Output from Arrests-logistic.R

library(effects)  # for Arrests data
library(car)  # for Anova()
data(Arrests)
Arrests$year <- as.factor(Arrests$year)

# all main effects
arrests.mod1 <- glm(released ~ ., family = binomial, data = Arrests)
Anova(arrests.mod1)
## Analysis of Deviance Table (Type II tests)
## 
## Response: released
##          LR Chisq Df Pr(>Chisq)    
## colour       19.5  1    9.8e-06 ***
## year          6.7  5       0.24    
## age           0.2  1       0.62    
## sex           0.0  1       0.95    
## employed     75.7  1    < 2e-16 ***
## citizen      23.9  1    1.0e-06 ***
## checks      203.6  1    < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# all two-way effects
arrests.mod2 <- glm(released ~ .^2, family = binomial, data = Arrests)
Anova(arrests.mod2)
## Analysis of Deviance Table (Type II tests)
## 
## Response: released
##                  LR Chisq Df Pr(>Chisq)    
## colour               18.7  1    1.5e-05 ***
## year                  6.4  5    0.26978    
## age                   1.3  1    0.26135    
## sex                   0.1  1    0.77137    
## employed             69.9  1    < 2e-16 ***
## citizen              23.6  1    1.2e-06 ***
## checks              195.9  1    < 2e-16 ***
## colour:year          21.6  5    0.00061 ***
## colour:age            8.5  1    0.00364 ** 
## colour:sex            0.3  1    0.59062    
## colour:employed       0.0  1    0.94505    
## colour:citizen        1.1  1    0.28922    
## colour:checks         0.0  1    0.91122    
## year:age             12.9  5    0.02424 *  
## year:sex              5.5  5    0.35283    
## year:employed         9.9  5    0.07949 .  
## year:citizen          7.8  5    0.16569    
## year:checks          17.1  5    0.00435 ** 
## age:sex               1.1  1    0.30329    
## age:employed          3.9  1    0.04850 *  
## age:citizen           0.0  1    0.90959    
## age:checks            0.3  1    0.56940    
## sex:employed          5.5  1    0.01886 *  
## sex:citizen           0.8  1    0.35748    
## sex:checks            1.1  1    0.30195    
## employed:citizen      0.1  1    0.71659    
## employed:checks       0.2  1    0.69018    
## citizen:checks        5.9  1    0.01546 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# backward selection, using AIC
arrests.step <- stepAIC(arrests.mod2, direction = "backward")
## Start:  AIC=4294
## released ~ (colour + year + age + sex + employed + citizen + 
##     checks)^2
## 
##                    Df Deviance  AIC
## - year:sex          5     4186 4290
## - year:citizen      5     4188 4292
## - colour:employed   1     4180 4292
## - colour:checks     1     4180 4292
## - age:citizen       1     4180 4292
## - employed:citizen  1     4180 4292
## - employed:checks   1     4180 4292
## - colour:sex        1     4180 4292
## - age:checks        1     4180 4292
## - sex:citizen       1     4181 4293
## - age:sex           1     4181 4293
## - sex:checks        1     4181 4293
## - colour:citizen    1     4181 4293
## - year:employed     5     4190 4294
##                     4180 4294
## - age:employed      1     4184 4296
## - year:age          5     4193 4297
## - sex:employed      1     4186 4298
## - citizen:checks    1     4186 4298
## - colour:age        1     4189 4301
## - year:checks       5     4197 4301
## - colour:year       5     4202 4306
## 
## Step:  AIC=4290
## released ~ colour + year + age + sex + employed + citizen + checks + 
##     colour:year + colour:age + colour:sex + colour:employed + 
##     colour:citizen + colour:checks + year:age + year:employed + 
##     year:citizen + year:checks + age:sex + age:employed + age:citizen + 
##     age:checks + sex:employed + sex:citizen + sex:checks + employed:citizen + 
##     employed:checks + citizen:checks
## 
##                    Df Deviance  AIC
## - year:citizen      5     4194 4288
## - colour:employed   1     4186 4288
## - colour:checks     1     4186 4288
## - age:citizen       1     4186 4288
## - employed:citizen  1     4186 4288
## - employed:checks   1     4186 4288
## - age:checks        1     4186 4288
## - age:sex           1     4186 4288
## - colour:sex        1     4186 4288
## - year:employed     5     4195 4289
## - colour:citizen    1     4187 4289
## - sex:checks        1     4187 4289
##                     4186 4290
## - sex:citizen       1     4188 4290
## - age:employed      1     4189 4291
## - year:age          5     4199 4293
## - sex:employed      1     4192 4294
## - citizen:checks    1     4192 4294
## - year:checks       5     4201 4295
## - colour:age        1     4194 4296
## - colour:year       5     4208 4302
## 
## Step:  AIC=4288
## released ~ colour + year + age + sex + employed + citizen + checks + 
##     colour:year + colour:age + colour:sex + colour:employed + 
##     colour:citizen + colour:checks + year:age + year:employed + 
##     year:checks + age:sex + age:employed + age:citizen + age:checks + 
##     sex:employed + sex:citizen + sex:checks + employed:citizen + 
##     employed:checks + citizen:checks
## 
##                    Df Deviance  AIC
## - age:citizen       1     4194 4286
## - colour:employed   1     4194 4286
## - colour:checks     1     4194 4286
## - employed:checks   1     4194 4286
## - age:checks        1     4194 4286
## - employed:citizen  1     4194 4286
## - age:sex           1     4194 4286
## - colour:sex        1     4194 4286
## - sex:checks        1     4195 4287
## - year:employed     5     4203 4287
## - colour:citizen    1     4195 4287
##                     4194 4288
## - sex:citizen       1     4196 4288
## - age:employed      1     4197 4289
## - year:age          5     4207 4291
## - year:checks       5     4207 4291
## - citizen:checks    1     4200 4292
## - sex:employed      1     4200 4292
## - colour:age        1     4202 4294
## - colour:year       5     4218 4302
## 
## Step:  AIC=4286
## released ~ colour + year + age + sex + employed + citizen + checks + 
##     colour:year + colour:age + colour:sex + colour:employed + 
##     colour:citizen + colour:checks + year:age + year:employed + 
##     year:checks + age:sex + age:employed + age:checks + sex:employed + 
##     sex:citizen + sex:checks + employed:citizen + employed:checks + 
##     citizen:checks
## 
##                    Df Deviance  AIC
## - colour:employed   1     4194 4284
## - colour:checks     1     4194 4284
## - employed:checks   1     4194 4284
## - age:checks        1     4194 4284
## - employed:citizen  1     4194 4284
## - age:sex           1     4194 4284
## - colour:sex        1     4194 4284
## - sex:checks        1     4195 4285
## - year:employed     5     4203 4285
## - colour:citizen    1     4195 4285
##                     4194 4286
## - sex:citizen       1     4196 4286
## - age:employed      1     4197 4287
## - year:age          5     4207 4289
## - year:checks       5     4207 4289
## - citizen:checks    1     4200 4290
## - sex:employed      1     4200 4290
## - colour:age        1     4203 4293
## - colour:year       5     4218 4300
## 
## Step:  AIC=4284
## released ~ colour + year + age + sex + employed + citizen + checks + 
##     colour:year + colour:age + colour:sex + colour:citizen + 
##     colour:checks + year:age + year:employed + year:checks + 
##     age:sex + age:employed + age:checks + sex:employed + sex:citizen + 
##     sex:checks + employed:citizen + employed:checks + citizen:checks
## 
##                    Df Deviance  AIC
## - colour:checks     1     4194 4282
## - employed:checks   1     4194 4282
## - age:checks        1     4194 4282
## - employed:citizen  1     4194 4282
## - age:sex           1     4194 4282
## - colour:sex        1     4194 4282
## - sex:checks        1     4195 4283
## - year:employed     5     4203 4283
## - colour:citizen    1     4195 4283
##                     4194 4284
## - sex:citizen       1     4196 4284
## - age:employed      1     4197 4285
## - year:age          5     4207 4287
## - year:checks       5     4207 4287
## - citizen:checks    1     4200 4288
## - sex:employed      1     4200 4288
## - colour:age        1     4203 4291
## - colour:year       5     4218 4298
## 
## Step:  AIC=4282
## released ~ colour + year + age + sex + employed + citizen + checks + 
##     colour:year + colour:age + colour:sex + colour:citizen + 
##     year:age + year:employed + year:checks + age:sex + age:employed + 
##     age:checks + sex:employed + sex:citizen + sex:checks + employed:citizen + 
##     employed:checks + citizen:checks
## 
##                    Df Deviance  AIC
## - employed:checks   1     4194 4280
## - age:checks        1     4194 4280
## - employed:citizen  1     4194 4280
## - age:sex           1     4194 4280
## - colour:sex        1     4194 4280
## - sex:checks        1     4195 4281
## - year:employed     5     4203 4281
##                     4194 4282
## - colour:citizen    1     4196 4282
## - sex:citizen       1     4196 4282
## - age:employed      1     4197 4283
## - year:age          5     4207 4285
## - year:checks       5     4207 4285
## - sex:employed      1     4200 4286
## - citizen:checks    1     4201 4287
## - colour:age        1     4203 4289
## - colour:year       5     4218 4296
## 
## Step:  AIC=4280
## released ~ colour + year + age + sex + employed + citizen + checks + 
##     colour:year + colour:age + colour:sex + colour:citizen + 
##     year:age + year:employed + year:checks + age:sex + age:employed + 
##     age:checks + sex:employed + sex:citizen + sex:checks + employed:citizen + 
##     citizen:checks
## 
##                    Df Deviance  AIC
## - employed:citizen  1     4194 4278
## - age:checks        1     4194 4278
## - age:sex           1     4194 4278
## - colour:sex        1     4194 4278
## - sex:checks        1     4195 4279
## - year:employed     5     4203 4279
##                     4194 4280
## - colour:citizen    1     4196 4280
## - sex:citizen       1     4196 4280
## - age:employed      1     4198 4282
## - year:age          5     4207 4283
## - year:checks       5     4208 4284
## - sex:employed      1     4200 4284
## - citizen:checks    1     4201 4285
## - colour:age        1     4203 4287
## - colour:year       5     4218 4294
## 
## Step:  AIC=4278
## released ~ colour + year + age + sex + employed + citizen + checks + 
##     colour:year + colour:age + colour:sex + colour:citizen + 
##     year:age + year:employed + year:checks + age:sex + age:employed + 
##     age:checks + sex:employed + sex:citizen + sex:checks + citizen:checks
## 
##                  Df Deviance  AIC
## - age:checks      1     4194 4276
## - age:sex         1     4195 4277
## - colour:sex      1     4195 4277
## - year:employed   5     4203 4277
## - sex:checks      1     4195 4277
## - colour:citizen  1     4196 4278
##                   4194 4278
## - sex:citizen     1     4197 4279
## - age:employed    1     4198 4280
## - year:age        5     4208 4282
## - year:checks     5     4208 4282
## - sex:employed    1     4201 4283
## - citizen:checks  1     4202 4284
## - colour:age      1     4204 4286
## - colour:year     5     4219 4293
## 
## Step:  AIC=4276
## released ~ colour + year + age + sex + employed + citizen + checks + 
##     colour:year + colour:age + colour:sex + colour:citizen + 
##     year:age + year:employed + year:checks + age:sex + age:employed + 
##     sex:employed + sex:citizen + sex:checks + citizen:checks
## 
##                  Df Deviance  AIC
## - age:sex         1     4195 4275
## - colour:sex      1     4195 4275
## - year:employed   5     4204 4276
## - sex:checks      1     4196 4276
## - colour:citizen  1     4196 4276
##                   4194 4276
## - sex:citizen     1     4197 4277
## - age:employed    1     4199 4279
## - year:age        5     4208 4280
## - year:checks     5     4208 4280
## - sex:employed    1     4201 4281
## - citizen:checks  1     4202 4282
## - colour:age      1     4204 4284
## - colour:year     5     4219 4291
## 
## Step:  AIC=4275
## released ~ colour + year + age + sex + employed + citizen + checks + 
##     colour:year + colour:age + colour:sex + colour:citizen + 
##     year:age + year:employed + year:checks + age:employed + sex:employed + 
##     sex:citizen + sex:checks + citizen:checks
## 
##                  Df Deviance  AIC
## - colour:sex      1     4195 4273
## - year:employed   5     4204 4274
## - sex:checks      1     4196 4274
## - colour:citizen  1     4197 4275
##                   4195 4275
## - sex:citizen     1     4198 4276
## - age:employed    1     4200 4278
## - year:checks     5     4208 4278
## - year:age        5     4209 4279
## - sex:employed    1     4201 4279
## - citizen:checks  1     4203 4281
## - colour:age      1     4204 4282
## - colour:year     5     4219 4289
## 
## Step:  AIC=4273
## released ~ colour + year + age + sex + employed + citizen + checks + 
##     colour:year + colour:age + colour:citizen + year:age + year:employed + 
##     year:checks + age:employed + sex:employed + sex:citizen + 
##     sex:checks + citizen:checks
## 
##                  Df Deviance  AIC
## - year:employed   5     4205 4273
## - sex:checks      1     4197 4273
##                   4195 4273
## - colour:citizen  1     4197 4273
## - sex:citizen     1     4199 4275
## - age:employed    1     4201 4277
## - year:checks     5     4209 4277
## - year:age        5     4209 4277
## - sex:employed    1     4202 4278
## - citizen:checks  1     4203 4279
## - colour:age      1     4205 4281
## - colour:year     5     4220 4288
## 
## Step:  AIC=4273
## released ~ colour + year + age + sex + employed + citizen + checks + 
##     colour:year + colour:age + colour:citizen + year:age + year:checks + 
##     age:employed + sex:employed + sex:citizen + sex:checks + 
##     citizen:checks
## 
##                  Df Deviance  AIC
## - sex:checks      1     4206 4272
## - colour:citizen  1     4207 4273
##                   4205 4273
## - year:checks     5     4216 4274
## - sex:citizen     1     4208 4274
## - year:age        5     4218 4276
## - sex:employed    1     4211 4277
## - age:employed    1     4211 4277
## - citizen:checks  1     4212 4278
## - colour:age      1     4214 4280
## - colour:year     5     4229 4287
## 
## Step:  AIC=4272
## released ~ colour + year + age + sex + employed + citizen + checks + 
##     colour:year + colour:age + colour:citizen + year:age + year:checks + 
##     age:employed + sex:employed + sex:citizen + citizen:checks
## 
##                  Df Deviance  AIC
## - colour:citizen  1     4208 4272
##                   4206 4272
## - sex:citizen     1     4209 4273
## - year:checks     5     4217 4273
## - sex:employed    1     4211 4275
## - year:age        5     4219 4275
## - age:employed    1     4213 4277
## - citizen:checks  1     4214 4278
## - colour:age      1     4216 4280
## - colour:year     5     4231 4287
## 
## Step:  AIC=4272
## released ~ colour + year + age + sex + employed + citizen + checks + 
##     colour:year + colour:age + year:age + year:checks + age:employed + 
##     sex:employed + sex:citizen + citizen:checks
## 
##                  Df Deviance  AIC
##                   4208 4272
## - sex:citizen     1     4211 4273
## - year:checks     5     4219 4273
## - sex:employed    1     4213 4275
## - year:age        5     4221 4275
## - citizen:checks  1     4215 4277
## - age:employed    1     4215 4277
## - colour:age      1     4217 4279
## - colour:year     5     4232 4286
anova(arrests.mod1, arrests.step, arrests.mod2, test = "Chisq")
## Analysis of Deviance Table
## 
## Model 1: released ~ colour + year + age + sex + employed + citizen + checks
## Model 2: released ~ colour + year + age + sex + employed + citizen + checks + 
##     colour:year + colour:age + year:age + year:checks + age:employed + 
##     sex:employed + sex:citizen + citizen:checks
## Model 3: released ~ (colour + year + age + sex + employed + citizen + 
##     checks)^2
##   Resid. Df Resid. Dev Df Deviance Pr(>Chi)    
## 1      5214       4292                         
## 2      5194       4208 20     84.1  7.7e-10 ***
## 3      5169       4180 25     28.2      0.3    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# one reduced model
arrests.mod <- glm(released ~ employed + citizen + checks + colour * year + colour * age, family = binomial, 
    data = Arrests)

# summary(arrests.mod)
Anova(arrests.mod)
## Analysis of Deviance Table (Type II tests)
## 
## Response: released
##             LR Chisq Df Pr(>Chisq)    
## employed        72.7  1    < 2e-16 ***
## citizen         25.8  1    3.8e-07 ***
## checks         205.2  1    < 2e-16 ***
## colour          19.6  1    9.7e-06 ***
## year             6.1  5    0.29785    
## age              0.5  1    0.49827    
## colour:year     21.7  5    0.00059 ***
## colour:age      13.9  1    0.00019 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
anova(arrests.mod1, arrests.mod, arrests.mod2)
## Analysis of Deviance Table
## 
## Model 1: released ~ colour + year + age + sex + employed + citizen + checks
## Model 2: released ~ employed + citizen + checks + colour * year + colour * 
##     age
## Model 3: released ~ (colour + year + age + sex + employed + citizen + 
##     checks)^2
##   Resid. Df Resid. Dev Df Deviance
## 1      5214       4292            
## 2      5209       4257  5     35.3
## 3      5169       4180 40     77.0
anova(arrests.mod1, arrests.mod, arrests.mod2, test = "Chisq")
## Analysis of Deviance Table
## 
## Model 1: released ~ colour + year + age + sex + employed + citizen + checks
## Model 2: released ~ employed + citizen + checks + colour * year + colour * 
##     age
## Model 3: released ~ (colour + year + age + sex + employed + citizen + 
##     checks)^2
##   Resid. Df Resid. Dev Df Deviance Pr(>Chi)    
## 1      5214       4292                         
## 2      5209       4257  5     35.3  1.3e-06 ***
## 3      5169       4180 40     77.0    4e-04 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Generated with R version 2.15.1 (2012-06-22) using the R package knitr (version 0.8.4) on Wed Sep 26 08:49:23 2012.