Resmapling Method

This exercise is to practise the resampling method in the book Introduction to Statistical Learning with R

Validation Approach

• Get started

# Import library 
library(ISLR); library(ggplot2); library(tidyverse)
# Rename the Auto dataset to df
df<-Auto # You can find out more about Auto data by typing command ?Auto
# Look at few rows of data
head(df)

• Splitting data into training set and test Our goal is to build a simple linear regression to predict mpg using horsepower

# Splitting data 
library(caTools)
sam<- sample.split(df$mpg, SplitRatio = 0.7)
training<- subset(df, sam==T)
test<-subset(df, sam==F)
# Check some info
dim(training); dim(test)

[1] 288   9
[1] 104   9

head(training)

Plotting a scatter plot between mpg and horsepower

plot(df$mpg~df$horsepower, main="Scatter Plot", xlab="Engine Displacement",ylab="Miles per gallon", pch=16, col=4)

Building a simple linear regression

lm1<-lm(mpg~horsepower, data=training)
# Get some statistics 
summary(lm1)

Call:
lm(formula = mpg ~ horsepower, data = training)

Residuals:
     Min       1Q   Median       3Q      Max 
-14.0013  -3.4124  -0.4896   2.6903  16.4652 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept) 40.660728   0.853695   47.63   <2e-16 ***
horsepower  -0.161937   0.007702  -21.03   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 5.037 on 286 degrees of freedom
Multiple R-squared:  0.6072,    Adjusted R-squared:  0.6058 
F-statistic: 442.1 on 1 and 286 DF,  p-value: < 2.2e-16

Testing our model

# Create a horsepower for prediction from test
t1<-data.frame(horsepower=test$horsepower)
# Predict the horsepower using the model
p1<- predict(lm1,newdata=t1)
# Check the accuracy
mean((test$mpg-p1)^2) # Mean Sum Square is 22.61 

[1] 20.89209

We can get diagnose plots

par(mfrow=c(2,2)) # Create a four row and four column 
plot(lm1)

We see some non-linear in the plot above, and so we should go for non-linear functions

# Using quadratic model
lm2<-lm(mpg~poly(horsepower,2), data=training) 
# Using cubic model
lm3<-lm(mpg~poly(horsepower,3), data=training) 
# Get summary 
summary(lm2)

Call:
lm(formula = mpg ~ poly(horsepower, 2), data = training)

Residuals:
     Min       1Q   Median       3Q      Max 
-15.0371  -2.5484  -0.1245   2.1726  15.6678 

Coefficients:
                      Estimate Std. Error t value Pr(>|t|)    
(Intercept)            23.8306     0.2664  89.449  < 2e-16 ***
poly(horsepower, 2)1 -105.9198     4.5212 -23.427  < 2e-16 ***
poly(horsepower, 2)2   37.8382     4.5212   8.369 2.64e-15 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 4.521 on 285 degrees of freedom
Multiple R-squared:  0.6847,    Adjusted R-squared:  0.6825 
F-statistic: 309.4 on 2 and 285 DF,  p-value: < 2.2e-16

Check the performance of the two models

# Predicting on the test set
p2<- predict(lm2, newdata=t1) # Predicting for model 2 (quadratic)
p3<-predict(lm3, newdata=t1)
# Get accuracy 
Poly2 <- rep(0,1)
Poly3<-c(0)
for ( i in 1){
  Poly2[i]<-mean((test$mpg-p2)^2)
  Poly3[i]<- mean((test$mpg-p3)^2) 
}
Poly2; Poly3

[1] 15.83542
[1] 15.74269

Examine the diagnose plot, and we see that residuals vs fitted plots look well.

# Create a four window
par(mfrow=c(2,2))
plot(lm2) # It looks well now without much pattern in the model

K-fold Cross validation

Building a simple linear regression model

# Using boot library for this task
library(boot)
# Using leave-one-out cross-validation
set.seed(123)
LONE<-glm(mpg~horsepower, data=df) # Fitting a linear regression using leave one out cross validation
MSE_Lone<-cv.glm(df, LONE) # Caculating the Mean Square error 
MSE_Lone$delta[1] # The mean square error of the model is 24.23

[1] 24.23151

We can fit different polynomial models using LOOCV (leave one out cross-validation)

# Create a for loop for this task
MSE<-rep(0,5) # Create five numbers 0
for ( i in 1:5){
  LOOCV<- glm(mpg~poly(horsepower,i), data=df)
  MSE[i]<- cv.glm(df,LOOCV)$delta[1]
}
MSE # Model accuracy for each polynomal order, starting from 1 to 5

[1] 24.23151 19.24821 19.33498 19.42443 19.03321

K-fold coss-validation

# Using loop for this task
MSE<-rep(0,5) # Create a list of 5 numbers 0
model_summary<-list(0,0,0,0,0) # Get summary for each model
# Fit a five polynomial models 
for ( i in 1:5){
  K_fold_model<-glm(mpg~poly(horsepower,i),data=df)
  MSE[i]<-cv.glm(df,K_fold_model,K=10)$delta[1]
  model_summary[i]<-list(K_fold_model)
}
MSE # Get the accuracy (mean square error) for each polynomial model. We can a list of model summary by typing model_summary 

[1] 24.35728 19.11644 19.21430 19.45361 18.89087

# Logistic Regression using cross-validation approach. Dataset is Default

# Check the dataset
Default$default<-as.factor(Default$default)
head(Default) # Using the dataset to predict a given customer can pay their debt or not with given predictors

Building a Logistic Regression and testing its performance

# Splitting dataset into two sets
library(caTools)
set.seed(1234)
sam_logis<-sample.split(Default$default, SplitRatio = 0.8)
Training<- subset(Default, sam_logis==TRUE)
Test<-subset(Default, sam_logis==FALSE)
# Constructing a logistic model on the training set
logis_model<-glm(default~student+balance+income, data=Training, family = "binomial")
# Testing the model
p_logis<-predict(logis_model, newdata = data.frame(Test[,-1]), type = "response") # Remove the response variable
# Using ifelse statement to assign 1 if it is defaut and 0 otherwise
Check<-ifelse(p_logis>=0.5,1,0)
# Adding the variable Check to the Test dataset
Test$Predicted<-p_logis
Test$Default_Predict<-Check
# Check first few rows
head(Test)

Calculating the error rate of the logistic regression

mean(Test$default!=Test$Default_Predict)

[1] 1

Using leave one out cross-validation to build a logistic regression

# Using the dataset Weekly to predict the Direction 
head(Weekly)

Weekly<-Weekly[,-8]
head(Weekly)

# Using the dataset Weekly to predict the Direction 
head(Weekly)

Weekly<-Weekly[,-1] # Year may not add values to the model, so remove it
head(Weekly)

Random Forest Model

# Using for loop to build leave one out logistic regression
Error<-rep(0, nrow(Weekly))
for ( i in 1:nrow(Weekly)){
  Logist_week<-glm(Direction~., data=Weekly[-i,], family = "binomial")
  pred<-predict.glm(Logist_week,newdata = Weekly[i,-8],type = "response")
  if (pred>=0.5){
    Error[i]<-"Up"
  }else{
    Error[i]<-"Down"
  }
}

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probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not 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algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities 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probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not 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occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities 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probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not 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algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurredglm.fit: algorithm did not convergeglm.fit: fitted probabilities numerically 0 or 1 occurred

Weekly$Predicted<-Error
head(Weekly)

# Calculating the error rate of the model
mean(Weekly$Direction!=Weekly$Predicted)*100

[1] 0.2754821

*Splitting data to train and test sets

library(randomForest)

package 㤼㸱randomForest㤼㸲 was built under R version 3.4.2randomForest 4.6-12
Type rfNews() to see new features/changes/bug fixes.

library(MASS)
library(caTools)
head(Boston) # Working with Boston Dataset

*Building the first random forest model

library(caTools)
library(tidyverse)
split<-sample.split(Boston,SplitRatio = 0.7) # Initializing split
Train<-subset(Boston, split==T) # Training set
Test<-subset(Boston,split==F) # Testing set
Test1<-Test %>% select(1:12) # Testing set after removing the response variable

• Checking different random forest models

RF1<-randomForest(medv~., data=Train, mtry=4, ntree=500, importance=T)
RF1

Call:
 randomForest(formula = medv ~ ., data = Train, mtry = 4, ntree = 500,      importance = T) 
               Type of random forest: regression
                     Number of trees: 500
No. of variables tried at each split: 4

          Mean of squared residuals: 12.20573
                    % Var explained: 85.92

plot(RF1)