ANLY 545–Homework 6-Lecture 10

library(visreg)

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library(vcd)

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## Loading required package: grid

library(vcdExtra)

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## Loading required package: gnm

library(effects)

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## Loading required package: carData

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## lattice theme set by effectsTheme()
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library(ggplot2)

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library(car)

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library(ca)

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library(dplyr)

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library(lmtest)

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library(ISLR)

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library(MASS)

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library(ROCR)

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Exercise 7.5. The Caesar data set in vcdExtra:

data("Caesar", package = "vcdExtra")
Caesar.df <- as.data.frame(Caesar)
Caesar.df$Infect <- as.numeric(Caesar.df$Infection %in%
                                 c("Type 1", "Type 2"))

To get a feel for this data set, let’s look at its structure:

str(Caesar)

##  'table' num [1:3, 1:2, 1:2, 1:2] 0 1 17 0 1 1 11 17 30 4 ...
##  - attr(*, "dimnames")=List of 4
##   ..$ Infection  : chr [1:3] "Type 1" "Type 2" "None"
##   ..$ Risk       : chr [1:2] "Yes" "No"
##   ..$ Antibiotics: chr [1:2] "Yes" "No"
##   ..$ Planned    : chr [1:2] "Yes" "No"

str(Caesar.df)

## 'data.frame':    24 obs. of  6 variables:
##  $ Infection  : Factor w/ 3 levels "Type 1","Type 2",..: 1 2 3 1 2 3 1 2 3 1 ...
##  $ Risk       : Factor w/ 2 levels "Yes","No": 1 1 1 2 2 2 1 1 1 2 ...
##  $ Antibiotics: Factor w/ 2 levels "Yes","No": 1 1 1 1 1 1 2 2 2 2 ...
##  $ Planned    : Factor w/ 2 levels "Yes","No": 1 1 1 1 1 1 1 1 1 1 ...
##  $ Freq       : num  0 1 17 0 1 1 11 17 30 4 ...
##  $ Infect     : num  1 1 0 1 1 0 1 1 0 1 ...

str(Caesar.df$Infect)

##  num [1:24] 1 1 0 1 1 0 1 1 0 1 ...

To add a new level of “0” for “none,” we use the following:

Caesar.df$Infection <- factor(Caesar.df$Infection, levels = c("None", "Type 1", "Type 2"))

We can reorder the variables to have level “No” as “zero” so that “No” will not be assigned to “One.”

Caesar.df$Risk <- factor(Caesar.df$Risk, levels = c("No", "Yes"))

Let’s look at the relation between Infection and the other factors:

Infection vs no infection:

Caesar.df.Inf <- glm(Infection ~ Risk + Antibiotics + Planned, family = binomial, weights = Freq, data = Caesar)

Caesar.df.Inf

## 
## Call:  glm(formula = Infection ~ Risk + Antibiotics + Planned, family = binomial, 
##     data = Caesar, weights = Freq)
## 
## Coefficients:
##   (Intercept)         RiskNo  AntibioticsNo      PlannedNo  
##        3.9890         1.2414        -2.6335        -0.7402  
## 
## Degrees of Freedom: 16 Total (i.e. Null);  13 Residual
## Null Deviance:       179.7 
## Residual Deviance: 154.5     AIC: 162.5

(a) Fit the main-effects logit model for the binary response, Infect

Caesar.ef <-allEffects(Caesar.df.Inf)
Caesar.ef

##  model: Infection ~ Risk + Antibiotics + Planned
## 
##  Risk effect
## Risk
##       Yes        No 
## 0.9090564 0.9719023 
## 
##  Antibiotics effect
## Antibiotics
##       Yes        No 
## 0.9857920 0.8328685 
## 
##  Planned effect
## Planned
##       Yes        No 
## 0.9641865 0.9277597

plot(Caesar.ef)

Results: It seems there was no risk of infection in the Caesarian section–antibiotics were taken. It was difficult to determine whether the Caesarian section was planned.

(b) Use summary or car::Anova to test the terms in this model

summary(Caesar.ef, test = "Chisq")

##  model: Infection ~ Risk + Antibiotics + Planned
## 
##  Risk effect
## Risk
##       Yes        No 
## 0.9090564 0.9719023 
## 
##  Lower 95 Percent Confidence Limits
## Risk
##       Yes        No 
## 0.8490996 0.9149531 
## 
##  Upper 95 Percent Confidence Limits
## Risk
##       Yes        No 
## 0.9466865 0.9910885 
## 
##  Antibiotics effect
## Antibiotics
##       Yes        No 
## 0.9857920 0.8328685 
## 
##  Lower 95 Percent Confidence Limits
## Antibiotics
##       Yes        No 
## 0.9545677 0.7341776 
## 
##  Upper 95 Percent Confidence Limits
## Antibiotics
##       Yes        No 
## 0.9956544 0.8999138 
## 
##  Planned effect
## Planned
##       Yes        No 
## 0.9641865 0.9277597 
## 
##  Lower 95 Percent Confidence Limits
## Planned
##       Yes        No 
## 0.9164305 0.8521633 
## 
##  Upper 95 Percent Confidence Limits
## Planned
##       Yes        No 
## 0.9850960 0.9662316

Results: Based on the summary above, there seems to be no risk involved with infection by Caesarian section.

(c) Interpret the coefficients in the fitted model in terms of their effect on the odds of infection.

coef(Caesar.df.Inf)

##   (Intercept)        RiskNo AntibioticsNo     PlannedNo 
##     3.9890313     1.2413990    -2.6335441    -0.7401842

exp(coef(Caesar.df.Inf))

##   (Intercept)        RiskNo AntibioticsNo     PlannedNo 
##   54.00255375    3.46045136    0.07182346    0.47702603

exp(10*coef(Caesar.df.Inf))

##   (Intercept)        RiskNo AntibioticsNo     PlannedNo 
##  2.109322e+17  2.462224e+05  3.653116e-12  6.101278e-04

Results: When the individual variable is increased by three, the exponent of improvement is improved by 2.46 %. (I am not so sure here.)

(d) Make one or more effect plots for this model, showing separate terms, or their combinations.

plot(Caesar.ef)

Results: Again, it seems there was no risk of infection in the Caesarian section–antibiotics were taken. It was difficult to determine whether the Caesarian section was planned.

plot(Caesar)

ANLY 545–Homework 6-Lecture 10

Charles Pierre

July 23, 2018

Exercise 7.5. The Caesar data set in vcdExtra:

To get a feel for this data set, let’s look at its structure:

To add a new level of “0” for “none,” we use the following:

We can reorder the variables to have level “No” as “zero” so that “No” will not be assigned to “One.”

Let’s look at the relation between Infection and the other factors:

Infection vs no infection:

(a) Fit the main-effects logit model for the binary response, Infect

Results: It seems there was no risk of infection in the Caesarian section–antibiotics were taken. It was difficult to determine whether the Caesarian section was planned.

(b) Use summary or car::Anova to test the terms in this model

Results: Based on the summary above, there seems to be no risk involved with infection by Caesarian section.

(c) Interpret the coefficients in the fitted model in terms of their effect on the odds of infection.

Results: When the individual variable is increased by three, the exponent of improvement is improved by 2.46 %. (I am not so sure here.)

(d) Make one or more effect plots for this model, showing separate terms, or their combinations.

Results: Again, it seems there was no risk of infection in the Caesarian section–antibiotics were taken. It was difficult to determine whether the Caesarian section was planned.

Results: In this plot, there is strong evidence of no risk of infection.