library(effects) # for effect plots
library(car) # for Anova()
library(MASS) # for stepAICdata(Arrests, package = "carData")
Arrests$year <- as.factor(Arrests$year)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 ' ' 1arrests.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 ' ' 1Add single two-way interactions, starting from the main effects model
add1(arrests.mod1, scope= ~.^2, test="Chisq")## Single term additions
##
## Model:
## released ~ colour + year + age + sex + employed + citizen + checks
## Df Deviance AIC LRT Pr(>Chi)
## <none> 4292 4316
## colour:year 5 4271 4305 21.43 0.00067 ***
## colour:age 1 4279 4305 13.60 0.00023 ***
## colour:sex 1 4292 4318 0.46 0.49840
## colour:employed 1 4292 4318 0.28 0.59926
## colour:citizen 1 4292 4318 0.15 0.70335
## colour:checks 1 4290 4316 2.19 0.13924
## year:age 5 4279 4313 13.63 0.01812 *
## year:sex 5 4287 4321 5.85 0.32156
## year:employed 5 4287 4321 5.12 0.40180
## year:citizen 5 4283 4317 9.40 0.09420 .
## year:checks 5 4277 4311 15.49 0.00845 **
## age:sex 1 4292 4318 0.36 0.55052
## age:employed 1 4285 4311 7.58 0.00591 **
## age:citizen 1 4292 4318 0.84 0.35866
## age:checks 1 4291 4317 1.38 0.24048
## sex:employed 1 4288 4314 4.63 0.03135 *
## sex:citizen 1 4290 4316 1.88 0.17025
## sex:checks 1 4292 4318 0.00 0.97113
## employed:citizen 1 4292 4318 0.42 0.51909
## employed:checks 1 4291 4317 1.63 0.20234
## citizen:checks 1 4280 4306 11.93 0.00055 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Drop single two-way interactions, starting from the all two-way model
drop1(arrests.mod2, test="Chisq")## Single term deletions
##
## Model:
## released ~ (colour + year + age + sex + employed + citizen +
## checks)^2
## Df Deviance AIC LRT Pr(>Chi)
## <none> 4180 4294
## colour:year 5 4202 4306 21.64 0.00061 ***
## colour:age 1 4189 4301 8.46 0.00364 **
## colour:sex 1 4180 4292 0.29 0.59062
## colour:employed 1 4180 4292 0.00 0.94505
## colour:citizen 1 4181 4293 1.12 0.28922
## colour:checks 1 4180 4292 0.01 0.91122
## year:age 5 4193 4297 12.91 0.02424 *
## year:sex 5 4186 4290 5.55 0.35283
## year:employed 5 4190 4294 9.85 0.07949 .
## year:citizen 5 4188 4292 7.83 0.16569
## year:checks 5 4197 4301 17.08 0.00435 **
## age:sex 1 4181 4293 1.06 0.30329
## age:employed 1 4184 4296 3.89 0.04850 *
## age:citizen 1 4180 4292 0.01 0.90959
## age:checks 1 4180 4292 0.32 0.56940
## sex:employed 1 4186 4298 5.51 0.01886 *
## sex:citizen 1 4181 4293 0.85 0.35748
## sex:checks 1 4181 4293 1.07 0.30195
## employed:citizen 1 4180 4292 0.13 0.71659
## employed:checks 1 4180 4292 0.16 0.69018
## citizen:checks 1 4186 4298 5.86 0.01546 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1MASS::stepAIC()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
## <none> 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
## <none> 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
## <none> 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
## <none> 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
## <none> 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
## <none> 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
## <none> 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
## <none> 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
## <none> 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
## <none> 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
## <none> 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
## <none> 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
## <none> 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
## <none> 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 4286anova(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 ' ' 1arrests.mod <- glm(released ~ employed + citizen + checks + colour*year + colour*age,
family=binomial, data=Arrests)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