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 19.544 1 9.83e-06 ***
## year 6.712 5 0.2430
## age 0.241 1 0.6237
## sex 0.003 1 0.9545
## employed 75.715 1 < 2.2e-16 ***
## citizen 23.853 1 1.04e-06 ***
## checks 203.562 1 < 2.2e-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 18.690 1 1.538e-05 ***
## year 6.394 5 0.2697805
## age 1.262 1 0.2613526
## sex 0.084 1 0.7713700
## employed 69.898 1 < 2.2e-16 ***
## citizen 23.641 1 1.161e-06 ***
## checks 195.890 1 < 2.2e-16 ***
## colour:year 21.643 5 0.0006121 ***
## colour:age 8.457 1 0.0036367 **
## colour:sex 0.289 1 0.5906163
## colour:employed 0.005 1 0.9450466
## colour:citizen 1.123 1 0.2892219
## colour:checks 0.012 1 0.9112238
## year:age 12.909 5 0.0242427 *
## year:sex 5.547 5 0.3528332
## year:employed 9.854 5 0.0794897 .
## year:citizen 7.833 5 0.1656900
## year:checks 17.079 5 0.0043521 **
## age:sex 1.060 1 0.3032908
## age:employed 3.893 1 0.0484968 *
## age:citizen 0.013 1 0.9095946
## age:checks 0.324 1 0.5694023
## sex:employed 5.514 1 0.0188645 *
## sex:citizen 0.847 1 0.3574757
## sex:checks 1.066 1 0.3019524
## employed:citizen 0.132 1 0.7165898
## employed:checks 0.159 1 0.6901753
## citizen:checks 5.863 1 0.0154587 *
## ---
## 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> 4292.4 4316.4
## colour:year 5 4270.9 4304.9 21.4324 0.0006710 ***
## colour:age 1 4278.8 4304.8 13.6001 0.0002262 ***
## colour:sex 1 4291.9 4317.9 0.4583 0.4983969
## colour:employed 1 4292.1 4318.1 0.2761 0.5992589
## colour:citizen 1 4292.2 4318.2 0.1450 0.7033531
## colour:checks 1 4290.2 4316.2 2.1864 0.1392356
## year:age 5 4278.7 4312.7 13.6326 0.0181198 *
## year:sex 5 4286.5 4320.5 5.8453 0.3215599
## year:employed 5 4287.3 4321.3 5.1167 0.4018001
## year:citizen 5 4283.0 4317.0 9.3982 0.0941972 .
## year:checks 5 4276.9 4310.9 15.4941 0.0084473 **
## age:sex 1 4292.0 4318.0 0.3564 0.5505184
## age:employed 1 4284.8 4310.8 7.5769 0.0059121 **
## age:citizen 1 4291.5 4317.5 0.8426 0.3586565
## age:checks 1 4291.0 4317.0 1.3778 0.2404818
## sex:employed 1 4287.7 4313.7 4.6335 0.0313530 *
## sex:citizen 1 4290.5 4316.5 1.8807 0.1702512
## sex:checks 1 4292.4 4318.4 0.0013 0.9711267
## employed:citizen 1 4292.0 4318.0 0.4157 0.5190904
## employed:checks 1 4290.8 4316.8 1.6254 0.2023424
## citizen:checks 1 4280.4 4306.4 11.9269 0.0005533 ***
## ---
## 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> 4180.1 4294.1
## colour:year 5 4201.7 4305.7 21.6428 0.0006121 ***
## colour:age 1 4188.5 4300.5 8.4569 0.0036367 **
## colour:sex 1 4180.4 4292.4 0.2894 0.5906163
## colour:employed 1 4180.1 4292.1 0.0048 0.9450466
## colour:citizen 1 4181.2 4293.2 1.1232 0.2892219
## colour:checks 1 4180.1 4292.1 0.0124 0.9112238
## year:age 5 4193.0 4297.0 12.9094 0.0242427 *
## year:sex 5 4185.6 4289.6 5.5469 0.3528332
## year:employed 5 4189.9 4293.9 9.8537 0.0794897 .
## year:citizen 5 4187.9 4291.9 7.8329 0.1656900
## year:checks 5 4197.2 4301.2 17.0792 0.0043521 **
## age:sex 1 4181.1 4293.1 1.0597 0.3032908
## age:employed 1 4184.0 4296.0 3.8927 0.0484968 *
## age:citizen 1 4180.1 4292.1 0.0129 0.9095946
## age:checks 1 4180.4 4292.4 0.3237 0.5694023
## sex:employed 1 4185.6 4297.6 5.5140 0.0188645 *
## sex:citizen 1 4180.9 4292.9 0.8467 0.3574757
## sex:checks 1 4181.1 4293.1 1.0656 0.3019524
## employed:citizen 1 4180.2 4292.2 0.1318 0.7165898
## employed:checks 1 4180.2 4292.2 0.1589 0.6901753
## citizen:checks 1 4185.9 4297.9 5.8634 0.0154587 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1MASS::stepAIC()arrests.step <- stepAIC(arrests.mod2, direction="backward")## Start: AIC=4294.08
## released ~ (colour + year + age + sex + employed + citizen +
## checks)^2
##
## Df Deviance AIC
## - year:sex 5 4185.6 4289.6
## - year:citizen 5 4187.9 4291.9
## - colour:employed 1 4180.1 4292.1
## - colour:checks 1 4180.1 4292.1
## - age:citizen 1 4180.1 4292.1
## - employed:citizen 1 4180.2 4292.2
## - employed:checks 1 4180.2 4292.2
## - colour:sex 1 4180.4 4292.4
## - age:checks 1 4180.4 4292.4
## - sex:citizen 1 4180.9 4292.9
## - age:sex 1 4181.1 4293.1
## - sex:checks 1 4181.1 4293.1
## - colour:citizen 1 4181.2 4293.2
## - year:employed 5 4189.9 4293.9
## <none> 4180.1 4294.1
## - age:employed 1 4184.0 4296.0
## - year:age 5 4193.0 4297.0
## - sex:employed 1 4185.6 4297.6
## - citizen:checks 1 4185.9 4297.9
## - colour:age 1 4188.5 4300.5
## - year:checks 5 4197.2 4301.2
## - colour:year 5 4201.7 4305.7
##
## Step: AIC=4289.63
## 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 4193.5 4287.5
## - colour:employed 1 4185.6 4287.6
## - colour:checks 1 4185.6 4287.6
## - age:citizen 1 4185.6 4287.6
## - employed:citizen 1 4185.7 4287.7
## - employed:checks 1 4185.8 4287.8
## - age:checks 1 4185.9 4287.9
## - age:sex 1 4186.2 4288.2
## - colour:sex 1 4186.2 4288.2
## - year:employed 5 4194.6 4288.6
## - colour:citizen 1 4186.7 4288.7
## - sex:checks 1 4186.8 4288.8
## <none> 4185.6 4289.6
## - sex:citizen 1 4188.2 4290.2
## - age:employed 1 4189.3 4291.3
## - year:age 5 4199.0 4293.0
## - sex:employed 1 4191.7 4293.7
## - citizen:checks 1 4191.9 4293.9
## - year:checks 5 4201.3 4295.3
## - colour:age 1 4193.9 4295.9
## - colour:year 5 4208.3 4302.3
##
## Step: AIC=4287.54
## 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 4193.5 4285.5
## - colour:employed 1 4193.5 4285.5
## - colour:checks 1 4193.6 4285.6
## - employed:checks 1 4193.7 4285.7
## - age:checks 1 4193.8 4285.8
## - employed:citizen 1 4193.9 4285.9
## - age:sex 1 4194.1 4286.1
## - colour:sex 1 4194.2 4286.2
## - sex:checks 1 4194.8 4286.8
## - year:employed 5 4202.9 4286.9
## - colour:citizen 1 4195.4 4287.4
## <none> 4193.5 4287.5
## - sex:citizen 1 4195.9 4287.9
## - age:employed 1 4197.3 4289.3
## - year:age 5 4206.7 4290.7
## - year:checks 5 4207.2 4291.2
## - citizen:checks 1 4199.6 4291.6
## - sex:employed 1 4199.8 4291.8
## - colour:age 1 4202.1 4294.1
## - colour:year 5 4217.9 4301.9
##
## Step: AIC=4285.54
## 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 4193.5 4283.5
## - colour:checks 1 4193.6 4283.6
## - employed:checks 1 4193.7 4283.7
## - age:checks 1 4193.8 4283.8
## - employed:citizen 1 4193.9 4283.9
## - age:sex 1 4194.1 4284.1
## - colour:sex 1 4194.2 4284.2
## - sex:checks 1 4194.8 4284.8
## - year:employed 5 4202.9 4284.9
## - colour:citizen 1 4195.4 4285.4
## <none> 4193.5 4285.5
## - sex:citizen 1 4195.9 4285.9
## - age:employed 1 4197.3 4287.3
## - year:age 5 4207.0 4289.0
## - year:checks 5 4207.2 4289.2
## - citizen:checks 1 4199.7 4289.7
## - sex:employed 1 4199.8 4289.8
## - colour:age 1 4203.1 4293.1
## - colour:year 5 4218.0 4300.0
##
## Step: AIC=4283.55
## 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 4193.6 4281.6
## - employed:checks 1 4193.7 4281.7
## - age:checks 1 4193.8 4281.8
## - employed:citizen 1 4193.9 4281.9
## - age:sex 1 4194.1 4282.1
## - colour:sex 1 4194.3 4282.3
## - sex:checks 1 4194.9 4282.9
## - year:employed 5 4202.9 4282.9
## - colour:citizen 1 4195.4 4283.4
## <none> 4193.5 4283.5
## - sex:citizen 1 4196.0 4284.0
## - age:employed 1 4197.3 4285.3
## - year:age 5 4207.0 4287.0
## - year:checks 5 4207.3 4287.3
## - citizen:checks 1 4199.7 4287.7
## - sex:employed 1 4199.8 4287.8
## - colour:age 1 4203.1 4291.1
## - colour:year 5 4218.0 4298.0
##
## Step: AIC=4281.57
## 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 4193.7 4279.7
## - age:checks 1 4193.9 4279.9
## - employed:citizen 1 4193.9 4279.9
## - age:sex 1 4194.1 4280.1
## - colour:sex 1 4194.3 4280.3
## - sex:checks 1 4194.9 4280.9
## - year:employed 5 4203.0 4281.0
## <none> 4193.6 4281.6
## - colour:citizen 1 4195.6 4281.6
## - sex:citizen 1 4196.0 4282.0
## - age:employed 1 4197.3 4283.3
## - year:age 5 4207.1 4285.1
## - year:checks 5 4207.3 4285.3
## - sex:employed 1 4199.8 4285.8
## - citizen:checks 1 4200.5 4286.5
## - colour:age 1 4203.1 4289.1
## - colour:year 5 4218.0 4296.0
##
## Step: AIC=4279.73
## 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 4194.0 4278.0
## - age:checks 1 4194.0 4278.0
## - age:sex 1 4194.3 4278.3
## - colour:sex 1 4194.4 4278.4
## - sex:checks 1 4195.2 4279.2
## - year:employed 5 4203.3 4279.3
## <none> 4193.7 4279.7
## - colour:citizen 1 4195.7 4279.7
## - sex:citizen 1 4196.2 4280.2
## - age:employed 1 4197.5 4281.5
## - year:age 5 4207.3 4283.3
## - year:checks 5 4207.6 4283.6
## - sex:employed 1 4200.4 4284.4
## - citizen:checks 1 4200.7 4284.7
## - colour:age 1 4203.3 4287.3
## - colour:year 5 4218.3 4294.3
##
## Step: AIC=4278.03
## 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 4194.3 4276.3
## - age:sex 1 4194.6 4276.6
## - colour:sex 1 4194.7 4276.7
## - year:employed 5 4203.4 4277.4
## - sex:checks 1 4195.5 4277.5
## - colour:citizen 1 4196.0 4278.0
## <none> 4194.0 4278.0
## - sex:citizen 1 4196.7 4278.7
## - age:employed 1 4198.0 4280.0
## - year:age 5 4207.5 4281.5
## - year:checks 5 4207.8 4281.8
## - sex:employed 1 4200.9 4282.9
## - citizen:checks 1 4201.6 4283.6
## - colour:age 1 4203.6 4285.6
## - colour:year 5 4218.5 4292.5
##
## Step: AIC=4276.33
## 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 4194.8 4274.8
## - colour:sex 1 4195.0 4275.0
## - year:employed 5 4203.7 4275.7
## - sex:checks 1 4195.8 4275.8
## - colour:citizen 1 4196.3 4276.3
## <none> 4194.3 4276.3
## - sex:citizen 1 4197.1 4277.1
## - age:employed 1 4199.0 4279.0
## - year:age 5 4207.7 4279.7
## - year:checks 5 4208.0 4280.0
## - sex:employed 1 4201.2 4281.2
## - citizen:checks 1 4202.2 4282.2
## - colour:age 1 4204.0 4284.0
## - colour:year 5 4218.7 4290.7
##
## Step: AIC=4274.78
## 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 4195.4 4273.4
## - year:employed 5 4204.3 4274.3
## - sex:checks 1 4196.4 4274.4
## - colour:citizen 1 4196.7 4274.7
## <none> 4194.8 4274.8
## - sex:citizen 1 4197.6 4275.6
## - age:employed 1 4200.2 4278.2
## - year:checks 5 4208.4 4278.4
## - year:age 5 4208.7 4278.7
## - sex:employed 1 4201.2 4279.2
## - citizen:checks 1 4202.6 4280.6
## - colour:age 1 4204.1 4282.1
## - colour:year 5 4219.3 4289.3
##
## Step: AIC=4273.43
## 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 4204.7 4272.7
## - sex:checks 1 4197.0 4273.0
## <none> 4195.4 4273.4
## - colour:citizen 1 4197.5 4273.5
## - sex:citizen 1 4199.0 4275.0
## - age:employed 1 4200.9 4276.9
## - year:checks 5 4209.0 4277.0
## - year:age 5 4209.1 4277.1
## - sex:employed 1 4201.7 4277.7
## - citizen:checks 1 4203.5 4279.5
## - colour:age 1 4204.8 4280.8
## - colour:year 5 4219.5 4287.5
##
## Step: AIC=4272.73
## 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 4206.4 4272.4
## - colour:citizen 1 4206.7 4272.7
## <none> 4204.7 4272.7
## - year:checks 5 4215.6 4273.6
## - sex:citizen 1 4208.2 4274.2
## - year:age 5 4218.0 4276.0
## - sex:employed 1 4210.9 4276.9
## - age:employed 1 4211.2 4277.2
## - citizen:checks 1 4212.3 4278.3
## - colour:age 1 4214.1 4280.1
## - colour:year 5 4229.0 4287.0
##
## Step: AIC=4272.41
## 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 4208.2 4272.2
## <none> 4206.4 4272.4
## - sex:citizen 1 4209.1 4273.1
## - year:checks 5 4217.4 4273.4
## - sex:employed 1 4211.1 4275.1
## - year:age 5 4219.4 4275.4
## - age:employed 1 4213.0 4277.0
## - citizen:checks 1 4213.5 4277.5
## - colour:age 1 4215.9 4279.9
## - colour:year 5 4230.8 4286.8
##
## Step: AIC=4272.25
## 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> 4208.2 4272.2
## - sex:citizen 1 4211.1 4273.1
## - year:checks 5 4219.4 4273.4
## - sex:employed 1 4212.9 4274.9
## - year:age 5 4221.1 4275.1
## - citizen:checks 1 4214.5 4276.5
## - age:employed 1 4214.7 4276.7
## - colour:age 1 4217.1 4279.1
## - colour:year 5 4232.1 4286.1anova(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 4292.4
## 2 5194 4208.2 20 84.127 7.738e-10 ***
## 3 5169 4180.1 25 28.165 0.3003
## ---
## 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 72.673 1 < 2.2e-16 ***
## citizen 25.783 1 3.820e-07 ***
## checks 205.211 1 < 2.2e-16 ***
## colour 19.572 1 9.687e-06 ***
## year 6.087 5 0.2978477
## age 0.459 1 0.4982736
## colour:year 21.720 5 0.0005917 ***
## colour:age 13.886 1 0.0001942 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1