##### Code for 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

## 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)) ### lower 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  
min(datum$Age) 
max(datum$Age)
exp(2.6016*(10-9))
# the oldest wolves were 123.8 times as likely to die as the youngest wolves


###Prediction


#What is the estimated mortality rate of a wild-born, 5-year-old wolf have, on average?
exp(-2.8894+2.6016+0.5354*5)/(1+exp(-2.8894+2.6016+0.5354*5))


##### DataSet 2

 
###Example - effects of age, birth location (wild or captive), and body condition (percent body fat)
### on litter sizes in red wolves
### Litter size is not normally distribution (skewed to the left) and isn't continuous


###import the data


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


### Run Analysis


results=glm(LitterSize~Age+BirthLoc+BodyCond,data=datum,family=poisson)
summary(results)

#glm(formula = LitterSize ~ Age + BirthLoc + BodyCond, family = poisson, 
#    data = datum)
#
#Deviance Residuals: 
#    Min       1Q   Median       3Q      Max  
#-1.6338  -0.7791  -0.2243   0.4249   2.7210  
#
#Coefficients:
#            Estimate Std. Error z value Pr(>|z|)    
#(Intercept) -0.08328    0.28494  -0.292 0.770082    
#Age         -0.20223    0.02939  -6.880 5.97e-12 ***
#BirthLoc     1.49315    0.17924   8.330  < 2e-16 ***
#BodyCond     2.22882    0.64759   3.442 0.000578 ***
#---
#Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 
#
#(Dispersion parameter for poisson family taken to be 1)
#
#    Null deviance: 224.25  on 98  degrees of freedom
#Residual deviance:  73.30  on 95  degrees of freedom
#AIC: 274.91

#Number of Fisher Scoring iterations: 5


###Examples


## Effects of age
exp(-0.20223)
#For each 1 year increase in age, wolves had 0.8169 times as many pups
# Hard to wrap head around - alternative:
exp(0.20223) ### or
1/exp(-0.20223) ### same thing
# For each 1 year DECREASE in age, wolves had 1.22413 times as many pups

#Alternatively, for each 1 year increase in age, wolves had 18.3% fewer pups
#(1-0.8169)


##Effects of Body Condition - Scaling
exp(2.22882)
# doesn't really make any sense because body condition only ranged from about 0.1 to 0.5
# 1 unit change in body condition is the change from 0 body fat to 100% body fat - doesn't make sense
exp(2.22882*0.1) ### scale the value
# for each 10% increase in body fat, wolves had 1.25 times as many pups
exp(2.22882*(0.5-0.1)) ### range in body fat values
# The fatest wolves had 2.438853 times as many pups as the skinniest wolves