Binomial and Multinomial Logistic Regression
Mikhilesh Dehane
6/21/2020
Logistic Regression - LR
Logistic regression helps to deal with categorical outcome variable. Logistic regression produces the probability that something will happen (or not)
EXERCISE 1 - In a case study, we try to figure out if we can use age, types of foods and gender to predict whether an individual is overweight. Use the LRclassP data, IVs are age, food and gender and DV is overweight (1 is yes, 0 is not) With the current data, what method should we use? Binominal or Multinomial regression, or we can use both? If we use another variable “health condition” (HC) as our DV, what method should we use? Binominal or Multinomial regression, or we can use both?
Catgegorical DV - Weight Gain (BINOMIAL/dicotomous - overweight or not), IV - Age continuous, Food categorical, gender categorical
library(readxl)## Warning: package 'readxl' was built under R version 3.6.3setwd("E:/mikhilesh/HU Sem VI ANLY 510 and 506/ANLY 510 Kao Principals and Applications/Lecture and other materials")
data <- read_xlsx("Lecture 9 LRclassP.xlsx")
names(data)## [1] "Age" "Food" "Gender" "Weight" "HC"str(data)## Classes 'tbl_df', 'tbl' and 'data.frame': 58 obs. of 5 variables:
## $ Age : num 31 35 44 34 60 31 47 71 69 66 ...
## $ Food : num 1 1 1 2 1 1 2 0 0 2 ...
## $ Gender: chr "Female" "Female" "Female" "Female" ...
## $ Weight: num 1 0 1 0 1 0 1 1 1 1 ...
## $ HC : chr "NotHealthy" "Healthy" "Average" "Healthy" ...summary(data)## Age Food Gender Weight
## Min. :30.00 Min. :0.0000 Length:58 Min. :0.0000
## 1st Qu.:39.00 1st Qu.:0.0000 Class :character 1st Qu.:0.0000
## Median :56.00 Median :1.0000 Mode :character Median :1.0000
## Mean :51.76 Mean :0.9655 Mean :0.5862
## 3rd Qu.:66.00 3rd Qu.:2.0000 3rd Qu.:1.0000
## Max. :74.00 Max. :2.0000 Max. :1.0000
## HC
## Length:58
## Class :character
## Mode :character
##
##
## #First lets check - whether we have complete predictors and variation across our categorical predictors
with(data, table(Age, Food, Gender, Weight, HC))## , , Gender = Female, Weight = 0, HC = Average
##
## Food
## Age 0 1 2
## 30 0 0 0
## 31 0 0 0
## 33 0 0 0
## 34 0 0 0
## 35 0 0 0
## 39 0 0 0
## 40 0 0 0
## 41 0 0 0
## 42 0 0 0
## 44 0 0 0
## 46 0 0 0
## 47 0 0 0
## 56 1 0 0
## 57 0 0 0
## 58 0 0 0
## 59 0 0 0
## 60 0 0 0
## 61 0 0 0
## 64 0 0 0
## 66 0 0 0
## 69 0 0 0
## 71 0 0 0
## 72 0 0 1
## 73 0 0 0
## 74 0 0 0
##
## , , Gender = Male, Weight = 0, HC = Average
##
## Food
## Age 0 1 2
## 30 0 0 1
## 31 0 0 0
## 33 0 0 0
## 34 0 0 0
## 35 0 0 0
## 39 2 0 0
## 40 0 1 0
## 41 2 0 0
## 42 0 0 0
## 44 0 0 0
## 46 0 0 0
## 47 0 0 0
## 56 0 0 0
## 57 0 0 1
## 58 0 0 0
## 59 0 0 0
## 60 0 0 0
## 61 0 0 0
## 64 0 0 0
## 66 0 0 0
## 69 0 0 0
## 71 0 0 0
## 72 0 0 0
## 73 0 0 0
## 74 0 0 0
##
## , , Gender = Female, Weight = 1, HC = Average
##
## Food
## Age 0 1 2
## 30 0 0 0
## 31 0 0 0
## 33 1 0 0
## 34 0 0 0
## 35 0 0 0
## 39 0 0 0
## 40 0 0 0
## 41 0 0 0
## 42 0 0 0
## 44 0 1 0
## 46 0 0 0
## 47 0 0 1
## 56 0 0 0
## 57 0 0 0
## 58 0 0 0
## 59 0 0 0
## 60 0 0 0
## 61 0 0 0
## 64 0 0 0
## 66 0 0 0
## 69 0 0 0
## 71 0 0 0
## 72 0 0 0
## 73 0 0 0
## 74 0 0 0
##
## , , Gender = Male, Weight = 1, HC = Average
##
## Food
## Age 0 1 2
## 30 0 0 0
## 31 0 0 0
## 33 0 0 0
## 34 0 0 0
## 35 0 0 0
## 39 0 0 0
## 40 0 0 0
## 41 0 0 0
## 42 0 0 0
## 44 0 0 0
## 46 0 0 0
## 47 0 0 0
## 56 0 0 0
## 57 0 0 0
## 58 0 0 0
## 59 0 0 0
## 60 0 0 0
## 61 0 0 0
## 64 0 0 0
## 66 0 0 0
## 69 0 0 0
## 71 0 0 0
## 72 0 0 0
## 73 0 0 0
## 74 0 0 0
##
## , , Gender = Female, Weight = 0, HC = Healthy
##
## Food
## Age 0 1 2
## 30 0 0 0
## 31 0 2 0
## 33 0 0 0
## 34 0 0 2
## 35 0 2 0
## 39 0 0 0
## 40 0 0 0
## 41 0 0 0
## 42 0 0 0
## 44 0 0 0
## 46 0 0 0
## 47 0 0 0
## 56 1 0 0
## 57 0 0 0
## 58 0 0 0
## 59 0 0 0
## 60 0 0 0
## 61 0 0 0
## 64 0 0 0
## 66 0 0 0
## 69 0 0 0
## 71 0 0 0
## 72 0 0 1
## 73 0 0 0
## 74 0 0 0
##
## , , Gender = Male, Weight = 0, HC = Healthy
##
## Food
## Age 0 1 2
## 30 2 0 1
## 31 0 0 0
## 33 0 0 0
## 34 0 0 0
## 35 0 0 0
## 39 0 0 0
## 40 0 1 0
## 41 0 0 0
## 42 0 0 0
## 44 0 0 0
## 46 0 0 0
## 47 0 0 0
## 56 0 0 0
## 57 0 0 1
## 58 0 0 2
## 59 0 0 0
## 60 0 0 0
## 61 0 0 0
## 64 0 0 0
## 66 0 0 0
## 69 0 0 0
## 71 0 0 0
## 72 0 0 0
## 73 0 0 0
## 74 0 0 0
##
## , , Gender = Female, Weight = 1, HC = Healthy
##
## Food
## Age 0 1 2
## 30 0 0 0
## 31 0 0 0
## 33 1 0 0
## 34 0 0 0
## 35 0 0 0
## 39 0 0 0
## 40 0 0 0
## 41 0 0 0
## 42 0 0 0
## 44 0 0 0
## 46 0 0 0
## 47 0 0 0
## 56 0 0 0
## 57 0 0 0
## 58 0 0 0
## 59 0 0 0
## 60 0 0 0
## 61 0 0 0
## 64 0 0 0
## 66 0 0 0
## 69 0 0 0
## 71 0 0 0
## 72 0 0 0
## 73 0 0 0
## 74 0 0 0
##
## , , Gender = Male, Weight = 1, HC = Healthy
##
## Food
## Age 0 1 2
## 30 0 0 0
## 31 0 0 0
## 33 0 0 0
## 34 0 0 0
## 35 0 0 0
## 39 0 0 0
## 40 0 0 0
## 41 0 0 0
## 42 0 0 0
## 44 0 0 0
## 46 1 0 0
## 47 0 0 0
## 56 0 0 0
## 57 0 0 0
## 58 0 0 0
## 59 0 0 0
## 60 0 0 0
## 61 0 0 0
## 64 0 0 0
## 66 0 0 0
## 69 0 0 0
## 71 0 0 0
## 72 0 0 0
## 73 0 0 0
## 74 0 0 0
##
## , , Gender = Female, Weight = 0, HC = NotHealthy
##
## Food
## Age 0 1 2
## 30 0 0 0
## 31 0 0 0
## 33 0 0 0
## 34 0 0 0
## 35 0 0 0
## 39 0 0 0
## 40 0 0 0
## 41 0 0 0
## 42 0 0 0
## 44 0 0 0
## 46 0 0 0
## 47 0 0 0
## 56 0 0 0
## 57 0 0 0
## 58 0 0 0
## 59 0 0 0
## 60 0 0 0
## 61 0 0 0
## 64 0 0 0
## 66 0 0 0
## 69 0 0 0
## 71 0 0 0
## 72 0 0 0
## 73 0 0 0
## 74 0 0 0
##
## , , Gender = Male, Weight = 0, HC = NotHealthy
##
## Food
## Age 0 1 2
## 30 0 0 0
## 31 0 0 0
## 33 0 0 0
## 34 0 0 0
## 35 0 0 0
## 39 0 0 0
## 40 0 0 0
## 41 0 0 0
## 42 0 0 0
## 44 0 0 0
## 46 0 0 0
## 47 0 0 0
## 56 0 0 0
## 57 0 0 0
## 58 0 0 0
## 59 0 0 0
## 60 0 0 0
## 61 0 0 0
## 64 0 0 0
## 66 0 0 0
## 69 0 0 0
## 71 0 0 0
## 72 0 0 0
## 73 0 0 0
## 74 0 0 0
##
## , , Gender = Female, Weight = 1, HC = NotHealthy
##
## Food
## Age 0 1 2
## 30 0 0 0
## 31 0 2 0
## 33 0 0 0
## 34 0 0 0
## 35 0 0 0
## 39 0 0 0
## 40 0 0 0
## 41 0 0 0
## 42 0 0 0
## 44 0 1 0
## 46 0 0 0
## 47 0 0 1
## 56 0 0 0
## 57 0 0 0
## 58 0 0 0
## 59 0 0 0
## 60 0 2 0
## 61 2 0 0
## 64 0 0 0
## 66 0 0 2
## 69 2 0 0
## 71 2 0 0
## 72 0 0 0
## 73 0 0 0
## 74 0 0 0
##
## , , Gender = Male, Weight = 1, HC = NotHealthy
##
## Food
## Age 0 1 2
## 30 0 0 0
## 31 0 0 0
## 33 0 0 0
## 34 0 0 0
## 35 0 0 0
## 39 0 0 0
## 40 0 0 0
## 41 0 0 0
## 42 2 0 0
## 44 0 0 0
## 46 1 0 0
## 47 0 0 0
## 56 0 0 0
## 57 0 0 0
## 58 0 0 0
## 59 0 0 2
## 60 0 0 0
## 61 0 0 0
## 64 0 0 2
## 66 0 0 0
## 69 0 4 0
## 71 0 0 0
## 72 0 0 0
## 73 0 2 0
## 74 0 2 0library(car)## Warning: package 'car' was built under R version 3.6.2## Loading required package: carDatascatterplot(data$Age, data$Weight)
scatterplot(data$Food, data$Food)
data$Age <- factor(data$Age)
factor(data$Age)## [1] 31 35 44 34 60 31 47 71 69 66 33 72 61 56 69 58 42 64 30 69 59 46 41 73 57
## [26] 40 30 39 74 31 35 44 34 60 31 47 71 69 66 33 72 61 56 69 58 42 64 30 69 59
## [51] 46 41 73 57 40 30 39 74
## 25 Levels: 30 31 33 34 35 39 40 41 42 44 46 47 56 57 58 59 60 61 64 66 ... 74data$Food <- factor(data$Food)
data$Food## [1] 1 1 1 2 1 1 2 0 0 2 0 2 0 0 1 2 0 2 0 1 2 0 0 1 2 1 2 0 1 1 1 1 2 1 1 2 0 0
## [39] 2 0 2 0 0 1 2 0 2 0 1 2 0 0 1 2 1 2 0 1
## Levels: 0 1 2data$Gender <- factor(data$Gender)
factor(data$Gender)## [1] Female Female Female Female Female Female Female Female Female Female
## [11] Female Female Female Female Male Male Male Male Male Male
## [21] Male Male Male Male Male Male Male Male Male Female
## [31] Female Female Female Female Female Female Female Female Female Female
## [41] Female Female Female Male Male Male Male Male Male Male
## [51] Male Male Male Male Male Male Male Male
## Levels: Female Malemodel3 <- glm(Weight ~ Food + Age, data = data, family = "binomial")
model3##
## Call: glm(formula = Weight ~ Food + Age, family = "binomial", data = data)
##
## Coefficients:
## (Intercept) Food1 Food2 Age31 Age33 Age34
## -2.257e+01 1.072e-06 -1.765e-06 2.257e+01 4.513e+01 -2.873e-11
## Age35 Age39 Age40 Age41 Age42 Age44
## -2.837e-06 -1.765e-06 -2.837e-06 -1.765e-06 4.513e+01 4.513e+01
## Age46 Age47 Age56 Age57 Age58 Age59
## 4.513e+01 4.513e+01 -1.765e-06 -5.886e-12 -8.613e-12 4.513e+01
## Age60 Age61 Age64 Age66 Age69 Age71
## 4.513e+01 4.513e+01 4.513e+01 4.513e+01 4.513e+01 4.513e+01
## Age72 Age73 Age74
## -1.404e-11 4.513e+01 4.513e+01
##
## Degrees of Freedom: 57 Total (i.e. Null); 31 Residual
## Null Deviance: 78.67
## Residual Deviance: 5.545 AIC: 59.55summary(model3)##
## Call:
## glm(formula = Weight ~ Food + Age, family = "binomial", data = data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.17741 -0.00002 0.00002 0.00002 1.17741
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.257e+01 3.408e+04 -0.001 0.999
## Food1 1.072e-06 4.174e+04 0.000 1.000
## Food2 -1.765e-06 4.820e+04 0.000 1.000
## Age31 2.257e+01 5.388e+04 0.000 1.000
## Age33 4.513e+01 4.820e+04 0.001 0.999
## Age34 -2.873e-11 4.820e+04 0.000 1.000
## Age35 -2.837e-06 6.376e+04 0.000 1.000
## Age39 -1.765e-06 4.820e+04 0.000 1.000
## Age40 -2.837e-06 6.376e+04 0.000 1.000
## Age41 -1.765e-06 4.820e+04 0.000 1.000
## Age42 4.513e+01 4.820e+04 0.001 0.999
## Age44 4.513e+01 6.376e+04 0.001 0.999
## Age46 4.513e+01 4.820e+04 0.001 0.999
## Age47 4.513e+01 4.820e+04 0.001 0.999
## Age56 -1.765e-06 4.820e+04 0.000 1.000
## Age57 -5.886e-12 4.820e+04 0.000 1.000
## Age58 -8.613e-12 4.820e+04 0.000 1.000
## Age59 4.513e+01 4.820e+04 0.001 0.999
## Age60 4.513e+01 6.376e+04 0.001 0.999
## Age61 4.513e+01 4.820e+04 0.001 0.999
## Age64 4.513e+01 4.820e+04 0.001 0.999
## Age66 4.513e+01 4.820e+04 0.001 0.999
## Age69 4.513e+01 4.820e+04 0.001 0.999
## Age71 4.513e+01 4.820e+04 0.001 0.999
## Age72 -1.404e-11 4.820e+04 0.000 1.000
## Age73 4.513e+01 6.376e+04 0.001 0.999
## Age74 4.513e+01 6.376e+04 0.001 0.999
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 78.6723 on 57 degrees of freedom
## Residual deviance: 5.5452 on 31 degrees of freedom
## AIC: 59.545
##
## Number of Fisher Scoring iterations: 21vif(model3) #Performing variance inflation factor## GVIF Df GVIF^(1/(2*Df))
## Food 269.9999 2 4.053600
## Age 269.9999 24 1.123708#Compare to the null model
model3chi <- model3$null.deviance-model3$deviance #calculate chisq
model3chi## [1] 73.12711cdf3 <- model3$df.null-model3$df.residual #calculate degrees of freedom
cdf3## [1] 26chisqp3 <- 1 - pchisq(model3chi, cdf3) #calculate probability
chisqp3## [1] 2.301179e-06#R square
R2.h3 <- model3chi/model3$null.deviance
R2.h3## [1] 0.9295155#Odds ratio
model3$coefficients #odds coefficient## (Intercept) Food1 Food2 Age31 Age33
## -2.256607e+01 1.071921e-06 -1.765217e-06 2.256607e+01 4.513214e+01
## Age34 Age35 Age39 Age40 Age41
## -2.873336e-11 -2.837149e-06 -1.765222e-06 -2.837144e-06 -1.765226e-06
## Age42 Age44 Age46 Age47 Age56
## 4.513214e+01 4.513213e+01 4.513214e+01 4.513214e+01 -1.765233e-06
## Age57 Age58 Age59 Age60 Age61
## -5.885508e-12 -8.613305e-12 4.513214e+01 4.513213e+01 4.513214e+01
## Age64 Age66 Age69 Age71 Age72
## 4.513214e+01 4.513214e+01 4.513213e+01 4.513214e+01 -1.404114e-11
## Age73 Age74
## 4.513213e+01 4.513213e+01exp(model3$coefficients) ## (Intercept) Food1 Food2 Age31 Age33 Age34
## 1.583732e-10 1.000001e+00 9.999982e-01 6.314192e+09 3.986918e+19 1.000000e+00
## Age35 Age39 Age40 Age41 Age42 Age44
## 9.999972e-01 9.999982e-01 9.999972e-01 9.999982e-01 3.986918e+19 3.986914e+19
## Age46 Age47 Age56 Age57 Age58 Age59
## 3.986918e+19 3.986926e+19 9.999982e-01 1.000000e+00 1.000000e+00 3.986926e+19
## Age60 Age61 Age64 Age66 Age69 Age71
## 3.986914e+19 3.986918e+19 3.986925e+19 3.986926e+19 3.986915e+19 3.986918e+19
## Age72 Age73 Age74
## 1.000000e+00 3.986914e+19 3.986914e+19#exp(confint(model3))#Try to perform different models
model <- glm(Weight ~ Age, data = data, family = "binomial") #Weight is dichotomous DV, hence using "bimodal"
model##
## Call: glm(formula = Weight ~ Age, family = "binomial", data = data)
##
## Coefficients:
## (Intercept) Age31 Age33 Age34 Age35 Age39
## -2.257e+01 2.257e+01 4.513e+01 -8.886e-07 -8.886e-07 -8.886e-07
## Age40 Age41 Age42 Age44 Age46 Age47
## -8.886e-07 -8.886e-07 4.513e+01 4.513e+01 4.513e+01 4.513e+01
## Age56 Age57 Age58 Age59 Age60 Age61
## -8.886e-07 -8.886e-07 -8.886e-07 4.513e+01 4.513e+01 4.513e+01
## Age64 Age66 Age69 Age71 Age72 Age73
## 4.513e+01 4.513e+01 4.513e+01 4.513e+01 -8.886e-07 4.513e+01
## Age74
## 4.513e+01
##
## Degrees of Freedom: 57 Total (i.e. Null); 33 Residual
## Null Deviance: 78.67
## Residual Deviance: 5.545 AIC: 55.55summary(model)##
## Call:
## glm(formula = Weight ~ Age, family = "binomial", data = data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.17741 -0.00002 0.00002 0.00002 1.17741
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.257e+01 2.410e+04 -0.001 0.999
## Age31 2.257e+01 2.410e+04 0.001 0.999
## Age33 4.513e+01 4.174e+04 0.001 0.999
## Age34 -8.886e-07 4.174e+04 0.000 1.000
## Age35 -8.886e-07 4.174e+04 0.000 1.000
## Age39 -8.886e-07 4.174e+04 0.000 1.000
## Age40 -8.886e-07 4.174e+04 0.000 1.000
## Age41 -8.886e-07 4.174e+04 0.000 1.000
## Age42 4.513e+01 4.174e+04 0.001 0.999
## Age44 4.513e+01 4.174e+04 0.001 0.999
## Age46 4.513e+01 4.174e+04 0.001 0.999
## Age47 4.513e+01 4.174e+04 0.001 0.999
## Age56 -8.886e-07 4.174e+04 0.000 1.000
## Age57 -8.886e-07 4.174e+04 0.000 1.000
## Age58 -8.886e-07 4.174e+04 0.000 1.000
## Age59 4.513e+01 4.174e+04 0.001 0.999
## Age60 4.513e+01 4.174e+04 0.001 0.999
## Age61 4.513e+01 4.174e+04 0.001 0.999
## Age64 4.513e+01 4.174e+04 0.001 0.999
## Age66 4.513e+01 4.174e+04 0.001 0.999
## Age69 4.513e+01 3.111e+04 0.001 0.999
## Age71 4.513e+01 4.174e+04 0.001 0.999
## Age72 -8.886e-07 4.174e+04 0.000 1.000
## Age73 4.513e+01 4.174e+04 0.001 0.999
## Age74 4.513e+01 4.174e+04 0.001 0.999
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 78.6723 on 57 degrees of freedom
## Residual deviance: 5.5452 on 33 degrees of freedom
## AIC: 55.545
##
## Number of Fisher Scoring iterations: 21#vif(model)
#Based o the results, the AGE model is not significant as predictor.
model2 <- glm(Weight ~ Gender, data = data, family = "binomial")
model2##
## Call: glm(formula = Weight ~ Gender, family = "binomial", data = data)
##
## Coefficients:
## (Intercept) GenderMale
## 0.5878 -0.4543
##
## Degrees of Freedom: 57 Total (i.e. Null); 56 Residual
## Null Deviance: 78.67
## Residual Deviance: 77.95 AIC: 81.95summary(model2)##
## Call:
## glm(formula = Weight ~ Gender, family = "binomial", data = data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.435 -1.235 0.940 1.121 1.121
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.5878 0.3944 1.490 0.136
## GenderMale -0.4543 0.5380 -0.844 0.399
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 78.672 on 57 degrees of freedom
## Residual deviance: 77.954 on 56 degrees of freedom
## AIC: 81.954
##
## Number of Fisher Scoring iterations: 4model4 <- glm(Weight ~ Age + Food, data = data, family = "binomial")
model4##
## Call: glm(formula = Weight ~ Age + Food, family = "binomial", data = data)
##
## Coefficients:
## (Intercept) Age31 Age33 Age34 Age35 Age39
## -2.257e+01 2.257e+01 4.513e+01 -3.534e-12 -2.556e-06 -1.823e-06
## Age40 Age41 Age42 Age44 Age46 Age47
## -2.556e-06 -1.823e-06 4.513e+01 4.513e+01 4.513e+01 4.513e+01
## Age56 Age57 Age58 Age59 Age60 Age61
## -1.823e-06 -1.608e-12 -1.879e-12 4.513e+01 4.513e+01 4.513e+01
## Age64 Age66 Age69 Age71 Age72 Age73
## 4.513e+01 4.513e+01 4.513e+01 4.513e+01 3.966e-13 4.513e+01
## Age74 Food1 Food2
## 4.513e+01 7.327e-07 -1.823e-06
##
## Degrees of Freedom: 57 Total (i.e. Null); 31 Residual
## Null Deviance: 78.67
## Residual Deviance: 5.545 AIC: 59.55summary(model4)##
## Call:
## glm(formula = Weight ~ Age + Food, family = "binomial", data = data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.17741 -0.00002 0.00002 0.00002 1.17741
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.257e+01 3.408e+04 -0.001 0.999
## Age31 2.257e+01 5.388e+04 0.000 1.000
## Age33 4.513e+01 4.820e+04 0.001 0.999
## Age34 -3.534e-12 4.820e+04 0.000 1.000
## Age35 -2.556e-06 6.376e+04 0.000 1.000
## Age39 -1.823e-06 4.820e+04 0.000 1.000
## Age40 -2.556e-06 6.376e+04 0.000 1.000
## Age41 -1.823e-06 4.820e+04 0.000 1.000
## Age42 4.513e+01 4.820e+04 0.001 0.999
## Age44 4.513e+01 6.376e+04 0.001 0.999
## Age46 4.513e+01 4.820e+04 0.001 0.999
## Age47 4.513e+01 4.820e+04 0.001 0.999
## Age56 -1.823e-06 4.820e+04 0.000 1.000
## Age57 -1.608e-12 4.820e+04 0.000 1.000
## Age58 -1.879e-12 4.820e+04 0.000 1.000
## Age59 4.513e+01 4.820e+04 0.001 0.999
## Age60 4.513e+01 6.376e+04 0.001 0.999
## Age61 4.513e+01 4.820e+04 0.001 0.999
## Age64 4.513e+01 4.820e+04 0.001 0.999
## Age66 4.513e+01 4.820e+04 0.001 0.999
## Age69 4.513e+01 4.820e+04 0.001 0.999
## Age71 4.513e+01 4.820e+04 0.001 0.999
## Age72 3.966e-13 4.820e+04 0.000 1.000
## Age73 4.513e+01 6.376e+04 0.001 0.999
## Age74 4.513e+01 6.376e+04 0.001 0.999
## Food1 7.327e-07 4.174e+04 0.000 1.000
## Food2 -1.823e-06 4.820e+04 0.000 1.000
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 78.6723 on 57 degrees of freedom
## Residual deviance: 5.5452 on 31 degrees of freedom
## AIC: 59.545
##
## Number of Fisher Scoring iterations: 21vif(model4)## GVIF Df GVIF^(1/(2*Df))
## Age 269.9999 24 1.123708
## Food 269.9999 2 4.053600model5 <- glm(Weight ~ Age + Gender, data = data, family = "binomial")
model5##
## Call: glm(formula = Weight ~ Age + Gender, family = "binomial", data = data)
##
## Coefficients:
## (Intercept) Age31 Age33 Age34 Age35 Age39
## -2.257e+01 2.257e+01 4.513e+01 -2.470e-06 -2.470e-06 -5.623e-07
## Age40 Age41 Age42 Age44 Age46 Age47
## -5.623e-07 -5.623e-07 4.513e+01 4.513e+01 4.513e+01 4.513e+01
## Age56 Age57 Age58 Age59 Age60 Age61
## -2.470e-06 -5.623e-07 -5.623e-07 4.513e+01 4.513e+01 4.513e+01
## Age64 Age66 Age69 Age71 Age72 Age73
## 4.513e+01 4.513e+01 4.513e+01 4.513e+01 -2.470e-06 4.513e+01
## Age74 GenderMale
## 4.513e+01 -1.907e-06
##
## Degrees of Freedom: 57 Total (i.e. Null); 32 Residual
## Null Deviance: 78.67
## Residual Deviance: 5.545 AIC: 57.55summary(model5)##
## Call:
## glm(formula = Weight ~ Age + Gender, family = "binomial", data = data)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.17741 -0.00002 0.00002 0.00002 1.17741
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.257e+01 4.820e+04 0.000 1.000
## Age31 2.257e+01 4.820e+04 0.000 1.000
## Age33 4.513e+01 5.903e+04 0.001 0.999
## Age34 -2.469e-06 5.903e+04 0.000 1.000
## Age35 -2.469e-06 5.903e+04 0.000 1.000
## Age39 -5.623e-07 4.174e+04 0.000 1.000
## Age40 -5.623e-07 4.174e+04 0.000 1.000
## Age41 -5.623e-07 4.174e+04 0.000 1.000
## Age42 4.513e+01 4.174e+04 0.001 0.999
## Age44 4.513e+01 5.903e+04 0.001 0.999
## Age46 4.513e+01 4.174e+04 0.001 0.999
## Age47 4.513e+01 5.903e+04 0.001 0.999
## Age56 -2.469e-06 5.903e+04 0.000 1.000
## Age57 -5.623e-07 4.174e+04 0.000 1.000
## Age58 -5.623e-07 4.174e+04 0.000 1.000
## Age59 4.513e+01 4.174e+04 0.001 0.999
## Age60 4.513e+01 5.903e+04 0.001 0.999
## Age61 4.513e+01 5.903e+04 0.001 0.999
## Age64 4.513e+01 4.174e+04 0.001 0.999
## Age66 4.513e+01 5.903e+04 0.001 0.999
## Age69 4.513e+01 3.408e+04 0.001 0.999
## Age71 4.513e+01 5.903e+04 0.001 0.999
## Age72 -2.469e-06 5.903e+04 0.000 1.000
## Age73 4.513e+01 4.174e+04 0.001 0.999
## Age74 4.513e+01 4.174e+04 0.001 0.999
## GenderMale -1.907e-06 4.174e+04 0.000 1.000
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 78.6723 on 57 degrees of freedom
## Residual deviance: 5.5452 on 32 degrees of freedom
## AIC: 57.545
##
## Number of Fisher Scoring iterations: 21vif(model5)## GVIF Df GVIF^(1/(2*Df))
## Age 22.5 24 1.067015
## Gender 22.5 1 4.7434171/vif(model5) #WHY DID WE DIVIDE 1 BY VIF(MODEL3) HERE? iS iT SOMETHING TO CHECK SIGNIFICANCE?## GVIF Df GVIF^(1/(2*Df))
## Age 0.04444444 0.04166667 0.9371941
## Gender 0.04444444 1.00000000 0.2108185#Compare different models
anova(model3, model, test = "Chisq")## Analysis of Deviance Table
##
## Model 1: Weight ~ Food + Age
## Model 2: Weight ~ Age
## Resid. Df Resid. Dev Df Deviance Pr(>Chi)
## 1 31 5.5452
## 2 33 5.5452 -2 -8.8818e-16 1##Age is a continuous variable so we have to test its linearity
#Linearity of logit
#logage <- log(data$Age)*data$Age
#logage #we create this new variable logage to check linearity
#Make it another predictor to check if there is interaction effect if yes, we cannot use it as predictor.
#modeltest <- glm(Weight ~ Age + logage, data = data, family = "binomial")
#modeltest
#summary(modeltest)library(multcomp)## Warning: package 'multcomp' was built under R version 3.6.3## Loading required package: mvtnorm## Loading required package: survival## Warning: package 'survival' was built under R version 3.6.2## Loading required package: TH.data## Warning: package 'TH.data' was built under R version 3.6.3## Loading required package: MASS##
## Attaching package: 'TH.data'## The following object is masked from 'package:MASS':
##
## geyserdata$predicted.probabilities <- fitted(model)
head(data[, c("Weight", "Age", "Gender", "predicted.probabilities")])## # A tibble: 6 x 4
## Weight Age Gender predicted.probabilities
## <dbl> <fct> <fct> <dbl>
## 1 1 31 Female 0.5
## 2 0 35 Female 0.000000000158
## 3 1 44 Female 1.00
## 4 0 34 Female 0.000000000158
## 5 1 60 Female 1.00
## 6 0 31 Female 0.5data[, c("Weight", "Age", "Gender", "predicted.probabilities")]## # A tibble: 58 x 4
## Weight Age Gender predicted.probabilities
## <dbl> <fct> <fct> <dbl>
## 1 1 31 Female 0.5
## 2 0 35 Female 0.000000000158
## 3 1 44 Female 1.00
## 4 0 34 Female 0.000000000158
## 5 1 60 Female 1.00
## 6 0 31 Female 0.5
## 7 1 47 Female 1.00
## 8 1 71 Female 1.00
## 9 1 69 Female 1.00
## 10 1 66 Female 1.00
## # ... with 48 more rowsEXERCISE 2 -
In the given scenario, a company has run three ads and we want to know which one works best. We also collected the ages of people who saw the ad as well as the time of day and we are interested if any of these predict on their own and of course whether they interact with the ad shown. We are going to look at some data on click-through rates (whether someone sees an ad on a platform (i.e. Facebook) and clicks it): 0 if they did not click, 1 if they did.
library(readxl)
setwd("E:/mikhilesh/HU Sem VI ANLY 510 and 506/ANLY 510 Kao Principals and Applications/Lecture and other materials")
data2 <- read_xlsx("Lecture 9 LogisticData.xlsx")
names(data2)## [1] "Age" "TimeOfDay" "Ad" "ClickThrough"str(data2)## Classes 'tbl_df', 'tbl' and 'data.frame': 2160 obs. of 4 variables:
## $ Age : num 69 31 66 33 35 72 61 44 34 56 ...
## $ TimeOfDay : num 1 2 3 2 3 1 2 1 3 3 ...
## $ Ad : num 0 1 2 0 1 2 0 1 2 0 ...
## $ ClickThrough: num 1 0 1 1 0 1 1 0 0 1 ...summary(data2)## Age TimeOfDay Ad ClickThrough
## Min. :23.00 Min. :1 Min. :0 Min. :0.0000
## 1st Qu.:38.00 1st Qu.:1 1st Qu.:0 1st Qu.:0.0000
## Median :52.00 Median :2 Median :1 Median :1.0000
## Mean :52.11 Mean :2 Mean :1 Mean :0.6634
## 3rd Qu.:66.00 3rd Qu.:3 3rd Qu.:2 3rd Qu.:1.0000
## Max. :80.00 Max. :3 Max. :2 Max. :1.0000
## NA's :1#First lets check - whether we have complete predictors and variation across our categorical predictors, and also no missisng values
with(data2, table(Age, TimeOfDay, Ad, ClickThrough))## , , Ad = 0, ClickThrough = 0
##
## TimeOfDay
## Age 1 2 3
## 23 1 2 1
## 24 0 3 1
## 25 1 4 1
## 26 2 5 0
## 27 0 3 2
## 28 0 1 0
## 29 0 1 1
## 30 1 3 0
## 31 0 2 2
## 32 1 2 3
## 33 1 3 0
## 34 0 2 3
## 35 0 2 3
## 36 5 2 1
## 37 1 3 1
## 38 1 3 1
## 39 1 4 1
## 40 2 0 1
## 41 3 2 0
## 42 0 2 3
## 43 0 2 1
## 44 3 2 1
## 45 3 1 2
## 46 0 3 2
## 47 0 0 0
## 48 2 0 0
## 49 2 1 1
## 50 0 3 0
## 51 1 0 1
## 52 0 3 1
## 53 1 3 0
## 54 0 0 3
## 55 2 3 1
## 56 0 6 0
## 57 1 3 0
## 58 3 2 1
## 59 1 2 5
## 60 2 3 0
## 61 0 2 1
## 62 0 2 0
## 63 0 4 1
## 64 0 4 0
## 65 0 2 3
## 66 1 4 0
## 67 1 3 2
## 68 2 2 3
## 69 3 2 3
## 70 0 4 5
## 71 0 4 0
## 72 2 3 5
## 73 3 1 1
## 74 4 7 1
## 75 1 2 2
## 76 0 1 1
## 77 1 2 1
## 78 5 2 2
## 79 3 2 2
## 80 1 2 3
##
## , , Ad = 1, ClickThrough = 0
##
## TimeOfDay
## Age 1 2 3
## 23 0 0 0
## 24 1 1 2
## 25 1 1 1
## 26 4 1 0
## 27 1 2 1
## 28 0 1 0
## 29 2 1 1
## 30 1 1 1
## 31 3 4 0
## 32 1 3 0
## 33 1 0 2
## 34 1 1 2
## 35 1 0 3
## 36 2 2 3
## 37 2 1 1
## 38 0 1 1
## 39 0 0 1
## 40 4 2 0
## 41 1 4 1
## 42 2 1 1
## 43 1 1 4
## 44 2 2 2
## 45 1 2 2
## 46 0 2 0
## 47 0 4 1
## 48 0 3 1
## 49 1 0 3
## 50 1 0 3
## 51 1 3 2
## 52 1 6 0
## 53 2 0 0
## 54 2 2 1
## 55 0 1 2
## 56 1 1 1
## 57 1 2 2
## 58 4 0 2
## 59 0 3 3
## 60 1 4 1
## 61 0 2 1
## 62 2 2 1
## 63 0 1 3
## 64 1 3 5
## 65 0 4 0
## 66 3 1 2
## 67 1 3 1
## 68 2 3 1
## 69 1 0 2
## 70 1 3 2
## 71 1 1 2
## 72 1 2 1
## 73 0 0 2
## 74 2 2 1
## 75 4 1 1
## 76 0 0 0
## 77 1 1 2
## 78 0 0 2
## 79 1 0 4
## 80 2 1 1
##
## , , Ad = 2, ClickThrough = 0
##
## TimeOfDay
## Age 1 2 3
## 23 3 0 0
## 24 1 1 1
## 25 2 1 1
## 26 2 1 1
## 27 1 0 1
## 28 1 0 1
## 29 4 1 2
## 30 0 0 1
## 31 4 0 2
## 32 3 0 0
## 33 1 1 1
## 34 0 1 1
## 35 0 0 1
## 36 2 1 1
## 37 1 1 0
## 38 0 0 0
## 39 2 1 0
## 40 3 0 1
## 41 2 0 1
## 42 0 1 0
## 43 3 1 0
## 44 3 1 1
## 45 0 2 0
## 46 1 0 0
## 47 2 1 1
## 48 3 0 1
## 49 2 1 2
## 50 2 1 1
## 51 1 0 4
## 52 0 3 1
## 53 2 1 0
## 54 3 0 0
## 55 2 0 0
## 56 2 0 2
## 57 1 0 2
## 58 1 0 0
## 59 2 1 1
## 60 2 0 0
## 61 1 0 0
## 62 1 1 2
## 63 0 1 1
## 64 2 0 1
## 65 3 0 1
## 66 6 0 1
## 67 3 3 1
## 68 0 0 2
## 69 1 1 0
## 70 3 0 1
## 71 1 1 1
## 72 2 0 1
## 73 1 2 3
## 74 1 0 2
## 75 1 0 2
## 76 0 0 1
## 77 2 1 0
## 78 1 2 3
## 79 2 0 0
## 80 2 0 4
##
## , , Ad = 0, ClickThrough = 1
##
## TimeOfDay
## Age 1 2 3
## 23 0 0 0
## 24 0 0 0
## 25 2 1 6
## 26 1 3 2
## 27 3 4 3
## 28 2 4 3
## 29 3 4 4
## 30 2 1 3
## 31 1 4 4
## 32 2 2 1
## 33 3 2 1
## 34 4 4 2
## 35 3 1 1
## 36 3 4 5
## 37 2 3 1
## 38 1 2 3
## 39 2 4 1
## 40 0 3 5
## 41 2 4 0
## 42 0 4 3
## 43 2 5 2
## 44 1 3 1
## 45 3 6 3
## 46 4 2 1
## 47 4 4 1
## 48 1 2 3
## 49 5 5 0
## 50 2 2 1
## 51 1 3 1
## 52 0 6 4
## 53 3 3 2
## 54 3 3 4
## 55 2 5 2
## 56 3 4 4
## 57 2 5 0
## 58 3 2 4
## 59 2 6 3
## 60 3 4 3
## 61 0 3 2
## 62 1 7 4
## 63 1 2 1
## 64 3 5 4
## 65 2 3 3
## 66 0 4 2
## 67 1 4 4
## 68 1 2 1
## 69 4 3 1
## 70 2 4 2
## 71 0 3 0
## 72 4 5 1
## 73 1 4 3
## 74 4 3 3
## 75 2 3 0
## 76 0 5 0
## 77 5 5 1
## 78 3 5 0
## 79 1 0 2
## 80 0 0 0
##
## , , Ad = 1, ClickThrough = 1
##
## TimeOfDay
## Age 1 2 3
## 23 0 0 0
## 24 0 0 0
## 25 2 4 4
## 26 3 3 3
## 27 1 4 3
## 28 2 6 7
## 29 0 5 3
## 30 1 3 3
## 31 2 2 4
## 32 1 5 4
## 33 1 3 1
## 34 4 3 1
## 35 1 2 4
## 36 3 0 2
## 37 4 3 6
## 38 2 5 2
## 39 2 1 5
## 40 7 0 2
## 41 4 4 3
## 42 2 4 1
## 43 4 3 4
## 44 2 2 3
## 45 2 1 2
## 46 1 2 7
## 47 3 3 4
## 48 4 3 4
## 49 1 3 3
## 50 2 2 4
## 51 6 4 2
## 52 0 1 5
## 53 0 2 4
## 54 4 5 4
## 55 0 5 3
## 56 4 3 7
## 57 3 1 2
## 58 2 1 3
## 59 2 7 1
## 60 2 3 2
## 61 3 1 3
## 62 2 3 1
## 63 3 5 2
## 64 1 5 4
## 65 4 0 0
## 66 2 1 4
## 67 2 2 5
## 68 5 4 5
## 69 2 1 5
## 70 0 4 6
## 71 3 2 3
## 72 1 0 4
## 73 5 0 3
## 74 2 1 6
## 75 2 4 2
## 76 3 4 4
## 77 2 7 2
## 78 1 4 1
## 79 4 2 1
## 80 0 0 0
##
## , , Ad = 2, ClickThrough = 1
##
## TimeOfDay
## Age 1 2 3
## 23 0 0 0
## 24 0 0 0
## 25 6 1 5
## 26 4 2 5
## 27 6 4 3
## 28 5 4 5
## 29 3 3 1
## 30 3 3 2
## 31 5 2 5
## 32 5 0 2
## 33 3 0 3
## 34 3 4 2
## 35 5 0 1
## 36 5 2 2
## 37 1 3 3
## 38 5 1 3
## 39 1 4 3
## 40 5 2 3
## 41 7 1 3
## 42 5 3 4
## 43 3 3 9
## 44 4 0 3
## 45 3 0 2
## 46 7 0 1
## 47 4 2 3
## 48 7 2 6
## 49 4 0 5
## 50 4 1 2
## 51 4 0 7
## 52 4 3 8
## 53 4 1 4
## 54 5 1 3
## 55 6 1 4
## 56 7 1 7
## 57 10 0 5
## 58 7 3 4
## 59 5 4 3
## 60 6 2 2
## 61 1 2 0
## 62 3 1 2
## 63 0 5 3
## 64 3 2 3
## 65 3 3 4
## 66 3 1 8
## 67 6 1 1
## 68 2 1 3
## 69 4 0 6
## 70 4 1 2
## 71 9 3 1
## 72 3 2 0
## 73 5 0 2
## 74 3 0 7
## 75 4 3 2
## 76 3 2 3
## 77 3 4 7
## 78 4 1 1
## 79 4 5 4
## 80 0 0 0#Results shows we have variationn across our data, and no missing value.data2$Ad <- factor(data2$Ad)
factor(data2$Ad)## [1] 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0
## [38] 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1
## [75] 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2
## [112] 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0
## [149] 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1
## [186] 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2
## [223] 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0
## [260] 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1
## [297] 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2
## [334] 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0
## [371] 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1
## [408] 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2
## [445] 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0
## [482] 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1
## [519] 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2
## [556] 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0
## [593] 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1
## [630] 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2
## [667] 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0
## [704] 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1
## [741] 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2
## [778] 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0
## [815] 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1
## [852] 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2
## [889] 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0
## [926] 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1
## [963] 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2
## [1000] 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0
## [1037] 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1
## [1074] 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2
## [1111] 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0
## [1148] 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1
## [1185] 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2
## [1222] 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0
## [1259] 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1
## [1296] 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2
## [1333] 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0
## [1370] 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1
## [1407] 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2
## [1444] 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0
## [1481] 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1
## [1518] 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2
## [1555] 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0
## [1592] 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1
## [1629] 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2
## [1666] 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0
## [1703] 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1
## [1740] 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2
## [1777] 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0
## [1814] 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1
## [1851] 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2
## [1888] 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0
## [1925] 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1
## [1962] 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2
## [1999] 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0
## [2036] 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1
## [2073] 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2
## [2110] 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0
## [2147] 1 2 0 1 2 0 1 2 0 1 2 0 1 2
## Levels: 0 1 2data2$ClickThrough <- factor(data2$ClickThrough)
data2$ClickThrough## [1] 1 0 1 1 0 1 1 0 0 1 1 1 1 0 1 1 1 1 1 0 0 1 1 1 0 1 1 1 1 1 1 1 1 1 0 0 0
## [38] 1 1 1 1 1 0 1 1 1 1 1 1 1 0 0 1 1 1 0 1 1 0 0 1 0 0 1 0 0 0 0 1 0 0 0 1 1
## [75] 1 0 1 1 0 1 1 0 1 1 1 0 0 0 0 0 0 1 1 0 1 1 1 1 1 1 0 1 1 0 0 1 0 0 0 0 1
## [112] 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 0 1 1 1 0 1 1 0 1
## [149] 1 1 1 1 1 1 0 1 1 1 1 1 0 1 0 0 0 0 1 0 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1
## [186] 0 1 1 1 1 0 1 1 0 1 1 1 1 0 1 1 1 0 1 1 0 1 0 1 0 1 0 0 1 0 1 0 1 1 0 0 1
## [223] 0 0 0 0 1 1 0 1 1 0 1 1 0 0 0 1 1 1 1 1 0 1 1 0 1 1 1 0 0 1 0 1 0 0 1 0 1
## [260] 0 1 0 1 1 0 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 1 1 0 1 1 0 1 0 1 1 1 1 0 0 1 1
## [297] 1 1 0 1 1 0 1 1 1 1 1 0 1 1 0 0 1 1 1 1 0 1 1 1 1 0 1 1 0 0 1 0 0 1 1 1 1
## [334] 0 1 1 0 0 1 0 1 0 0 1 0 1 1 1 1 1 1 0 1 1 0 1 0 0 1 1 1 0 1 0 1 1 0 0 1 1
## [371] 1 1 1 0 0 1 1 1 1 0 1 0 0 1 0 1 1 0 1 1 1 1 1 1 1 1 0 0 1 1 1 0 0 0 1 0 1
## [408] 1 1 1 1 1 1 1 0 1 1 0 1 0 1 1 1 0 0 1 1 1 1 0 1 0 0 1 0 0 1 1 0 0 1 1 0 1
## [445] 1 1 1 1 1 0 0 1 1 0 0 0 1 0 0 0 1 1 1 0 1 0 0 1 1 0 1 1 0 1 1 1 1 0 1 0 1
## [482] 1 1 1 1 1 0 1 1 1 1 0 0 1 1 1 1 1 0 0 1 1 1 1 1 0 0 0 1 1 0 1 1 0 1 1 1 1
## [519] 1 0 1 0 1 0 1 1 1 1 1 1 0 1 1 0 0 1 1 0 1 1 1 0 1 0 1 1 0 0 1 1 0 1 0 1 1
## [556] 1 1 1 1 1 0 1 1 0 1 0 1 1 1 0 0 1 0 1 0 1 0 1 1 0 1 1 0 0 1 0 1 1 0 1 1 1
## [593] 1 1 1 1 0 1 1 1 0 0 1 0 1 0 1 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 1 1 0 1 0 0
## [630] 1 1 1 1 0 0 1 0 1 1 0 1 1 1 1 1 1 0 0 1 0 1 1 0 0 1 1 1 0 0 1 1 1 0 1 1 1
## [667] 1 0 1 1 1 0 1 1 1 0 0 1 1 1 0 1 1 1 0 0 1 1 0 1 1 0 1 1 0 0 1 0 1 1 0 1 0
## [704] 0 1 0 1 1 0 1 1 1 1 1 1 0 1 0 1 1 0 1 0 1 0 1 0 0 1 1 1 1 0 0 0 1 0 1 1 0
## [741] 1 1 0 1 1 0 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 0 1 0 1 1 1 0 1 1 1 1 0 1
## [778] 0 1 1 0 0 0 0 1 1 1 1 1 0 1 1 0 1 1 0 1 1 1 1 1 1 1 0 0 0 1 0 0 1 0 1 1 0
## [815] 1 1 0 0 1 1 1 1 1 1 0 1 1 1 1 0 0 0 1 1 1 1 0 0 1 1 0 0 0 1 0 1 1 1 1 1 1
## [852] 0 0 1 1 0 0 1 1 0 1 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 0 1 1 1 1 1
## [889] 1 1 1 0 1 0 1 0 1 1 1 0 0 1 0 0 1 1 0 1 1 0 1 0 0 1 0 0 1 1 0 1 1 1 1 1 1
## [926] 1 1 0 1 1 1 0 0 1 1 1 0 0 1 0 1 0 0 0 0 0 0 1 0 1 0 1 0 0 0 1 1 1 1 1 0 1
## [963] 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 0 1 0 0 1 1 1 0 1 1 1 0 1 1 0 1 1 0 1 1
## [1000] 1 1 0 0 0 1 1 0 1 1 1 1 1 1 0 0 1 0 1 1 1 1 0 1 1 1 0 1 1 1 0 0 1 1 1 1 1
## [1037] 0 0 1 1 1 0 0 1 0 1 0 1 1 1 1 1 1 1 0 1 1 1 1 0 0 0 0 0 1 1 0 0 0 1 1 0 1
## [1074] 1 1 1 1 1 1 1 0 1 1 0 0 1 1 1 1 1 1 0 0 1 0 1 0 1 0 1 0 0 0 1 1 0 1 1 1 0
## [1111] 0 0 1 0 0 1 1 1 1 1 0 0 0 1 1 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 1 1 0 0 1 1 1
## [1148] 1 1 1 1 0 1 1 1 1 1 1 0 0 0 0 1 1 0 0 1 0 0 0 1 1 0 1 1 1 1 1 0 1 1 1 1 0
## [1185] 0 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 0 1 1 1 1 0 1 0 1 1 1 0 1 1 0 1
## [1222] 0 1 0 1 0 1 1 1 0 0 1 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 0 0 1
## [1259] 1 1 1 1 1 1 1 1 0 0 1 1 1 0 0 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 0 0
## [1296] 0 1 0 0 0 0 1 1 0 1 1 1 1 1 1 0 1 0 1 1 1 1 1 0 0 0 1 1 1 1 0 0 1 1 1 0 1
## [1333] 0 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 0 1 1 1 1 0 1 1 0 1
## [1370] 1 1 1 0 1 1 0 1 1 0 0 1 0 0 0 0 1 0 1 1 1 1 1 1 1 1 0 0 1 0 0 1 0 1 1 1 1
## [1407] 1 1 1 0 1 0 1 0 0 1 1 1 1 1 0 0 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 0 0 0 1 0 1
## [1444] 1 1 1 0 0 1 0 1 0 1 0 1 1 1 1 0 1 1 1 0 0 1 1 0 0 0 1 1 1 1 0 1 1 0 1 1 0
## [1481] 1 1 0 1 1 1 1 1 0 1 1 0 1 1 0 0 0 1 0 1 1 1 1 1 1 1 0 1 1 0 1 1 0 1 1 0 1
## [1518] 1 1 0 0 0 1 0 1 1 1 0 0 1 1 0 1 1 1 0 1 1 1 1 1 1 0 1 1 0 1 1 1 1 0 1 1 0
## [1555] 1 0 1 0 0 1 1 0 1 1 1 1 0 0 1 0 1 1 1 1 1 1 1 1 0 0 1 0 1 0 1 1 1 0 1 0 0
## [1592] 0 1 1 0 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 0 0 1 1 1 1 1 0 1 1 0 1 0 1 1 1 1 1
## [1629] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0
## [1666] 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 0 1 0 1 0 0 1 0 1
## [1703] 1 0 0 1 0 0 1 1 1 0 0 0 0 1 1 1 1 1 0 1 1 1 1 0 1 1 1 0 1 0 0 1 1 1 1 0 1
## [1740] 1 1 0 0 1 1 1 0 1 1 1 1 1 1 0 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 0 0 1 0 0 0 1
## [1777] 1 0 1 1 1 1 0 0 0 0 0 1 1 1 0 0 1 1 1 0 1 0 0 1 0 1 1 0 0 1 0 1 1 0 1 1 1
## [1814] 0 1 0 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1 0 1
## [1851] 0 1 1 1 0 0 1 1 0 0 1 1 1 1 0 0 1 1 1 0 1 0 0 1 1 1 1 0 1 1 1 1 1 1 0 1 1
## [1888] 0 1 1 0 0 1 0 1 1 1 1 1 0 1 0 1 1 0 0 1 1 0 0 1 1 1 0 1 1 1 0 1 1 0 0 1 1
## [1925] 1 1 0 1 1 0 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 0 0 1 1 0 0 0 1 1 1
## [1962] 1 1 0 0 1 0 1 1 0 1 0 1 0 1 0 0 1 0 1 1 0 1 1 0 1 0 1 1 1 0 1 0 1 1 1 0 1
## [1999] 0 0 0 0 1 1 1 0 1 0 1 1 0 1 1 0 1 1 1 1 0 1 1 1 0 0 1 1 0 0 1 1 1 1 1 1 0
## [2036] 1 1 0 1 0 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 1 1 0 0 1 0 1 1 1 1 1 0 0 1 1 1 1
## [2073] 1 0 0 0 1 1 1 1 1 0 1 1 1 0 1 1 1 1 0 0 0 0 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1
## [2110] 1 0 1 1 1 0 1 1 1 1 0 1 1 1 0 1 0 1 1 1 1 0 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1
## [2147] 1 0 0 0 1 0 1 1 0 1 1 0 1 1
## Levels: 0 1data2$TimeOfDay <- factor(data2$TimeOfDay)
data2$TimeOfDay## [1] 1 2 3 2 3 1 2 1 3 3 1 2 3 2
## [15] 1 3 2 1 1 2 3 2 1 3 2 3 1 1
## [29] 3 2 2 3 1 1 2 3 2 3 1 2 1 3
## [43] 3 1 2 3 2 1 3 2 1 1 2 3 2 1
## [57] 3 2 3 1 1 3 2 2 3 1 1 2 3 2
## [71] 3 1 2 1 3 3 1 2 3 2 1 3 2 1
## [85] 1 2 3 2 1 3 2 3 1 1 3 2 2 3
## [99] 1 1 2 3 2 3 1 2 1 3 3 1 2 3
## [113] 2 1 3 2 1 1 2 3 2 1 3 2 3 1
## [127] 1 3 2 2 3 1 2 3 1 2 1 3 3 1
## [141] 2 3 2 1 3 2 1 1 2 3 2 1 3 2
## [155] 3 1 1 3 2 2 3 1 1 2 3 2 3 1
## [169] 2 1 3 3 1 2 3 2 1 3 2 1 <NA> 2
## [183] 3 2 1 3 2 3 1 1 3 2 2 3 1 1
## [197] 2 3 2 3 1 2 1 3 3 1 2 3 2 1
## [211] 3 2 1 1 2 3 2 1 3 2 3 1 1 3
## [225] 2 2 3 1 1 2 3 2 3 1 2 1 3 3
## [239] 1 2 3 2 1 3 2 1 1 2 3 2 1 3
## [253] 2 3 1 1 3 2 2 3 1 2 3 1 2 1
## [267] 3 3 1 2 3 2 1 3 2 1 1 2 3 2
## [281] 1 3 2 3 1 1 3 2 2 3 1 1 2 3
## [295] 2 3 1 2 1 3 3 1 2 3 2 1 3 2
## [309] 1 1 2 3 2 1 3 2 3 1 1 3 2 2
## [323] 3 1 1 2 3 2 3 1 2 1 3 3 1 2
## [337] 3 2 1 3 2 1 1 2 3 2 1 3 2 3
## [351] 1 1 3 2 2 3 1 1 2 3 2 3 1 2
## [365] 1 3 3 1 2 3 2 1 3 2 1 1 2 3
## [379] 2 1 3 2 3 1 1 3 2 2 3 1 2 3
## [393] 1 2 1 3 3 1 2 3 2 1 3 2 1 1
## [407] 2 3 2 1 3 2 3 1 1 3 2 2 3 1
## [421] 1 2 3 2 3 1 2 1 3 3 1 2 3 2
## [435] 1 3 2 1 1 2 3 2 1 3 2 3 1 1
## [449] 3 2 2 3 1 1 2 3 2 3 1 2 1 3
## [463] 3 1 2 3 2 1 3 2 1 1 2 3 2 1
## [477] 3 2 3 1 1 3 2 2 3 1 2 3 1 2
## [491] 1 3 3 1 2 3 2 1 3 2 1 1 2 3
## [505] 2 1 3 2 3 1 1 3 2 2 3 1 1 2
## [519] 3 2 3 1 2 1 3 3 1 2 3 2 1 3
## [533] 2 1 1 2 3 2 1 3 2 3 1 1 3 2
## [547] 2 3 1 1 2 3 2 3 1 2 1 3 3 1
## [561] 2 3 2 1 3 2 1 1 2 3 2 1 3 2
## [575] 3 1 1 3 2 2 3 1 1 2 3 2 3 1
## [589] 2 1 3 3 1 2 3 2 1 3 2 1 1 2
## [603] 3 2 1 3 2 3 1 1 3 2 2 3 1 2
## [617] 3 1 2 1 3 3 1 2 3 2 1 3 2 1
## [631] 1 2 3 2 1 3 2 3 1 1 3 2 2 3
## [645] 1 1 2 3 2 3 1 2 1 3 3 1 2 3
## [659] 2 1 3 2 1 1 2 3 2 1 3 2 3 1
## [673] 1 3 2 2 3 1 1 2 3 2 3 1 2 1
## [687] 3 3 1 2 3 2 1 3 2 1 1 2 3 2
## [701] 1 3 2 3 1 1 3 2 2 3 1 2 3 1
## [715] 2 1 3 3 1 2 3 2 1 3 2 1 1 2
## [729] 3 2 1 3 2 3 1 1 3 2 2 3 1 1
## [743] 2 3 2 3 1 2 1 3 3 1 2 3 2 1
## [757] 3 2 1 1 2 3 2 1 3 2 3 1 1 3
## [771] 2 2 3 1 1 2 3 2 3 1 2 1 3 3
## [785] 1 2 3 2 1 3 2 1 1 2 3 2 1 3
## [799] 2 3 1 1 3 2 2 3 1 1 2 3 2 3
## [813] 1 2 1 3 3 1 2 3 2 1 3 2 1 1
## [827] 2 3 2 1 3 2 3 1 1 3 2 2 3 1
## [841] 2 3 1 2 1 3 3 1 2 3 2 1 3 2
## [855] 1 1 2 3 2 1 3 2 3 1 1 3 2 2
## [869] 3 1 1 2 3 2 3 1 2 1 3 3 1 2
## [883] 3 2 1 3 2 1 1 2 3 2 1 3 2 3
## [897] 1 1 3 2 2 3 1 1 2 3 2 3 1 2
## [911] 1 3 3 1 2 3 2 1 3 2 1 1 2 3
## [925] 2 1 3 2 3 1 1 3 2 2 3 1 2 3
## [939] 1 2 1 3 3 1 2 3 2 1 3 2 1 1
## [953] 2 3 2 1 3 2 3 1 1 3 2 2 3 1
## [967] 1 2 3 2 3 1 2 1 3 3 1 2 3 2
## [981] 1 3 2 1 1 2 3 2 1 3 2 3 1 1
## [995] 3 2 2 3 1 1 2 3 2 3 1 2 1 3
## [1009] 3 1 2 3 2 1 3 2 1 1 2 3 2 1
## [1023] 3 2 3 1 1 3 2 2 3 1 1 2 3 2
## [1037] 3 1 2 1 3 3 1 2 3 2 1 3 2 1
## [1051] 1 2 3 2 1 3 2 3 1 1 3 2 2 3
## [1065] 1 2 3 1 2 1 3 3 1 2 3 2 1 3
## [1079] 2 1 1 2 3 2 1 3 2 3 1 1 3 2
## [1093] 2 3 1 1 2 3 2 3 1 2 1 3 3 1
## [1107] 2 3 2 1 3 2 1 1 2 3 2 1 3 2
## [1121] 3 1 1 3 2 2 3 1 1 2 3 2 3 1
## [1135] 2 1 3 3 1 2 3 2 1 3 2 1 1 2
## [1149] 3 2 1 3 2 3 1 1 3 2 2 3 1 2
## [1163] 3 1 2 1 3 3 1 2 3 2 1 3 2 1
## [1177] 1 2 3 2 1 3 2 3 1 1 3 2 2 3
## [1191] 1 1 2 3 2 3 1 2 1 3 3 1 2 3
## [1205] 2 1 3 2 1 1 2 3 2 1 3 2 3 1
## [1219] 1 3 2 2 3 1 1 2 3 2 3 1 2 1
## [1233] 3 3 1 2 3 2 1 3 2 1 1 2 3 2
## [1247] 1 3 2 3 1 1 3 2 2 3 1 1 2 3
## [1261] 2 3 1 2 1 3 3 1 2 3 2 1 3 2
## [1275] 1 1 2 3 2 1 3 2 3 1 1 3 2 2
## [1289] 3 1 2 3 1 2 1 3 3 1 2 3 2 1
## [1303] 3 2 1 1 2 3 2 1 3 2 3 1 1 3
## [1317] 2 2 3 1 1 2 3 2 3 1 2 1 3 3
## [1331] 1 2 3 2 1 3 2 1 1 2 3 2 1 3
## [1345] 2 3 1 1 3 2 2 3 1 1 2 3 2 3
## [1359] 1 2 1 3 3 1 2 3 2 1 3 2 1 1
## [1373] 2 3 2 1 3 2 3 1 1 3 2 2 3 1
## [1387] 2 3 1 2 1 3 3 1 2 3 2 1 3 2
## [1401] 1 1 2 3 2 1 3 2 3 1 1 3 2 2
## [1415] 3 1 1 2 3 2 3 1 2 1 3 3 1 2
## [1429] 3 2 1 3 2 1 1 2 3 2 1 3 2 3
## [1443] 1 1 3 2 2 3 1 1 2 3 2 3 1 2
## [1457] 1 3 3 1 2 3 2 1 3 2 1 1 2 3
## [1471] 2 1 3 2 3 1 1 3 2 2 3 1 1 2
## [1485] 3 2 3 1 2 1 3 3 1 2 3 2 1 3
## [1499] 2 1 1 2 3 2 1 3 2 3 1 1 3 2
## [1513] 2 3 1 2 3 1 2 1 3 3 1 2 3 2
## [1527] 1 3 2 1 1 2 3 2 1 3 2 3 1 1
## [1541] 3 2 2 3 1 1 2 3 2 3 1 2 1 3
## [1555] 3 1 2 3 2 1 3 2 1 1 2 3 2 1
## [1569] 3 2 3 1 1 3 2 2 3 1 1 2 3 2
## [1583] 3 1 2 1 3 3 1 2 3 2 1 3 2 1
## [1597] 1 2 3 2 1 3 2 3 1 1 3 2 2 3
## [1611] 1 2 3 1 2 1 3 3 1 2 3 2 1 3
## [1625] 2 1 1 2 3 2 1 3 2 3 1 1 3 2
## [1639] 2 3 1 1 2 3 2 3 1 2 1 3 3 1
## [1653] 2 3 2 1 3 2 1 1 2 3 2 1 3 2
## [1667] 3 1 1 3 2 2 3 1 1 2 3 2 3 1
## [1681] 2 1 3 3 1 2 3 2 1 3 2 1 1 2
## [1695] 3 2 1 3 2 3 1 1 3 2 2 3 1 1
## [1709] 2 3 2 3 1 2 1 3 3 1 2 3 2 1
## [1723] 3 2 1 1 2 3 2 1 3 2 3 1 1 3
## [1737] 2 2 3 1 2 3 1 2 1 3 3 1 2 3
## [1751] 2 1 3 2 1 1 2 3 2 1 3 2 3 1
## [1765] 1 3 2 2 3 1 1 2 3 2 3 1 2 1
## [1779] 3 3 1 2 3 2 1 3 2 1 1 2 3 2
## [1793] 1 3 2 3 1 1 3 2 2 3 1 1 2 3
## [1807] 2 3 1 2 1 3 3 1 2 3 2 1 3 2
## [1821] 1 1 2 3 2 1 3 2 3 1 1 3 2 2
## [1835] 3 1 2 3 1 2 1 3 3 1 2 3 2 1
## [1849] 3 2 1 1 2 3 2 1 3 2 3 1 1 3
## [1863] 2 2 3 1 1 2 3 2 3 1 2 1 3 3
## [1877] 1 2 3 2 1 3 2 1 1 2 3 2 1 3
## [1891] 2 3 1 1 3 2 2 3 1 1 2 3 2 3
## [1905] 1 2 1 3 3 1 2 3 2 1 3 2 1 1
## [1919] 2 3 2 1 3 2 3 1 1 3 2 2 3 1
## [1933] 1 2 3 2 3 1 2 1 3 3 1 2 3 2
## [1947] 1 3 2 1 1 2 3 2 1 3 2 3 1 1
## [1961] 3 2 2 3 1 2 3 1 2 1 3 3 1 2
## [1975] 3 2 1 3 2 1 1 2 3 2 1 3 2 3
## [1989] 1 1 3 2 2 3 1 1 2 3 2 3 1 2
## [2003] 1 3 3 1 2 3 2 1 3 2 1 1 2 3
## [2017] 2 1 3 2 3 1 1 3 2 2 3 1 1 2
## [2031] 3 2 3 1 2 1 3 3 1 2 3 2 1 3
## [2045] 2 1 1 2 3 2 1 3 2 3 1 1 3 2
## [2059] 2 3 1 2 3 1 2 1 3 3 1 2 3 2
## [2073] 1 3 2 1 1 2 3 2 1 3 2 3 1 1
## [2087] 3 2 2 3 1 1 2 3 2 3 1 2 1 3
## [2101] 3 1 2 3 2 1 3 2 1 1 2 3 2 1
## [2115] 3 2 3 1 1 3 2 2 3 1 1 2 3 2
## [2129] 3 1 2 1 3 3 1 2 3 2 1 3 2 1
## [2143] 1 2 3 2 1 3 2 3 1 1 3 2 2 3
## [2157] 1 1 2 3
## Levels: 1 2 3library(car)
#scatterplot(data2$Ad, data2$ClickThrough)
#scatterplot(data2$TimeOfDay, data2$ClickThrough)model6 <- glm(ClickThrough ~ Ad, data = data2, family = "binomial") # DV clickthrough - dichotomous/binomial, IV AD
model6##
## Call: glm(formula = ClickThrough ~ Ad, family = "binomial", data = data2)
##
## Coefficients:
## (Intercept) Ad1 Ad2
## 0.3997 0.2439 0.6262
##
## Degrees of Freedom: 2159 Total (i.e. Null); 2157 Residual
## Null Deviance: 2759
## Residual Deviance: 2728 AIC: 2734summary(model6)##
## Call:
## glm(formula = ClickThrough ~ Ad, family = "binomial", data = data2)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.6323 -1.3512 0.7828 0.9190 1.0131
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.39968 0.07603 5.257 1.46e-07 ***
## Ad1 0.24387 0.10923 2.233 0.0256 *
## Ad2 0.62617 0.11371 5.507 3.66e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 2759.3 on 2159 degrees of freedom
## Residual deviance: 2728.2 on 2157 degrees of freedom
## AIC: 2734.2
##
## Number of Fisher Scoring iterations: 4#REsults shows Ad1 and 2 have sme impact on clickthrough or not
#vif(model6) #Performing variance inflation factor#Compare to the null model
model6chi <- model6$null.deviance-model6$deviance #calculate deviance/chisq
model6chi## [1] 31.12551cdf6 <- model6$df.null-model6$df.residual #calculate degrees of freedom
cdf6## [1] 2chisqp6 <- 1 - pchisq(model6chi, cdf6) #calculate probability
chisqp6 # probalibity is 1.742537e-07 so we have an overall very significant model## [1] 1.742537e-07#R square
R2.h6 <- model6chi/model6$null.deviance
R2.h6## [1] 0.01128004#Odds ratio
model6$coefficients #odds coefficient## (Intercept) Ad1 Ad2
## 0.3996814 0.2438688 0.6261715exp(model6$coefficients) ## (Intercept) Ad1 Ad2
## 1.491349 1.276177 1.870436# ODD RATIO Results suggests that 1. if you watch Ad 1 there is a 27% more chance that you clickthrough compared to those participants who didn't watch any Ad, and 2. if you watch Ad 2 there is a 87% more chance that you clickthrough compared to those participants who didn't watch any Ad.
exp(confint(model6)) ## Waiting for profiling to be done...## 2.5 % 97.5 %
## (Intercept) 1.285733 1.732381
## Ad1 1.030452 1.581378
## Ad2 1.497939 2.339636#Try to perform different models
model7 <- glm(ClickThrough ~ Ad + TimeOfDay, data = data2, family = "binomial") #ClickThrough is dichotomous DV, hence using "bimodal"
model7##
## Call: glm(formula = ClickThrough ~ Ad + TimeOfDay, family = "binomial",
## data = data2)
##
## Coefficients:
## (Intercept) Ad1 Ad2 TimeOfDay2 TimeOfDay3
## 0.38706 0.22930 0.60653 -0.05024 0.12248
##
## Degrees of Freedom: 2158 Total (i.e. Null); 2154 Residual
## (1 observation deleted due to missingness)
## Null Deviance: 2759
## Residual Deviance: 2725 AIC: 2735summary(model7)##
## Call:
## glm(formula = ClickThrough ~ Ad + TimeOfDay, family = "binomial",
## data = data2)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.6730 -1.3456 0.7937 0.9483 1.0381
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.38706 0.10698 3.618 0.000297 ***
## Ad1 0.22930 0.10996 2.085 0.037044 *
## Ad2 0.60653 0.11745 5.164 2.42e-07 ***
## TimeOfDay2 -0.05024 0.11501 -0.437 0.662219
## TimeOfDay3 0.12248 0.11462 1.069 0.285245
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 2758.5 on 2158 degrees of freedom
## Residual deviance: 2724.7 on 2154 degrees of freedom
## (1 observation deleted due to missingness)
## AIC: 2734.7
##
## Number of Fisher Scoring iterations: 4vif(model7)## GVIF Df GVIF^(1/(2*Df))
## Ad 1.071806 2 1.017487
## TimeOfDay 1.071806 2 1.017487#Based on the results, the TimeofDay model is not significant as predictor.
#Compare to the null model
model7chi <- model7$null.deviance-model7$deviance #calculate deviance/chisq
model7chi## [1] 33.78481cdf7 <- model7$df.null-model7$df.residual #calculate degrees of freedom
cdf7## [1] 4chisqp7 <- 1 - pchisq(model7chi, cdf7) #calculate probability
chisqp7 # probalibity is 8.248783e-07 so we have an overall very significant model, but predictor timeofday is not significantg at all## [1] 8.248783e-07model8 <- glm(ClickThrough ~ Ad + Age, data = data2, family = "binomial")
model8##
## Call: glm(formula = ClickThrough ~ Ad + Age, family = "binomial", data = data2)
##
## Coefficients:
## (Intercept) Ad1 Ad2 Age
## 0.655635 0.241318 0.624296 -0.004864
##
## Degrees of Freedom: 2159 Total (i.e. Null); 2156 Residual
## Null Deviance: 2759
## Residual Deviance: 2725 AIC: 2733summary(model8)##
## Call:
## glm(formula = ClickThrough ~ Ad + Age, family = "binomial", data = data2)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.6964 -1.3698 0.7939 0.9464 1.0646
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.655635 0.168435 3.893 9.92e-05 ***
## Ad1 0.241318 0.109316 2.208 0.0273 *
## Ad2 0.624296 0.113789 5.486 4.10e-08 ***
## Age -0.004864 0.002849 -1.707 0.0877 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 2759.3 on 2159 degrees of freedom
## Residual deviance: 2725.3 on 2156 degrees of freedom
## AIC: 2733.3
##
## Number of Fisher Scoring iterations: 4vif(model8)## GVIF Df GVIF^(1/(2*Df))
## Ad 1.000146 2 1.000036
## Age 1.000146 1 1.000073#Based on the results, the Age model may be significant at 0.1 level but not at 0.05 level. We have two predictors in this model, so we need to first make sure we are not violating assumption of multicollinearity - Number of Fisher Scoring iterations: 4 shows no multicollinearity problem
#Compare to the null model
model8chi <- model8$null.deviance-model8$deviance #calculate deviance/chisq
model8chi## [1] 34.04591cdf8 <- model8$df.null-model8$df.residual #calculate degrees of freedom
cdf8## [1] 3chisqp8 <- 1 - pchisq(model8chi, cdf8) #calculate probability
chisqp8 # probalibity is 1.937465e-07 so we have an overall very significant model## [1] 1.937465e-07#R square
R2.h8 <- model8chi/model8$null.deviance
R2.h8## [1] 0.01233841#Odds ratio
model8$coefficients #odds coefficient## (Intercept) Ad1 Ad2 Age
## 0.655635062 0.241317817 0.624296221 -0.004864286exp(model8$coefficients) ## (Intercept) Ad1 Ad2 Age
## 1.9263655 1.2729255 1.8669316 0.9951475# ODD RATIO Results suggests that whenyou get 1 year older, you have about 0.005% less chance of clickthrough (Age -0.004864286; continuous valriable - interpreted slightly different)
exp(confint(model8)) ## Waiting for profiling to be done...## 2.5 % 97.5 %
## (Intercept) 1.3862297 2.683446
## Ad1 1.0276492 1.577608
## Ad2 1.4948999 2.335602
## Age 0.9895978 1.000714#Compare different models
anova(model8, model6, test = "Chisq")## Analysis of Deviance Table
##
## Model 1: ClickThrough ~ Ad + Age
## Model 2: ClickThrough ~ Ad
## Resid. Df Resid. Dev Df Deviance Pr(>Chi)
## 1 2156 2725.3
## 2 2157 2728.2 -1 -2.9204 0.08747 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#Age is a continuous variable so we have to tgest its linearity
#Linearity of logit
library(multcomp)
logage2 <- log(data2$Age)*data2$Age
logage2 #We create this new variable logage2 to test linearity## [1] 292.15335 106.45360 276.51721 115.38475 124.43718 307.91996 250.76331
## [8] 166.50434 119.89626 225.41969 292.15335 235.50569 156.98212 245.66067
## [15] 266.16852 102.03592 292.15335 240.57471 176.11750 106.45360 180.95694
## [22] 152.25645 313.20354 230.45392 302.65027 147.55518 102.03592 142.87890
## [29] 318.50082 142.87890 271.33517 215.40514 318.50082 129.00668 271.33517
## [36] 190.69919 84.71051 93.30173 161.73160 250.76331 302.65027 334.47302
## [43] 318.50082 119.89626 345.18638 240.57471 334.47302 286.92652 334.47302
## [50] 138.22827 84.71051 313.20354 185.81765 318.50082 97.65158 245.66067
## [57] 115.38475 190.69919 235.50569 266.16852 235.50569 230.45392 313.20354
## [64] 318.50082 235.50569 88.98760 129.00668 176.11750 161.73160 142.87890
## [71] 115.38475 80.47190 97.65158 84.71051 286.92652 97.65158 250.76331
## [78] 297.39467 292.15335 80.47190 110.90355 156.98212 110.90355 230.45392
## [85] 129.00668 266.16852 200.52311 205.46467 97.65158 106.45360 225.41969
## [92] 302.65027 152.25645 334.47302 329.13573 147.55518 313.20354 156.98212
## [99] 84.71051 334.47302 250.76331 80.47190 266.16852 313.20354 166.50434
## [106] 255.88233 84.71051 323.81161 133.60396 88.98760 147.55518 281.71441
## [113] 286.92652 271.33517 185.81765 297.39467 345.18638 286.92652 88.98760
## [120] 245.66067 329.13573 102.03592 318.50082 329.13573 307.91996 115.38475
## [127] 307.91996 276.51721 276.51721 255.88233 80.47190 339.82329 147.55518
## [134] 240.57471 97.65158 84.71051 147.55518 292.15335 297.39467 255.88233
## [141] 302.65027 205.46467 266.16852 313.20354 102.03592 200.52311 161.73160
## [148] 124.43718 323.81161 93.30173 185.81765 106.45360 271.33517 245.66067
## [155] 292.15335 147.55518 124.43718 313.20354 93.30173 215.40514 323.81161
## [162] 329.13573 292.15335 80.47190 276.51721 240.57471 129.00668 281.71441
## [169] 129.00668 334.47302 205.46467 271.33517 80.47190 161.73160 255.88233
## [176] 286.92652 106.45360 129.00668 281.71441 240.57471 210.42547 97.65158
## [183] 334.47302 276.51721 261.01749 225.41969 142.87890 185.81765 93.30173
## [190] 152.25645 334.47302 161.73160 180.95694 138.22827 276.51721 115.38475
## [197] 329.13573 171.29981 133.60396 124.43718 80.47190 180.95694 323.81161
## [204] 147.55518 147.55518 235.50569 302.65027 329.13573 261.01749 271.33517
## [211] 245.66067 266.16852 106.45360 84.71051 276.51721 110.90355 266.16852
## [218] 110.90355 235.50569 88.98760 129.00668 110.90355 345.18638 215.40514
## [225] 195.60115 339.82329 276.51721 245.66067 235.50569 97.65158 240.57471
## [232] 281.71441 88.98760 152.25645 318.50082 225.41969 261.01749 245.66067
## [239] 88.98760 106.45360 276.51721 102.03592 220.40333 205.46467 161.73160
## [246] 225.41969 307.91996 334.47302 313.20354 88.98760 124.43718 225.41969
## [253] 80.47190 225.41969 323.81161 235.50569 161.73160 166.50434 220.40333
## [260] 266.16852 339.82329 106.45360 88.98760 88.98760 171.29981 345.18638
## [267] 225.41969 176.11750 161.73160 119.89626 240.57471 93.30173 142.87890
## [274] 80.47190 152.25645 84.71051 161.73160 271.33517 115.38475 97.65158
## [281] 266.16852 161.73160 88.98760 102.03592 297.39467 313.20354 205.46467
## [288] 171.29981 119.89626 106.45360 323.81161 255.88233 297.39467 200.52311
## [295] 297.39467 195.60115 80.47190 220.40333 276.51721 200.52311 161.73160
## [302] 350.56213 286.92652 210.42547 266.16852 245.66067 166.50434 205.46467
## [309] 129.00668 292.15335 166.50434 200.52311 171.29981 235.50569 297.39467
## [316] 142.87890 80.47190 230.45392 318.50082 133.60396 133.60396 225.41969
## [323] 152.25645 156.98212 147.55518 245.66067 142.87890 261.01749 102.03592
## [330] 210.42547 266.16852 245.66067 276.51721 166.50434 276.51721 323.81161
## [337] 345.18638 205.46467 345.18638 88.98760 200.52311 318.50082 318.50082
## [344] 185.81765 307.91996 133.60396 80.47190 220.40333 200.52311 225.41969
## [351] 185.81765 152.25645 292.15335 152.25645 210.42547 255.88233 345.18638
## [358] 147.55518 334.47302 245.66067 124.43718 240.57471 286.92652 345.18638
## [365] 171.29981 97.65158 297.39467 235.50569 261.01749 88.98760 345.18638
## [372] 255.88233 133.60396 147.55518 190.69919 119.89626 180.95694 281.71441
## [379] 230.45392 297.39467 84.71051 276.51721 97.65158 302.65027 318.50082
## [386] 161.73160 334.47302 115.38475 129.00668 185.81765 220.40333 266.16852
## [393] 281.71441 215.40514 185.81765 215.40514 161.73160 266.16852 205.46467
## [400] 147.55518 235.50569 76.27329 171.29981 106.45360 185.81765 72.11637
## [407] 225.41969 152.25645 297.39467 200.52311 210.42547 281.71441 171.29981
## [414] 225.41969 292.15335 220.40333 102.03592 115.38475 205.46467 210.42547
## [421] 313.20354 119.89626 93.30173 138.22827 156.98212 240.57471 292.15335
## [428] 318.50082 276.51721 350.56213 240.57471 142.87890 297.39467 124.43718
## [435] 180.95694 323.81161 240.57471 210.42547 190.69919 240.57471 297.39467
## [442] 115.38475 318.50082 84.71051 205.46467 205.46467 245.66067 190.69919
## [449] 147.55518 171.29981 93.30173 185.81765 124.43718 318.50082 255.88233
## [456] 190.69919 88.98760 318.50082 142.87890 110.90355 161.73160 334.47302
## [463] 106.45360 200.52311 93.30173 110.90355 152.25645 195.60115 266.16852
## [470] 205.46467 180.95694 119.89626 166.50434 318.50082 225.41969 313.20354
## [477] 156.98212 195.60115 281.71441 276.51721 210.42547 302.65027 307.91996
## [484] 129.00668 225.41969 138.22827 205.46467 133.60396 318.50082 281.71441
## [491] 147.55518 339.82329 147.55518 129.00668 97.65158 147.55518 161.73160
## [498] 297.39467 215.40514 176.11750 124.43718 230.45392 215.40514 106.45360
## [505] 255.88233 102.03592 313.20354 230.45392 185.81765 185.81765 323.81161
## [512] 106.45360 261.01749 76.27329 93.30173 88.98760 266.16852 240.57471
## [519] 88.98760 138.22827 307.91996 281.71441 323.81161 156.98212 190.69919
## [526] 271.33517 129.00668 180.95694 205.46467 276.51721 334.47302 245.66067
## [533] 102.03592 339.82329 84.71051 220.40333 210.42547 225.41969 133.60396
## [540] 276.51721 171.29981 76.27329 235.50569 152.25645 166.50434 133.60396
## [547] 261.01749 220.40333 302.65027 339.82329 180.95694 200.52311 261.01749
## [554] 215.40514 235.50569 97.65158 261.01749 84.71051 97.65158 133.60396
## [561] 133.60396 80.47190 334.47302 185.81765 235.50569 171.29981 302.65027
## [568] 297.39467 133.60396 152.25645 84.71051 339.82329 84.71051 307.91996
## [575] 297.39467 292.15335 276.51721 138.22827 156.98212 345.18638 80.47190
## [582] 220.40333 345.18638 350.56213 276.51721 119.89626 110.90355 88.98760
## [589] 129.00668 313.20354 225.41969 161.73160 255.88233 235.50569 200.52311
## [596] 152.25645 97.65158 225.41969 200.52311 276.51721 129.00668 230.45392
## [603] 200.52311 286.92652 161.73160 97.65158 93.30173 171.29981 230.45392
## [610] 215.40514 334.47302 180.95694 334.47302 255.88233 266.16852 240.57471
## [617] 276.51721 185.81765 276.51721 152.25645 176.11750 80.47190 329.13573
## [624] 345.18638 255.88233 200.52311 156.98212 156.98212 286.92652 161.73160
## [631] 142.87890 297.39467 235.50569 281.71441 276.51721 205.46467 80.47190
## [638] 152.25645 142.87890 210.42547 180.95694 119.89626 205.46467 180.95694
## [645] 102.03592 323.81161 200.52311 281.71441 88.98760 292.15335 313.20354
## [652] 106.45360 84.71051 350.56213 106.45360 276.51721 215.40514 297.39467
## [659] 76.27329 147.55518 119.89626 152.25645 276.51721 97.65158 323.81161
## [666] 93.30173 93.30173 115.38475 106.45360 307.91996 307.91996 302.65027
## [673] 281.71441 297.39467 323.81161 225.41969 297.39467 119.89626 138.22827
## [680] 210.42547 339.82329 210.42547 329.13573 80.47190 297.39467 156.98212
## [687] 230.45392 195.60115 255.88233 185.81765 313.20354 307.91996 323.81161
## [694] 313.20354 129.00668 307.91996 115.38475 225.41969 205.46467 334.47302
## [701] 147.55518 180.95694 176.11750 266.16852 220.40333 129.00668 142.87890
## [708] 245.66067 124.43718 292.15335 292.15335 93.30173 93.30173 115.38475
## [715] 180.95694 110.90355 261.01749 286.92652 345.18638 266.16852 292.15335
## [722] 323.81161 72.11637 215.40514 102.03592 97.65158 245.66067 240.57471
## [729] 334.47302 230.45392 106.45360 271.33517 166.50434 345.18638 230.45392
## [736] 106.45360 190.69919 102.03592 156.98212 345.18638 205.46467 88.98760
## [743] 185.81765 133.60396 106.45360 334.47302 235.50569 276.51721 225.41969
## [750] 115.38475 138.22827 166.50434 190.69919 292.15335 156.98212 255.88233
## [757] 110.90355 210.42547 302.65027 261.01749 245.66067 195.60115 210.42547
## [764] 180.95694 286.92652 156.98212 302.65027 200.52311 166.50434 176.11750
## [771] 119.89626 307.91996 297.39467 215.40514 215.40514 156.98212 276.51721
## [778] 138.22827 166.50434 119.89626 156.98212 323.81161 323.81161 350.56213
## [785] 119.89626 345.18638 129.00668 97.65158 129.00668 110.90355 138.22827
## [792] 156.98212 339.82329 138.22827 142.87890 266.16852 230.45392 318.50082
## [799] 152.25645 124.43718 106.45360 307.91996 124.43718 313.20354 318.50082
## [806] 240.57471 152.25645 166.50434 220.40333 215.40514 245.66067 297.39467
## [813] 225.41969 102.03592 147.55518 147.55518 240.57471 147.55518 302.65027
## [820] 297.39467 93.30173 190.69919 142.87890 230.45392 281.71441 133.60396
## [827] 171.29981 345.18638 230.45392 133.60396 225.41969 235.50569 250.76331
## [834] 166.50434 190.69919 80.47190 281.71441 250.76331 210.42547 185.81765
## [841] 84.71051 171.29981 210.42547 195.60115 161.73160 230.45392 93.30173
## [848] 230.45392 240.57471 124.43718 225.41969 97.65158 215.40514 93.30173
## [855] 323.81161 313.20354 180.95694 190.69919 292.15335 119.89626 220.40333
## [862] 205.46467 334.47302 171.29981 220.40333 250.76331 271.33517 286.92652
## [869] 161.73160 318.50082 80.47190 138.22827 80.47190 84.71051 225.41969
## [876] 225.41969 250.76331 200.52311 225.41969 345.18638 302.65027 339.82329
## [883] 171.29981 334.47302 313.20354 205.46467 93.30173 180.95694 318.50082
## [890] 185.81765 292.15335 220.40333 230.45392 313.20354 180.95694 166.50434
## [897] 329.13573 318.50082 286.92652 334.47302 318.50082 329.13573 215.40514
## [904] 166.50434 302.65027 102.03592 307.91996 302.65027 297.39467 350.56213
## [911] 323.81161 313.20354 323.81161 180.95694 76.27329 88.98760 152.25645
## [918] 225.41969 307.91996 220.40333 215.40514 225.41969 176.11750 161.73160
## [925] 339.82329 115.38475 271.33517 350.56213 225.41969 230.45392 195.60115
## [932] 281.71441 339.82329 133.60396 80.47190 323.81161 80.47190 190.69919
## [939] 225.41969 161.73160 195.60115 255.88233 76.27329 281.71441 281.71441
## [946] 124.43718 180.95694 230.45392 339.82329 339.82329 72.11637 152.25645
## [953] 119.89626 88.98760 115.38475 190.69919 133.60396 276.51721 225.41969
## [960] 334.47302 171.29981 176.11750 97.65158 138.22827 102.03592 88.98760
## [967] 210.42547 266.16852 147.55518 106.45360 276.51721 205.46467 307.91996
## [974] 307.91996 240.57471 220.40333 133.60396 345.18638 313.20354 261.01749
## [981] 230.45392 215.40514 106.45360 106.45360 119.89626 255.88233 106.45360
## [988] 161.73160 313.20354 129.00668 76.27329 133.60396 302.65027 171.29981
## [995] 230.45392 334.47302 80.47190 110.90355 292.15335 240.57471 245.66067
## [1002] 124.43718 102.03592 195.60115 180.95694 266.16852 318.50082 318.50082
## [1009] 281.71441 313.20354 240.57471 281.71441 190.69919 152.25645 240.57471
## [1016] 220.40333 110.90355 266.16852 110.90355 190.69919 302.65027 292.15335
## [1023] 106.45360 235.50569 281.71441 176.11750 93.30173 190.69919 261.01749
## [1030] 133.60396 339.82329 235.50569 200.52311 200.52311 345.18638 255.88233
## [1037] 266.16852 235.50569 97.65158 147.55518 200.52311 119.89626 129.00668
## [1044] 245.66067 334.47302 286.92652 161.73160 119.89626 286.92652 307.91996
## [1051] 133.60396 180.95694 80.47190 110.90355 345.18638 200.52311 205.46467
## [1058] 152.25645 281.71441 235.50569 286.92652 302.65027 292.15335 166.50434
## [1065] 255.88233 106.45360 313.20354 147.55518 318.50082 286.92652 220.40333
## [1072] 350.56213 329.13573 129.00668 318.50082 266.16852 138.22827 250.76331
## [1079] 220.40333 281.71441 84.71051 255.88233 210.42547 119.89626 323.81161
## [1086] 292.15335 266.16852 97.65158 138.22827 102.03592 245.66067 115.38475
## [1093] 176.11750 106.45360 297.39467 210.42547 286.92652 225.41969 76.27329
## [1100] 133.60396 245.66067 302.65027 106.45360 124.43718 97.65158 350.56213
## [1107] 329.13573 106.45360 161.73160 129.00668 250.76331 318.50082 129.00668
## [1114] 245.66067 185.81765 115.38475 334.47302 147.55518 152.25645 255.88233
## [1121] 345.18638 190.69919 339.82329 195.60115 93.30173 190.69919 142.87890
## [1128] 195.60115 220.40333 161.73160 147.55518 302.65027 180.95694 180.95694
## [1135] 215.40514 281.71441 205.46467 124.43718 345.18638 329.13573 84.71051
## [1142] 329.13573 106.45360 281.71441 166.50434 185.81765 190.69919 297.39467
## [1149] 185.81765 318.50082 166.50434 230.45392 93.30173 286.92652 152.25645
## [1156] 345.18638 318.50082 250.76331 195.60115 302.65027 166.50434 225.41969
## [1163] 93.30173 230.45392 286.92652 190.69919 230.45392 176.11750 147.55518
## [1170] 255.88233 266.16852 110.90355 266.16852 102.03592 119.89626 255.88233
## [1177] 80.47190 195.60115 318.50082 276.51721 124.43718 230.45392 161.73160
## [1184] 261.01749 350.56213 307.91996 88.98760 161.73160 84.71051 124.43718
## [1191] 313.20354 271.33517 297.39467 205.46467 235.50569 318.50082 80.47190
## [1198] 261.01749 84.71051 119.89626 286.92652 215.40514 220.40333 261.01749
## [1205] 156.98212 276.51721 80.47190 215.40514 313.20354 180.95694 200.52311
## [1212] 329.13573 142.87890 185.81765 286.92652 171.29981 195.60115 230.45392
## [1219] 225.41969 133.60396 185.81765 323.81161 323.81161 133.60396 176.11750
## [1226] 281.71441 119.89626 286.92652 266.16852 80.47190 323.81161 261.01749
## [1233] 185.81765 185.81765 329.13573 261.01749 266.16852 240.57471 292.15335
## [1240] 318.50082 215.40514 124.43718 220.40333 281.71441 255.88233 190.69919
## [1247] 93.30173 200.52311 225.41969 313.20354 195.60115 292.15335 176.11750
## [1254] 205.46467 339.82329 115.38475 271.33517 190.69919 215.40514 138.22827
## [1261] 240.57471 240.57471 166.50434 185.81765 152.25645 266.16852 129.00668
## [1268] 195.60115 240.57471 235.50569 176.11750 110.90355 297.39467 345.18638
## [1275] 205.46467 200.52311 110.90355 161.73160 147.55518 185.81765 129.00668
## [1282] 297.39467 190.69919 220.40333 176.11750 93.30173 88.98760 156.98212
## [1289] 124.43718 129.00668 176.11750 276.51721 334.47302 313.20354 334.47302
## [1296] 93.30173 271.33517 230.45392 240.57471 271.33517 281.71441 210.42547
## [1303] 215.40514 307.91996 176.11750 230.45392 84.71051 240.57471 323.81161
## [1310] 142.87890 97.65158 171.29981 230.45392 329.13573 245.66067 88.98760
## [1317] 323.81161 171.29981 195.60115 129.00668 185.81765 166.50434 133.60396
## [1324] 318.50082 235.50569 152.25645 142.87890 84.71051 185.81765 210.42547
## [1331] 97.65158 271.33517 286.92652 115.38475 220.40333 220.40333 205.46467
## [1338] 345.18638 180.95694 195.60115 266.16852 88.98760 276.51721 334.47302
## [1345] 200.52311 200.52311 119.89626 339.82329 171.29981 292.15335 225.41969
## [1352] 97.65158 152.25645 286.92652 318.50082 345.18638 240.57471 313.20354
## [1359] 138.22827 133.60396 345.18638 156.98212 80.47190 142.87890 210.42547
## [1366] 220.40333 339.82329 147.55518 235.50569 80.47190 161.73160 190.69919
## [1373] 88.98760 205.46467 281.71441 215.40514 339.82329 245.66067 161.73160
## [1380] 106.45360 171.29981 345.18638 129.00668 220.40333 161.73160 152.25645
## [1387] 276.51721 110.90355 156.98212 129.00668 195.60115 205.46467 271.33517
## [1394] 292.15335 235.50569 106.45360 110.90355 166.50434 176.11750 323.81161
## [1401] 205.46467 110.90355 156.98212 215.40514 245.66067 185.81765 93.30173
## [1408] 156.98212 339.82329 240.57471 161.73160 261.01749 156.98212 245.66067
## [1415] 339.82329 176.11750 119.89626 302.65027 110.90355 313.20354 161.73160
## [1422] 147.55518 142.87890 176.11750 266.16852 147.55518 271.33517 156.98212
## [1429] 93.30173 329.13573 97.65158 307.91996 88.98760 276.51721 240.57471
## [1436] 220.40333 180.95694 235.50569 129.00668 205.46467 220.40333 276.51721
## [1443] 271.33517 93.30173 142.87890 142.87890 271.33517 119.89626 220.40333
## [1450] 80.47190 180.95694 350.56213 339.82329 200.52311 80.47190 313.20354
## [1457] 152.25645 205.46467 200.52311 286.92652 345.18638 225.41969 245.66067
## [1464] 200.52311 93.30173 250.76331 345.18638 152.25645 255.88233 171.29981
## [1471] 190.69919 119.89626 102.03592 210.42547 266.16852 334.47302 166.50434
## [1478] 176.11750 88.98760 266.16852 245.66067 84.71051 138.22827 329.13573
## [1485] 161.73160 302.65027 210.42547 281.71441 255.88233 235.50569 80.47190
## [1492] 142.87890 286.92652 84.71051 307.91996 281.71441 350.56213 240.57471
## [1499] 110.90355 147.55518 180.95694 318.50082 161.73160 339.82329 240.57471
## [1506] 235.50569 102.03592 93.30173 292.15335 190.69919 307.91996 339.82329
## [1513] 297.39467 185.81765 110.90355 281.71441 318.50082 195.60115 133.60396
## [1520] 147.55518 200.52311 261.01749 250.76331 281.71441 88.98760 138.22827
## [1527] 93.30173 292.15335 297.39467 200.52311 318.50082 133.60396 292.15335
## [1534] 166.50434 119.89626 230.45392 240.57471 210.42547 302.65027 195.60115
## [1541] 119.89626 142.87890 230.45392 235.50569 245.66067 339.82329 88.98760
## [1548] 185.81765 119.89626 318.50082 297.39467 210.42547 334.47302 350.56213
## [1555] 318.50082 210.42547 195.60115 286.92652 205.46467 171.29981 129.00668
## [1562] 271.33517 190.69919 215.40514 261.01749 190.69919 190.69919 205.46467
## [1569] 323.81161 245.66067 84.71051 281.71441 235.50569 261.01749 261.01749
## [1576] 119.89626 215.40514 313.20354 133.60396 286.92652 80.47190 297.39467
## [1583] 161.73160 250.76331 225.41969 286.92652 329.13573 240.57471 271.33517
## [1590] 261.01749 313.20354 245.66067 110.90355 147.55518 110.90355 185.81765
## [1597] 345.18638 133.60396 166.50434 161.73160 200.52311 138.22827 119.89626
## [1604] 142.87890 215.40514 180.95694 190.69919 210.42547 171.29981 323.81161
## [1611] 93.30173 266.16852 297.39467 190.69919 152.25645 245.66067 185.81765
## [1618] 119.89626 152.25645 88.98760 190.69919 190.69919 97.65158 276.51721
## [1625] 266.16852 171.29981 129.00668 93.30173 138.22827 323.81161 93.30173
## [1632] 84.71051 281.71441 133.60396 339.82329 171.29981 329.13573 250.76331
## [1639] 84.71051 286.92652 115.38475 297.39467 80.47190 329.13573 302.65027
## [1646] 110.90355 240.57471 190.69919 302.65027 80.47190 84.71051 215.40514
## [1653] 93.30173 171.29981 115.38475 195.60115 97.65158 339.82329 302.65027
## [1660] 171.29981 334.47302 323.81161 302.65027 166.50434 185.81765 195.60115
## [1667] 281.71441 200.52311 292.15335 292.15335 142.87890 297.39467 97.65158
## [1674] 80.47190 97.65158 271.33517 195.60115 147.55518 93.30173 190.69919
## [1681] 166.50434 129.00668 210.42547 215.40514 171.29981 84.71051 115.38475
## [1688] 106.45360 235.50569 281.71441 205.46467 245.66067 334.47302 84.71051
## [1695] 276.51721 72.11637 152.25645 318.50082 166.50434 195.60115 220.40333
## [1702] 88.98760 106.45360 156.98212 250.76331 210.42547 97.65158 171.29981
## [1709] 133.60396 261.01749 102.03592 350.56213 115.38475 106.45360 106.45360
## [1716] 152.25645 171.29981 80.47190 255.88233 171.29981 180.95694 220.40333
## [1723] 180.95694 106.45360 297.39467 185.81765 80.47190 166.50434 334.47302
## [1730] 235.50569 345.18638 292.15335 119.89626 230.45392 225.41969 142.87890
## [1737] 129.00668 220.40333 84.71051 235.50569 129.00668 129.00668 166.50434
## [1744] 220.40333 281.71441 106.45360 345.18638 225.41969 84.71051 129.00668
## [1751] 138.22827 84.71051 185.81765 240.57471 210.42547 307.91996 93.30173
## [1758] 318.50082 276.51721 200.52311 166.50434 161.73160 166.50434 147.55518
## [1765] 245.66067 266.16852 307.91996 245.66067 286.92652 271.33517 230.45392
## [1772] 152.25645 271.33517 297.39467 200.52311 93.30173 110.90355 286.92652
## [1779] 276.51721 255.88233 271.33517 97.65158 307.91996 250.76331 195.60115
## [1786] 240.57471 152.25645 271.33517 176.11750 156.98212 76.27329 255.88233
## [1793] 138.22827 225.41969 230.45392 245.66067 106.45360 129.00668 180.95694
## [1800] 161.73160 129.00668 180.95694 266.16852 339.82329 97.65158 261.01749
## [1807] 142.87890 220.40333 102.03592 72.11637 318.50082 225.41969 156.98212
## [1814] 323.81161 205.46467 124.43718 115.38475 176.11750 307.91996 334.47302
## [1821] 124.43718 102.03592 255.88233 266.16852 230.45392 210.42547 200.52311
## [1828] 318.50082 281.71441 200.52311 185.81765 220.40333 106.45360 329.13573
## [1835] 102.03592 345.18638 142.87890 176.11750 230.45392 307.91996 133.60396
## [1842] 292.15335 250.76331 161.73160 88.98760 138.22827 339.82329 215.40514
## [1849] 235.50569 215.40514 334.47302 266.16852 93.30173 106.45360 329.13573
## [1856] 235.50569 318.50082 271.33517 76.27329 110.90355 235.50569 286.92652
## [1863] 119.89626 88.98760 152.25645 307.91996 334.47302 84.71051 292.15335
## [1870] 124.43718 292.15335 245.66067 307.91996 138.22827 84.71051 138.22827
## [1877] 147.55518 80.47190 281.71441 323.81161 176.11750 97.65158 88.98760
## [1884] 133.60396 350.56213 240.57471 220.40333 318.50082 215.40514 334.47302
## [1891] 307.91996 124.43718 166.50434 102.03592 215.40514 80.47190 205.46467
## [1898] 225.41969 281.71441 115.38475 97.65158 350.56213 166.50434 138.22827
## [1905] 225.41969 271.33517 271.33517 302.65027 72.11637 106.45360 281.71441
## [1912] 156.98212 110.90355 185.81765 240.57471 240.57471 88.98760 286.92652
## [1919] 334.47302 88.98760 152.25645 171.29981 88.98760 334.47302 176.11750
## [1926] 84.71051 220.40333 318.50082 334.47302 152.25645 297.39467 176.11750
## [1933] 88.98760 302.65027 161.73160 329.13573 205.46467 93.30173 339.82329
## [1940] 250.76331 334.47302 339.82329 156.98212 102.03592 80.47190 124.43718
## [1947] 240.57471 80.47190 245.66067 106.45360 307.91996 205.46467 339.82329
## [1954] 313.20354 215.40514 286.92652 176.11750 185.81765 124.43718 292.15335
## [1961] 230.45392 119.89626 240.57471 261.01749 276.51721 225.41969 225.41969
## [1968] 302.65027 255.88233 286.92652 180.95694 297.39467 302.65027 205.46467
## [1975] 138.22827 215.40514 72.11637 225.41969 171.29981 235.50569 334.47302
## [1982] 185.81765 142.87890 205.46467 76.27329 255.88233 156.98212 235.50569
## [1989] 225.41969 115.38475 161.73160 180.95694 110.90355 176.11750 156.98212
## [1996] 110.90355 129.00668 93.30173 230.45392 129.00668 240.57471 195.60115
## [2003] 323.81161 190.69919 88.98760 307.91996 271.33517 205.46467 297.39467
## [2010] 110.90355 271.33517 261.01749 180.95694 318.50082 240.57471 185.81765
## [2017] 329.13573 200.52311 102.03592 292.15335 190.69919 93.30173 339.82329
## [2024] 266.16852 138.22827 138.22827 266.16852 215.40514 124.43718 240.57471
## [2031] 161.73160 200.52311 292.15335 152.25645 240.57471 225.41969 286.92652
## [2038] 307.91996 255.88233 205.46467 106.45360 152.25645 106.45360 110.90355
## [2045] 84.71051 138.22827 339.82329 102.03592 302.65027 339.82329 84.71051
## [2052] 271.33517 210.42547 205.46467 307.91996 271.33517 297.39467 205.46467
## [2059] 334.47302 261.01749 276.51721 271.33517 115.38475 339.82329 266.16852
## [2066] 286.92652 195.60115 119.89626 180.95694 240.57471 266.16852 97.65158
## [2073] 302.65027 156.98212 266.16852 161.73160 97.65158 261.01749 255.88233
## [2080] 255.88233 156.98212 329.13573 161.73160 345.18638 245.66067 129.00668
## [2087] 133.60396 334.47302 240.57471 281.71441 276.51721 240.57471 215.40514
## [2094] 129.00668 205.46467 250.76331 225.41969 152.25645 84.71051 156.98212
## [2101] 129.00668 200.52311 225.41969 106.45360 142.87890 215.40514 345.18638
## [2108] 119.89626 129.00668 245.66067 88.98760 166.50434 334.47302 215.40514
## [2115] 297.39467 176.11750 250.76331 176.11750 323.81161 142.87890 266.16852
## [2122] 84.71051 195.60115 297.39467 334.47302 147.55518 313.20354 80.47190
## [2129] 84.71051 88.98760 161.73160 133.60396 161.73160 215.40514 225.41969
## [2136] 97.65158 255.88233 261.01749 215.40514 235.50569 190.69919 147.55518
## [2143] 110.90355 230.45392 156.98212 261.01749 147.55518 240.57471 318.50082
## [2150] 307.91996 250.76331 281.71441 220.40333 133.60396 261.01749 200.52311
## [2157] 176.11750 142.87890 225.41969 235.50569#Make it another predictor to check if there is interaction effect if yes, we cannot use it as predictor.
modeltest2 <- glm(ClickThrough ~ Ad + Age + logage2, data = data2, family = "binomial")
modeltest2##
## Call: glm(formula = ClickThrough ~ Ad + Age + logage2, family = "binomial",
## data = data2)
##
## Coefficients:
## (Intercept) Ad1 Ad2 Age logage2
## -2.04692 0.23276 0.62351 0.27439 -0.05678
##
## Degrees of Freedom: 2159 Total (i.e. Null); 2155 Residual
## Null Deviance: 2759
## Residual Deviance: 2716 AIC: 2726summary(modeltest2)##
## Call:
## glm(formula = ClickThrough ~ Ad + Age + logage2, family = "binomial",
## data = data2)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.7103 -1.3693 0.7962 0.9458 1.1642
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.04692 0.92104 -2.222 0.02626 *
## Ad1 0.23276 0.10958 2.124 0.03366 *
## Ad2 0.62351 0.11403 5.468 4.55e-08 ***
## Age 0.27439 0.09379 2.925 0.00344 **
## logage2 -0.05678 0.01907 -2.978 0.00290 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 2759.3 on 2159 degrees of freedom
## Residual deviance: 2716.5 on 2155 degrees of freedom
## AIC: 2726.5
##
## Number of Fisher Scoring iterations: 4#Logage p-value 0.00290 potentially violate the assumption - so we can not use age as a predictorlibrary(multcomp)
data2$predicted.probabilities2 <- fitted(model6)
head(data2[, c("ClickThrough", "Ad", "Age", "predicted.probabilities2")])## # A tibble: 6 x 4
## ClickThrough Ad Age predicted.probabilities2
## <fct> <fct> <dbl> <dbl>
## 1 1 0 69 0.599
## 2 0 1 31 0.656
## 3 1 2 66 0.736
## 4 1 0 33 0.599
## 5 0 1 35 0.656
## 6 1 2 72 0.736data2[, c("ClickThrough", "Ad", "Age", "predicted.probabilities2")]## # A tibble: 2,160 x 4
## ClickThrough Ad Age predicted.probabilities2
## <fct> <fct> <dbl> <dbl>
## 1 1 0 69 0.599
## 2 0 1 31 0.656
## 3 1 2 66 0.736
## 4 1 0 33 0.599
## 5 0 1 35 0.656
## 6 1 2 72 0.736
## 7 1 0 61 0.599
## 8 0 1 44 0.656
## 9 0 2 34 0.736
## 10 1 0 56 0.599
## # ... with 2,150 more rowsSummary Write Up 2 -
A logistic regression model was conducted to predict whether a participant will click the link is influenced by types of advertisements. A significant regression equation was found (x2(2) = 31.13, p < .001), with a Pseudo-R2of .01. Both intercept (z = 5.26, p < .001. b = .40), advertisement one (z = 2.23, p = .026. b = .24) and advertisement two (z = 5.51, p < .001. b = .63) were statistically significant. The odds ratio of advertisement one is 1.28, which suggests that individuals who see advertisement one, would have a 1.28 times of chance to click the related website than those individuals who don’t see any advertisements; the odds ratio of advertisement two is 1.87, which suggests that individuals who see advertisement two, would have a 1.87 times of chance to click the related website than those individuals who don’t see any advertisements.
#EXERCIS 3 - MultiNomial Logistic Regression
#Health Condition is a multinomial outcome/dependent variable - "NotHealthy" "Healthy" "Average"
#Clean or organize data as we have more than two groups
library(mlogit)## Warning: package 'mlogit' was built under R version 3.6.3## Loading required package: dfidx## Warning: package 'dfidx' was built under R version 3.6.3##
## Attaching package: 'dfidx'## The following object is masked from 'package:MASS':
##
## select## The following object is masked from 'package:stats':
##
## filterdata$HC <- factor(data$HC)
factor(data$HC)## [1] NotHealthy Healthy Average Healthy NotHealthy Healthy
## [7] Average NotHealthy NotHealthy NotHealthy Healthy Healthy
## [13] NotHealthy Healthy NotHealthy Healthy NotHealthy NotHealthy
## [19] Healthy NotHealthy NotHealthy NotHealthy Average NotHealthy
## [25] Average Healthy Healthy Average NotHealthy NotHealthy
## [31] Healthy NotHealthy Healthy NotHealthy Healthy NotHealthy
## [37] NotHealthy NotHealthy NotHealthy Average Average NotHealthy
## [43] Average NotHealthy Healthy NotHealthy NotHealthy Healthy
## [49] NotHealthy NotHealthy Healthy Average NotHealthy Healthy
## [55] Average Average Average NotHealthy
## Levels: Average Healthy NotHealthy#In addition, we have to transfer the data to a specific format for R to ran the multinominal regression
newdata <- mlogit.data(data, choice = "HC", shape = "wide")
newdata## ~~~~~~~
## first 10 observations out of 174
## ~~~~~~~
## Age Food Gender Weight HC predicted.probabilities chid alt idx
## 1 31 1 Female 1 FALSE 5.000000e-01 1 Average 1:rage
## 2 31 1 Female 1 FALSE 5.000000e-01 1 Healthy 1:lthy
## 3 31 1 Female 1 TRUE 5.000000e-01 1 NotHealthy 1:lthy
## 4 35 1 Female 0 FALSE 1.583729e-10 2 Average 2:rage
## 5 35 1 Female 0 TRUE 1.583729e-10 2 Healthy 2:lthy
## 6 35 1 Female 0 FALSE 1.583729e-10 2 NotHealthy 2:lthy
## 7 44 1 Female 1 TRUE 1.000000e+00 3 Average 3:rage
## 8 44 1 Female 1 FALSE 1.000000e+00 3 Healthy 3:lthy
## 9 44 1 Female 1 FALSE 1.000000e+00 3 NotHealthy 3:lthy
## 10 34 2 Female 0 FALSE 1.583729e-10 4 Average 4:rage
##
## ~~~ indexes ~~~~
## chid alt
## 1 1 Average
## 2 1 Healthy
## 3 1 NotHealthy
## 4 2 Average
## 5 2 Healthy
## 6 2 NotHealthy
## 7 3 Average
## 8 3 Healthy
## 9 3 NotHealthy
## 10 4 Average
## indexes: 1, 2summary(newdata)## Age Food Gender Weight HC
## 69 : 18 0:60 Female:84 Min. :0.0000 Mode :logical
## 30 : 12 1:60 Male :90 1st Qu.:0.0000 FALSE:116
## 31 : 12 2:54 Median :1.0000 TRUE :58
## 33 : 6 Mean :0.5862
## 34 : 6 3rd Qu.:1.0000
## 35 : 6 Max. :1.0000
## (Other):114
## predicted.probabilities chid alt
## Min. :0.0000 Min. : 1.0 Average :58
## 1st Qu.:0.0000 1st Qu.:15.0 Healthy :58
## Median :1.0000 Median :29.5 NotHealthy:58
## Mean :0.5862 Mean :29.5
## 3rd Qu.:1.0000 3rd Qu.:44.0
## Max. :1.0000 Max. :58.0
##
## idx.chid idx.alt
## Min. : 1.0 Average :58
## 1st Qu.:15.0 Healthy :58
## Median :29.5 NotHealthy:58
## Mean :29.5 NA
## 3rd Qu.:44.0 NA
## Max. :58.0 NA
## #To Checks which combination has interaction effect which is Age:NotHealth.
#Now we use another variable: HC as the outcome variable
modelHC <- mlogit(HC ~ 1|Age + Weight:Weight, data = newdata, reflevel = "Healthy")
modelHC##
## Call:
## mlogit(formula = HC ~ 1 | Age + Weight:Weight, data = newdata, reflevel = "Healthy", method = "nr")
##
## Coefficients:
## (Intercept):Average (Intercept):NotHealthy Age31:Average
## -1.09861 -19.31522 -19.05270
## Age31:NotHealthy Age33:Average Age33:NotHealthy
## -0.83609 -19.05270 -39.65615
## Age34:Average Age34:NotHealthy Age35:Average
## -19.05270 -0.83609 -19.05270
## Age35:NotHealthy Age39:Average Age39:NotHealthy
## -0.83609 21.24992 19.31522
## Age40:Average Age40:NotHealthy Age41:Average
## 1.09861 0.64646 21.24992
## Age41:NotHealthy Age42:Average Age42:NotHealthy
## 19.31522 -19.05270 -0.83609
## Age44:Average Age44:NotHealthy Age46:Average
## -0.38394 -2.31864 -37.72145
## Age46:NotHealthy Age47:Average Age47:NotHealthy
## -20.98740 -0.38394 -2.31864
## Age56:Average Age56:NotHealthy Age57:Average
## 1.09861 0.64646 1.09861
## Age57:NotHealthy Age58:Average Age58:NotHealthy
## 0.64646 -19.05270 -0.83609
## Age59:Average Age59:NotHealthy Age60:Average
## -19.05270 -0.83609 -19.05270
## Age60:NotHealthy Age61:Average Age61:NotHealthy
## -0.83609 -19.05270 -0.83609
## Age64:Average Age64:NotHealthy Age66:Average
## -19.05270 -0.83609 -19.05270
## Age66:NotHealthy Age69:Average Age69:NotHealthy
## -0.83609 -19.05270 -0.83609
## Age71:Average Age71:NotHealthy Age72:Average
## -19.05270 -0.83609 1.09861
## Age72:NotHealthy Age73:Average Age73:NotHealthy
## 0.64646 -19.05270 -0.83609
## Age74:Average Age74:NotHealthy Weight:Average
## -19.05270 -0.83609 20.15131
## Weight:NotHealthy
## 40.30262summary(modelHC)##
## Call:
## mlogit(formula = HC ~ 1 | Age + Weight:Weight, data = newdata,
## reflevel = "Healthy", method = "nr")
##
## Frequencies of alternatives:choice
## Healthy Average NotHealthy
## 0.2931 0.2069 0.5000
##
## nr method
## 18 iterations, 0h:0m:0s
## g'(-H)^-1g = 5.69E-07
## gradient close to zero
##
## Coefficients :
## Estimate Std. Error z-value Pr(>|z|)
## (Intercept):Average -1.09861 1.15470 -0.9514 0.3414
## (Intercept):NotHealthy -19.31522 9029.96411 -0.0021 0.9983
## Age31:Average -19.05270 16799.10829 -0.0011 0.9991
## Age31:NotHealthy -0.83609 19072.23888 0.0000 1.0000
## Age33:Average -19.05270 29096.90745 -0.0007 0.9995
## Age33:NotHealthy -39.65615 27822.93674 -0.0014 0.9989
## Age34:Average -19.05270 16799.10793 -0.0011 0.9991
## Age34:NotHealthy -0.83609 19072.23841 0.0000 1.0000
## Age35:Average -19.05270 16799.10793 -0.0011 0.9991
## Age35:NotHealthy -0.83609 19072.23841 0.0000 1.0000
## Age39:Average 21.24992 16799.10784 0.0013 0.9990
## Age39:NotHealthy 19.31522 25415.74905 0.0008 0.9994
## Age40:Average 1.09861 1.82574 0.6017 0.5474
## Age40:NotHealthy 0.64646 14480.88040 0.0000 1.0000
## Age41:Average 21.24992 16799.10802 0.0013 0.9990
## Age41:NotHealthy 19.31522 25415.74917 0.0008 0.9994
## Age42:Average -19.05270 37563.94640 -0.0005 0.9996
## Age42:NotHealthy -0.83609 30465.88562 0.0000 1.0000
## Age44:Average -0.38394 31221.55692 0.0000 1.0000
## Age44:NotHealthy -2.31864 27822.93629 -0.0001 0.9999
## Age46:Average -37.72145 31221.55772 -0.0012 0.9990
## Age46:NotHealthy -20.98740 25415.74641 -0.0008 0.9993
## Age47:Average -0.38394 31221.55681 0.0000 1.0000
## Age47:NotHealthy -2.31864 27822.93618 -0.0001 0.9999
## Age56:Average 1.09861 1.82574 0.6017 0.5474
## Age56:NotHealthy 0.64646 14480.88040 0.0000 1.0000
## Age57:Average 1.09861 1.82574 0.6017 0.5474
## Age57:NotHealthy 0.64646 14480.88040 0.0000 1.0000
## Age58:Average -19.05270 16799.10793 -0.0011 0.9991
## Age58:NotHealthy -0.83609 19072.23841 0.0000 1.0000
## Age59:Average -19.05270 37563.94640 -0.0005 0.9996
## Age59:NotHealthy -0.83609 30465.88562 0.0000 1.0000
## Age60:Average -19.05270 37563.94648 -0.0005 0.9996
## Age60:NotHealthy -0.83609 30465.88572 0.0000 1.0000
## Age61:Average -19.05270 37563.94648 -0.0005 0.9996
## Age61:NotHealthy -0.83609 30465.88572 0.0000 1.0000
## Age64:Average -19.05270 37563.94648 -0.0005 0.9996
## Age64:NotHealthy -0.83609 30465.88572 0.0000 1.0000
## Age66:Average -19.05270 37563.94648 -0.0005 0.9996
## Age66:NotHealthy -0.83609 30465.88572 0.0000 1.0000
## Age69:Average -19.05270 32167.84166 -0.0006 0.9995
## Age69:NotHealthy -0.83609 27203.49557 0.0000 1.0000
## Age71:Average -19.05270 37563.94640 -0.0005 0.9996
## Age71:NotHealthy -0.83609 30465.88562 0.0000 1.0000
## Age72:Average 1.09861 1.82574 0.6017 0.5474
## Age72:NotHealthy 0.64646 14480.88040 0.0000 1.0000
## Age73:Average -19.05270 37563.94640 -0.0005 0.9996
## Age73:NotHealthy -0.83609 30465.88562 0.0000 1.0000
## Age74:Average -19.05270 37563.94648 -0.0005 0.9996
## Age74:NotHealthy -0.83609 30465.88572 0.0000 1.0000
## Weight:Average 20.15131 29096.90739 0.0007 0.9994
## Weight:NotHealthy 40.30262 23757.52298 0.0017 0.9986
##
## Log-Likelihood: -13.34
## McFadden R^2: 0.77719
## Likelihood ratio test : chisq = 93.062 (p.value = 0.00021018)# Very Significangt model - p.value = 0.00021018
#Odds Ratio
exp(modelHC$coefficients) ## (Intercept):Average (Intercept):NotHealthy Age31:Average
## 3.333333e-01 4.087961e-09 5.315191e-09
## Age31:NotHealthy Age33:Average Age33:NotHealthy
## 4.334020e-01 5.315193e-09 5.991711e-18
## Age34:Average Age34:NotHealthy Age35:Average
## 5.315190e-09 4.334019e-01 5.315190e-09
## Age35:NotHealthy Age39:Average Age39:NotHealthy
## 4.334019e-01 1.693260e+09 2.446207e+08
## Age40:Average Age40:NotHealthy Age41:Average
## 3.000000e+00 1.908779e+00 1.693260e+09
## Age41:NotHealthy Age42:Average Age42:NotHealthy
## 2.446207e+08 5.315193e-09 4.334021e-01
## Age44:Average Age44:NotHealthy Age46:Average
## 6.811720e-01 9.840708e-02 4.147451e-17
## Age46:NotHealthy Age47:Average Age47:NotHealthy
## 7.678716e-10 6.811720e-01 9.840708e-02
## Age56:Average Age56:NotHealthy Age57:Average
## 3.000000e+00 1.908779e+00 3.000000e+00
## Age57:NotHealthy Age58:Average Age58:NotHealthy
## 1.908779e+00 5.315190e-09 4.334019e-01
## Age59:Average Age59:NotHealthy Age60:Average
## 5.315193e-09 4.334021e-01 5.315193e-09
## Age60:NotHealthy Age61:Average Age61:NotHealthy
## 4.334021e-01 5.315193e-09 4.334021e-01
## Age64:Average Age64:NotHealthy Age66:Average
## 5.315193e-09 4.334021e-01 5.315193e-09
## Age66:NotHealthy Age69:Average Age69:NotHealthy
## 4.334021e-01 5.315193e-09 4.334021e-01
## Age71:Average Age71:NotHealthy Age72:Average
## 5.315193e-09 4.334021e-01 3.000000e+00
## Age72:NotHealthy Age73:Average Age73:NotHealthy
## 1.908779e+00 5.315193e-09 4.334021e-01
## Age74:Average Age74:NotHealthy Weight:Average
## 5.315193e-09 4.334021e-01 5.644198e+08
## Weight:NotHealthy
## 3.185698e+17
## attr(,"names.sup.coef")
## character(0)
## attr(,"fixed")
## (Intercept):Average (Intercept):NotHealthy Age31:Average
## FALSE FALSE FALSE
## Age31:NotHealthy Age33:Average Age33:NotHealthy
## FALSE FALSE FALSE
## Age34:Average Age34:NotHealthy Age35:Average
## FALSE FALSE FALSE
## Age35:NotHealthy Age39:Average Age39:NotHealthy
## FALSE FALSE FALSE
## Age40:Average Age40:NotHealthy Age41:Average
## FALSE FALSE FALSE
## Age41:NotHealthy Age42:Average Age42:NotHealthy
## FALSE FALSE FALSE
## Age44:Average Age44:NotHealthy Age46:Average
## FALSE FALSE FALSE
## Age46:NotHealthy Age47:Average Age47:NotHealthy
## FALSE FALSE FALSE
## Age56:Average Age56:NotHealthy Age57:Average
## FALSE FALSE FALSE
## Age57:NotHealthy Age58:Average Age58:NotHealthy
## FALSE FALSE FALSE
## Age59:Average Age59:NotHealthy Age60:Average
## FALSE FALSE FALSE
## Age60:NotHealthy Age61:Average Age61:NotHealthy
## FALSE FALSE FALSE
## Age64:Average Age64:NotHealthy Age66:Average
## FALSE FALSE FALSE
## Age66:NotHealthy Age69:Average Age69:NotHealthy
## FALSE FALSE FALSE
## Age71:Average Age71:NotHealthy Age72:Average
## FALSE FALSE FALSE
## Age72:NotHealthy Age73:Average Age73:NotHealthy
## FALSE FALSE FALSE
## Age74:Average Age74:NotHealthy Weight:Average
## FALSE FALSE FALSE
## Weight:NotHealthy
## FALSE
## attr(,"sup")
## character(0)data.frame(exp(modelHC$coefficients))## exp.modelHC.coefficients.
## (Intercept):Average 3.333333e-01
## (Intercept):NotHealthy 4.087961e-09
## Age31:Average 5.315191e-09
## Age31:NotHealthy 4.334020e-01
## Age33:Average 5.315193e-09
## Age33:NotHealthy 5.991711e-18
## Age34:Average 5.315190e-09
## Age34:NotHealthy 4.334019e-01
## Age35:Average 5.315190e-09
## Age35:NotHealthy 4.334019e-01
## Age39:Average 1.693260e+09
## Age39:NotHealthy 2.446207e+08
## Age40:Average 3.000000e+00
## Age40:NotHealthy 1.908779e+00
## Age41:Average 1.693260e+09
## Age41:NotHealthy 2.446207e+08
## Age42:Average 5.315193e-09
## Age42:NotHealthy 4.334021e-01
## Age44:Average 6.811720e-01
## Age44:NotHealthy 9.840708e-02
## Age46:Average 4.147451e-17
## Age46:NotHealthy 7.678716e-10
## Age47:Average 6.811720e-01
## Age47:NotHealthy 9.840708e-02
## Age56:Average 3.000000e+00
## Age56:NotHealthy 1.908779e+00
## Age57:Average 3.000000e+00
## Age57:NotHealthy 1.908779e+00
## Age58:Average 5.315190e-09
## Age58:NotHealthy 4.334019e-01
## Age59:Average 5.315193e-09
## Age59:NotHealthy 4.334021e-01
## Age60:Average 5.315193e-09
## Age60:NotHealthy 4.334021e-01
## Age61:Average 5.315193e-09
## Age61:NotHealthy 4.334021e-01
## Age64:Average 5.315193e-09
## Age64:NotHealthy 4.334021e-01
## Age66:Average 5.315193e-09
## Age66:NotHealthy 4.334021e-01
## Age69:Average 5.315193e-09
## Age69:NotHealthy 4.334021e-01
## Age71:Average 5.315193e-09
## Age71:NotHealthy 4.334021e-01
## Age72:Average 3.000000e+00
## Age72:NotHealthy 1.908779e+00
## Age73:Average 5.315193e-09
## Age73:NotHealthy 4.334021e-01
## Age74:Average 5.315193e-09
## Age74:NotHealthy 4.334021e-01
## Weight:Average 5.644198e+08
## Weight:NotHealthy 3.185698e+17