# Code for Lecture 23 - glm continued, logistic regression



####Example - effects of age and birth location (wild or captive) on Survival in wolves
### Survival is not normally distribution (binomial) and isn't continuous


###import the data



datum=read.csv(file.choose())



###Analyze the data using glm



results=glm(Mortality~Age+BirthLoc,data=datum,family=binomial) ### runs a 'logistic' regression
summary(results) ### examine results


#Call:
#glm(formula = Mortality ~ Age + BirthLoc, family = binomial, 
#    data = datum)
#
#Deviance Residuals: 
#    Min       1Q   Median       3Q      Max  
#-2.2567  -0.6995   0.2488   0.7646   1.9844  
#
#Coefficients:
#            Estimate Std. Error z value Pr(>|z|)    
#(Intercept)  -2.8894     0.7143  -4.045 5.24e-05 ***
#Age           0.5354     0.1298   4.123 3.74e-05 ***
#BirthLoc      2.6016     0.6323   4.115 3.88e-05 ***
#---
#Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 
#
#(Dispersion parameter for binomial family taken to be 1)
#
#    Null deviance: 133.574  on 98  degrees of freedom
#Residual deviance:  92.696  on 96  degrees of freedom
#AIC: 98.696
#
#Number of Fisher Scoring iterations: 5

### Note that coefficient estimates cannot be interpreted as is.

### To make conclusions about effect, must take exp to the coefficient power

### Value represents a multiplier effect of dependent variable on ODDS of an outcome



### Examples


### Average mortality rate of of Age 0 individuals in the captive born group
exp(-2.8894)/(1+exp(-2.8894))


### Effect of Birth Location


exp(2.6016)


### Wild born wolves are 13.48 times as likely to die as captive born wolves

### Alternatively, The odds of wild-born wolves dying was 13.48 times that of captive born wolves

###confidence limits

exp(confint(results))

### confint(results)
### exp(1.337) ### lower confidence limit on odds ratio
### exp(3.8752) ### upper confidence limit on odds ratio


### Effect of Age

exp(0.5354)


### For each 1 year increase in age, wolves were 1.708131 times as likely to die.
### Alternatively, for each 1 year increase in age, the odds of mortality increased by 1.708131 times  



#Predictions

### What is the probability of mortality for a 5-year-old, captive-born wolf?

NewData=data.frame(BirthLoc=0,Age=5)
predict(results,NewData,type="response")

### There are no prediction intervals for a non-normal response. 
### You have to give R the argument type="response" if you want the predicted Y value. Otherwise it just gives you the prediction of the linear model