maranhao - Pernambuco == 0 0.023559 0.148886 0.158
## Ceara - Pernambuco == 0 0.216344 0.142291 1.520
## Amazonas - Pernambuco == 0 0.223584 0.142062 1.574
## Tocantins - Pernambuco == 0 0.318164 0.139184 2.286
## Minas Gerais - Pernambuco == 0 0.424495 0.136196 3.117
## Goias - Pernambuco == 0 0.430458 0.136036 3.164
## Piau - Pernambuco == 0 0.433109 0.135965 3.185
## Bahia - Pernambuco == 0 0.601785 0.131749 4.568
## Rio - Pernambuco == 0 -0.486992 0.131520 -3.703
## Sao Paulo - Pernambuco == 0 0.735545 0.128796 5.711
## Paraiba - Pernambuco == 0 0.067778 0.128273 0.528
## Mato Grosso - Pernambuco == 0 0.674462 0.118620 5.686
## Ceara - Maranhao == 0 0.192785 0.141370 1.364
## Amazonas - Maranhao == 0 0.200025 0.141139 1.417
## Tocantins - Maranhao == 0 0.294605 0.138243 2.131
## Minas Gerais - Maranhao == 0 0.400936 0.135233 2.965
## Goias - Maranhao == 0 0.406899 0.135072 3.012
## Piau - Maranhao == 0 0.409550 0.135001 3.034
## Bahia - Maranhao == 0 0.578226 0.130753 4.422
## Rio - Maranhao == 0 -0.510551 0.130523 -3.912
## Sao Paulo - Maranhao == 0 0.711986 0.127778 5.572
## Paraiba - Maranhao == 0 0.044219 0.127250 0.348
## Mato Grosso - Maranhao == 0 0.650903 0.117513 5.539
## Amazonas - Ceara == 0 0.007240 0.134164 0.054
## Tocantins - Ceara == 0 0.101820 0.131113 0.777
## Minas Gerais - Ceara == 0 0.208151 0.127936 1.627
## Goias - Ceara == 0 0.214114 0.127766 1.676
## Piau - Ceara == 0 0.216765 0.127690 1.698
## Bahia - Ceara == 0 0.385440 0.123191 3.129
## Rio - Ceara == 0 -0.703336 0.122947 -5.721
## Sao Paulo - Ceara == 0 0.519201 0.120029 4.326
## Paraiba - Ceara == 0 -0.148566 0.119466 -1.244
## Mato Grosso - Ceara == 0 0.458118 0.109036 4.202
## Tocantins - Amazonas == 0 0.094580 0.130864 0.723
## Minas Gerais - Amazonas == 0 0.200911 0.127682 1.574
## Goias - Amazonas == 0 0.206874 0.127511 1.622
## Piau - Amazonas == 0 0.209525 0.127435 1.644
## Bahia - Amazonas == 0 0.378200 0.122926 3.077
## Rio - Amazonas == 0 -0.710576 0.122682 -5.792
## Sao Paulo - Amazonas == 0 0.511961 0.119757 4.275
## Paraiba - Amazonas == 0 -0.155806 0.119193 -1.307
## Mato Grosso - Amazonas == 0 0.450878 0.108737 4.146
## Minas Gerais - Tocantins == 0 0.106331 0.124472 0.854
## Goias - Tocantins == 0 0.112294 0.124297 0.903
## Piau - Tocantins == 0 0.114945 0.124219 0.925
## Bahia - Tocantins == 0 0.283620 0.119589 2.372
## Rio - Tocantins == 0 -0.805156 0.119338 -6.747
## Sao Paulo - Tocantins == 0 0.417381 0.116329 3.588
## Paraiba - Tocantins == 0 -0.250386 0.115749 -2.163
## Mato Grosso - Tocantins == 0 0.356298 0.104950 3.395
## Goias - Minas Gerais == 0 0.005963 0.120941 0.049
## Piau - Minas Gerais == 0 0.008614 0.120861 0.071
## Bahia - Minas Gerais == 0 0.177289 0.116098 1.527
## Rio - Minas Gerais == 0 -0.911487 0.115839 -7.869
## Sao Paulo - Minas Gerais == 0 0.311050 0.112737 2.759
## Paraiba - Minas Gerais == 0 -0.356717 0.112138 -3.181
## Mato Grosso - Minas Gerais == 0 0.249967 0.100954 2.476
## Piau - Goias == 0 0.002651 0.120681 0.022
## Bahia - Goias == 0 0.171326 0.115910 1.478
## Rio - Goias == 0 -0.917450 0.115650 -7.933
## Sao Paulo - Goias == 0 0.305087 0.112543 2.711
## Paraiba - Goias == 0 -0.362680 0.111943 -3.240
## Mato Grosso - Goias == 0 0.244004 0.100737 2.422
## Bahia - Piau == 0 0.168676 0.115827 1.456
## Rio - Piau == 0 -0.920101 0.115567 -7.962
## Sao Paulo - Piau == 0 0.302436 0.112457 2.689
## Paraiba - Piau == 0 -0.365331 0.111857 -3.266
## Mato Grosso - Piau == 0 0.241353 0.100642 2.398
## Rio - Bahia == 0 -1.088777 0.110575 -9.846
## Sao Paulo - Bahia == 0 0.133761 0.107321 1.246
## Paraiba - Bahia == 0 -0.534006 0.106692 -5.005
## Mato Grosso - Bahia == 0 0.072677 0.094868 0.766
## Sao Paulo - Rio == 0 1.222537 0.107041 11.421
## Paraiba - Rio == 0 0.554770 0.106410 5.214
## Mato Grosso - Rio == 0 1.161454 0.094551 12.284
## Paraiba - Sao Paulo == 0 -0.667767 0.103024 -6.482
## Mato Grosso - Sao Paulo == 0 -0.061083 0.090724 -0.673
## Mato Grosso - Paraiba == 0 0.606684 0.089978 6.743
## Pr(>|z|)
## Distrito Federal - Sergipe == 0 1.0000
## Alagoas - Sergipe == 0 1.0000
## Espirito Santo - Sergipe == 0 0.9318
## Acre - Sergipe == 0 <0.01 ***
## Rondonia - Sergipe == 0 <0.01 ***
## Amapa - Sergipe == 0 <0.01 ***
## Santa Catarina - Sergipe == 0 <0.01 ***
## Roraima - Sergipe == 0 <0.01 ***
## Pará - Sergipe == 0 <0.01 ***
## Pernambuco - Sergipe == 0 <0.01 ***
## Maranhao - Sergipe == 0 <0.01 ***
## Ceara - Sergipe == 0 <0.01 ***
## Amazonas - Sergipe == 0 <0.01 ***
## Tocantins - Sergipe == 0 <0.01 ***
## Minas Gerais - Sergipe == 0 <0.01 ***
## Goias - Sergipe == 0 <0.01 ***
## Piau - Sergipe == 0 <0.01 ***
## Bahia - Sergipe == 0 <0.01 ***
## Rio - Sergipe == 0 <0.01 ***
## Sao Paulo - Sergipe == 0 <0.01 ***
## Paraiba - Sergipe == 0 <0.01 ***
## Mato Grosso - Sergipe == 0 <0.01 ***
## Alagoas - Distrito Federal == 0 1.0000
## Espirito Santo - Distrito Federal == 0 0.9798
## Acre - Distrito Federal == 0 <0.01 ***
## Rondonia - Distrito Federal == 0 <0.01 ***
## Amapa - Distrito Federal == 0 <0.01 ***
## Santa Catarina - Distrito Federal == 0 <0.01 ***
## Roraima - Distrito Federal == 0 <0.01 ***
## Pará - Distrito Federal == 0 <0.01 ***
## Pernambuco - Distrito Federal == 0 <0.01 ***
## Maranhao - Distrito Federal == 0 <0.01 ***
## Ceara - Distrito Federal == 0 <0.01 ***
## Amazonas - Distrito Federal == 0 <0.01 ***
## Tocantins - Distrito Federal == 0 <0.01 ***
## Minas Gerais - Distrito Federal == 0 <0.01 ***
## Goias - Distrito Federal == 0 <0.01 ***
## Piau - Distrito Federal == 0 <0.01 ***
## Bahia - Distrito Federal == 0 <0.01 ***
## Rio - Distrito Federal == 0 <0.01 ***
## Sao Paulo - Distrito Federal == 0 <0.01 ***
## Paraiba - Distrito Federal == 0 <0.01 ***
## Mato Grosso - Distrito Federal == 0 <0.01 ***
## Espirito Santo - Alagoas == 0 1.0000
## Acre - Alagoas == 0 <0.01 ***
## Rondonia - Alagoas == 0 <0.01 ***
## Amapa - Alagoas == 0 <0.01 ***
## Santa Catarina - Alagoas == 0 <0.01 ***
## Roraima - Alagoas == 0 <0.01 ***
## Pará - Alagoas == 0 <0.01 ***
## Pernambuco - Alagoas == 0 <0.01 ***
## Maranhao - Alagoas == 0 <0.01 ***
## Ceara - Alagoas == 0 <0.01 ***
## Amazonas - Alagoas == 0 <0.01 ***
## Tocantins - Alagoas == 0 <0.01 ***
## Minas Gerais - Alagoas == 0 <0.01 ***
## Goias - Alagoas == 0 <0.01 ***
## Piau - Alagoas == 0 <0.01 ***
## Bahia - Alagoas == 0 <0.01 ***
## Rio - Alagoas == 0 <0.01 ***
## Sao Paulo - Alagoas == 0 <0.01 ***
## Paraiba - Alagoas == 0 <0.01 ***
## Mato Grosso - Alagoas == 0 <0.01 ***
## Acre - Espirito Santo == 0 <0.01 **
## Rondonia - Espirito Santo == 0 <0.01 ***
## Amapa - Espirito Santo == 0 <0.01 ***
## Santa Catarina - Espirito Santo == 0 <0.01 ***
## Roraima - Espirito Santo == 0 <0.01 ***
## Pará - Espirito Santo == 0 <0.01 ***
## Pernambuco - Espirito Santo == 0 <0.01 ***
## Maranhao - Espirito Santo == 0 <0.01 ***
## Ceara - Espirito Santo == 0 <0.01 ***
## Amazonas - Espirito Santo == 0 <0.01 ***
## Tocantins - Espirito Santo == 0 <0.01 ***
## Minas Gerais - Espirito Santo == 0 <0.01 ***
## Goias - Espirito Santo == 0 <0.01 ***
## Piau - Espirito Santo == 0 <0.01 ***
## Bahia - Espirito Santo == 0 <0.01 ***
## Rio - Espirito Santo == 0 0.0218 *
## Sao Paulo - Espirito Santo == 0 <0.01 ***
## Paraiba - Espirito Santo == 0 <0.01 ***
## Mato Grosso - Espirito Santo == 0 <0.01 ***
## Rondonia - Acre == 0 1.0000
## Amapa - Acre == 0 1.0000
## Santa Catarina - Acre == 0 0.9850
## Roraima - Acre == 0 0.9842
## Pará - Acre == 0 0.9819
## Pernambuco - Acre == 0 0.9806
## Maranhao - Acre == 0 0.9514
## Ceara - Acre == 0 0.1367
## Amazonas - Acre == 0 0.1174
## Tocantins - Acre == 0 0.0119 *
## Minas Gerais - Acre == 0 <0.01 ***
## Goias - Acre == 0 <0.01 ***
## Piau - Acre == 0 <0.01 ***
## Bahia - Acre == 0 <0.01 ***
## Rio - Acre == 0 0.9990
## Sao Paulo - Acre == 0 <0.01 ***
## Paraiba - Acre == 0 0.6322
## Mato Grosso - Acre == 0 <0.01 ***
## Amapa - Rondonia == 0 1.0000
## Santa Catarina - Rondonia == 0 0.9999
## Roraima - Rondonia == 0 0.9999
## Pará - Rondonia == 0 0.9999
## Pernambuco - Rondonia == 0 0.9999
## Maranhao - Rondonia == 0 0.9993
## Ceara - Rondonia == 0 0.4508
## Amazonas - Rondonia == 0 0.4109
## Tocantins - Rondonia == 0 0.0731 .
## Minas Gerais - Rondonia == 0 <0.01 **
## Goias - Rondonia == 0 <0.01 **
## Piau - Rondonia == 0 <0.01 **
## Bahia - Rondonia == 0 <0.01 ***
## Rio - Rondonia == 0 0.8733
## Sao Paulo - Rondonia == 0 <0.01 ***
## Paraiba - Rondonia == 0 0.9586
## Mato Grosso - Rondonia == 0 <0.01 ***
## Santa Catarina - Amapa == 0 1.0000
## Roraima - Amapa == 0 1.0000
## Pará - Amapa == 0 1.0000
## Pernambuco - Amapa == 0 1.0000
## Maranhao - Amapa == 0 1.0000
## Ceara - Amapa == 0 0.7948
## Amazonas - Amapa == 0 0.7609
## Tocantins - Amapa == 0 0.2394
## Minas Gerais - Amapa == 0 0.0200 *
## Goias - Amapa == 0 0.0171 *
## Piau - Amapa == 0 0.0148 *
## Bahia - Amapa == 0 <0.01 ***
## Rio - Amapa == 0 0.4366
## Sao Paulo - Amapa == 0 <0.01 ***
## Paraiba - Amapa == 0 0.9993
## Mato Grosso - Amapa == 0 <0.01 ***
## Roraima - Santa Catarina == 0 1.0000
## Pará - Santa Catarina == 0 1.0000
## Pernambuco - Santa Catarina == 0 1.0000
## Maranhao - Santa Catarina == 0 1.0000
## Ceara - Santa Catarina == 0 0.9957
## Amazonas - Santa Catarina == 0 0.9931
## Tocantins - Santa Catarina == 0 0.7473
## Minas Gerais - Santa Catarina == 0 0.1673
## Goias - Santa Catarina == 0 0.1478
## Piau - Santa Catarina == 0 0.1399
## Bahia - Santa Catarina == 0 <0.01 ***
## Rio - Santa Catarina == 0 0.0373 *
## Sao Paulo - Santa Catarina == 0 <0.01 ***
## Paraiba - Santa Catarina == 0 1.0000
## Mato Grosso - Santa Catarina == 0 <0.01 ***
## Pará - Roraima == 0 1.0000
## Pernambuco - Roraima == 0 1.0000
## Maranhao - Roraima == 0 1.0000
## Ceara - Roraima == 0 0.9958
## Amazonas - Roraima == 0 0.9935
## Tocantins - Roraima == 0 0.7554
## Minas Gerais - Roraima == 0 0.1719
## Goias - Roraima == 0 0.1500
## Piau - Roraima == 0 0.1416
## Bahia - Roraima == 0 <0.01 ***
## Rio - Roraima == 0 0.0351 *
## Sao Paulo - Roraima == 0 <0.01 ***
## Paraiba - Roraima == 0 1.0000
## Mato Grosso - Roraima == 0 <0.01 ***
## Pernambuco - Pará == 0 1.0000
## Maranhao - Pará == 0 1.0000
## Ceara - Pará == 0 0.9965
## Amazonas - Pará == 0 0.9946
## Tocantins - Pará == 0 0.7677
## Minas Gerais - Pará == 0 0.1796
## Goias - Pará == 0 0.1577
## Piau - Pará == 0 0.1494
## Bahia - Pará == 0 <0.01 ***
## Rio - Pará == 0 0.0333 *
## Sao Paulo - Pará == 0 <0.01 ***
## Paraiba - Pará == 0 1.0000
## Mato Grosso - Pará == 0 <0.01 ***
## Maranhao - Pernambuco == 0 1.0000
## Ceara - Pernambuco == 0 0.9969
## Amazonas - Pernambuco == 0 0.9951
## Tocantins - Pernambuco == 0 0.7750
## Minas Gerais - Pernambuco == 0 0.1835
## Goias - Pernambuco == 0 0.1610
## Piau - Pernambuco == 0 0.1539
## Bahia - Pernambuco == 0 <0.01 ***
## Rio - Pernambuco == 0 0.0320 *
## Sao Paulo - Pernambuco == 0 <0.01 ***
## Paraiba - Pernambuco == 0 1.0000
## Mato Grosso - Pernambuco == 0 <0.01 ***
## Ceara - Maranhao == 0 0.9993
## Amazonas - Maranhao == 0 0.9988
## Tocantins - Maranhao == 0 0.8680
## Minas Gerais - Maranhao == 0 0.2650
## Goias - Maranhao == 0 0.2380
## Piau - Maranhao == 0 0.2263
## Bahia - Maranhao == 0 <0.01 **
## Rio - Maranhao == 0 0.0150 *
## Sao Paulo - Maranhao == 0 <0.01 ***
## Paraiba - Maranhao == 0 1.0000
## Mato Grosso - Maranhao == 0 <0.01 ***
## Amazonas - Ceara == 0 1.0000
## Tocantins - Ceara == 0 1.0000
## Minas Gerais - Ceara == 0 0.9923
## Goias - Ceara == 0 0.9888
## Piau - Ceara == 0 0.9870
## Bahia - Ceara == 0 0.1792
## Rio - Ceara == 0 <0.01 ***
## Sao Paulo - Ceara == 0 <0.01 **
## Paraiba - Ceara == 0 0.9998
## Mato Grosso - Ceara == 0 <0.01 **
## Tocantins - Amazonas == 0 1.0000
## Minas Gerais - Amazonas == 0 0.9950
## Goias - Amazonas == 0 0.9926
## Piau - Amazonas == 0 0.9911
## Bahia - Amazonas == 0 0.2046
## Rio - Amazonas == 0 <0.01 ***
## Sao Paulo - Amazonas == 0 <0.01 **
## Paraiba - Amazonas == 0 0.9997
## Mato Grosso - Amazonas == 0 <0.01 **
## Minas Gerais - Tocantins == 0 1.0000
## Goias - Tocantins == 0 1.0000
## Piau - Tocantins == 0 1.0000
## Bahia - Tocantins == 0 0.7150
## Rio - Tocantins == 0 <0.01 ***
## Sao Paulo - Tocantins == 0 0.0462 *
## Paraiba - Tocantins == 0 0.8504
## Mato Grosso - Tocantins == 0 0.0849 .
## Goias - Minas Gerais == 0 1.0000
## Piau - Minas Gerais == 0 1.0000
## Bahia - Minas Gerais == 0 0.9967
## Rio - Minas Gerais == 0 <0.01 ***
## Sao Paulo - Minas Gerais == 0 0.4051
## Paraiba - Minas Gerais == 0 0.1571
## Mato Grosso - Minas Gerais == 0 0.6340
## Piau - Goias == 0 1.0000
## Bahia - Goias == 0 0.9979
## Rio - Goias == 0 <0.01 ***
## Sao Paulo - Goias == 0 0.4438
## Paraiba - Goias == 0 0.1337
## Mato Grosso - Goias == 0 0.6766
## Bahia - Piau == 0 0.9983
## Rio - Piau == 0 <0.01 ***
## Sao Paulo - Piau == 0 0.4612
## Paraiba - Piau == 0 0.1247
## Mato Grosso - Piau == 0 0.6940
## Rio - Bahia == 0 <0.01 ***
## Sao Paulo - Bahia == 0 0.9998
## Paraiba - Bahia == 0 <0.01 ***
## Mato Grosso - Bahia == 0 1.0000
## Sao Paulo - Rio == 0 <0.01 ***
## Paraiba - Rio == 0 <0.01 ***
## Mato Grosso - Rio == 0 <0.01 ***
## Paraiba - Sao Paulo == 0 <0.01 ***
## Mato Grosso - Sao Paulo == 0 1.0000
## Mato Grosso - Paraiba == 0 <0.01 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Adjusted p values reported -- single-step method)
The legal Amazon comprises the states of Acre, Amapá, Pará, Amazonas, Rondonia, Roraima, and part of Mato Grosso, Tocantins, and Maranhão.
On parle de régression logistique.
La proba. de fumer peut-elle s’expliquer par l’âge ?
##
## Call:
## glm(formula = secu$smoker ~ secu$age, family = "binomial")
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -0.7054 -0.6890 -0.6676 -0.6480 1.8302
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.184440 0.198907 -5.955 2.6e-09 ***
## secu$age -0.004422 0.004833 -0.915 0.36
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1356.6 on 1337 degrees of freedom
## Residual deviance: 1355.8 on 1336 degrees of freedom
## AIC: 1359.8
##
## Number of Fisher Scoring iterations: 4
Est-ce que le montant des charges de santé permet de prédire la proba de fumer ?
secu$chargesT <- cut(secu$charges, breaks = seq(from = 0, to = 70000, by = 5000))
ni <- tapply(secu$smoker, INDEX = secu$chargesT, FUN = length)
nT <- tapply(secu$smoker, INDEX = secu$chargesT, FUN = sum)
nProp <- nT/ni
xT <- seq(from = 2500, to = 67500, by = 5000)
dfCharges <- data.frame(xT, nProp, nT, ni)
##
## Call:
## glm(formula = secu$smoker ~ secu$charges, family = "binomial")
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.7137 -0.2990 -0.1623 -0.1018 2.2494
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -5.698e+00 3.064e-01 -18.60 <2e-16 ***
## secu$charges 2.535e-04 1.593e-05 15.91 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1356.63 on 1337 degrees of freedom
## Residual deviance: 503.65 on 1336 degrees of freedom
## AIC: 507.65
##
## Number of Fisher Scoring iterations: 6
On va essayer d’expliquer le statut à la fin des observations.
##
## Call:
## glm(formula = status ~ sex, family = "binomial", data = Aids2)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.3915 -1.3915 0.9775 0.9775 1.0182
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.3868 0.2160 1.791 0.0733 .
## sexM 0.1036 0.2195 0.472 0.6370
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 3777.5 on 2842 degrees of freedom
## Residual deviance: 3777.3 on 2841 degrees of freedom
## AIC: 3781.3
##
## Number of Fisher Scoring iterations: 4
##
## Call:
## glm(formula = status ~ age, family = "binomial", data = Aids2)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.5696 -1.3663 0.9450 0.9917 1.1303
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.111819 0.149300 0.749 0.4539
## age 0.010065 0.003881 2.593 0.0095 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 3777.5 on 2842 degrees of freedom
## Residual deviance: 3770.7 on 2841 degrees of freedom
## AIC: 3774.7
##
## Number of Fisher Scoring iterations: 4
Aids2$ageT <- cut(Aids2$age, breaks = seq(from = 0, to = 100, by = 10))
ni <- tapply(as.numeric(Aids2$status)-1, INDEX = Aids2$ageT, FUN = length)
nT <- tapply(as.numeric(Aids2$status)-1, INDEX = Aids2$ageT, FUN = sum)
nProp <- nT/ni
xT <- seq(from = 5, to = 95, by = 10)
dfage <- data.frame(xT, nProp, nT, ni)
modL <- modL02
plot(
x = dfage$xT,
y = dfage$nProp,
col = 'red', lwd = 3, xlim = c(0, 100),
ylim = c(0, 1), xlab = "âge", ylab = "Proba(death)")
lines(
x = seq(from = 0, to = 100, by = 10),
y = predict(modL, list(
age = seq(from = 0, to = 100, by = 10)),
type = "response"),
col = 'blue', lwd = 4, lty = 3)
legend("topleft", c("obs", "logit"), lwd = 3, col = c("red", "blue"))
##
## Call:
## glm(formula = status ~ age * sex, family = "binomial", data = Aids2)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.8256 -1.3734 0.9517 0.9873 1.5777
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.90485 0.54783 -1.652 0.0986 .
## age 0.03473 0.01383 2.512 0.0120 *
## sexM 1.10907 0.56968 1.947 0.0516 .
## age:sexM -0.02706 0.01441 -1.878 0.0604 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 3777.5 on 2842 degrees of freedom
## Residual deviance: 3766.6 on 2839 degrees of freedom
## AIC: 3774.6
##
## Number of Fisher Scoring iterations: 4
## [1] 3781.269
## [1] 3774.705
## [1] 3774.648
On garde le modèle modL02
.
Survie en jours = date mort - date diagnostic
##
## Call:
## glm(formula = surv ~ age, family = "Gamma", data = Aids2, subset = surv >
## 0)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -3.2565 -0.9426 -0.2280 0.3740 3.0442
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.539e-03 1.543e-04 9.969 < 2e-16 ***
## age 2.471e-05 4.199e-06 5.884 4.47e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for Gamma family taken to be 0.7935563)
##
## Null deviance: 3219.5 on 2813 degrees of freedom
## Residual deviance: 3192.0 on 2812 degrees of freedom
## AIC: 39502
##
## Number of Fisher Scoring iterations: 6