### snail additional analyses exercise
# preliminaries

library(MASS)
data(snails)
spA<-snails[1:48,]; spB<-snails[48:96,]
snails$deadORalive<-cbind(snails$Deaths,20-snails$Deaths) 


# ignoring interactions
par(mfrow=c(2,2))
m3<-glm(deadORalive ~ Species+Temp+Rel.Hum, family=quasibinomial, data=snails)
plot(m3)
summary(m3)
#Call:
#glm(formula = deadORalive ~ Species + Temp + Rel.Hum, family = quasibinomial, 
#    data = snails)
#
#Deviance Residuals: 
#   Min      1Q  Median      3Q     Max  
#-4.451  -2.050  -1.086   1.482   3.746  
#
#Coefficients:
#            Estimate Std. Error t value Pr(>|t|)    
#(Intercept)  2.04946    1.64006   1.250 0.214606    
#SpeciesB     1.02829    0.28270   3.637 0.000454 ***
#Temp         0.07257    0.03313   2.191 0.030997 *  
#Rel.Hum     -0.08290    0.02363  -3.508 0.000700 ***
#---
#Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#
#(Dispersion parameter for quasibinomial family taken to be 3.884657)
#
#    Null deviance: 539.72  on 95  degrees of freedom
#Residual deviance: 417.15  on 92  degrees of freedom
#AIC: NA
#
#Number of Fisher Scoring iterations: 5

## We can see that the two species differ significantly in terms of overall mortality 
## as we could easily see from the initial barplots, spB suffered overall far higher mortality.
## Next we see in terms of significance that relative humidity had a strong effect on survival,
## but the effect of temperature was only weakly significant. 
## But if you look at the estimated effect size, the model shows little difference in the magnitudes
## of the trends with temperature and relative humidity.


m4<-glm(deadORalive ~ Species+Temp+Rel.Hum, family=quasibinomial, data=snails)
plot(m3)
summary(m4)
#call:
#glm(formula = deadORalive ~ Species * Temp * Rel.Hum, family = quasibinomial, 
#    data = snails)
#
#Deviance Residuals: 
#    Min       1Q   Median       3Q      Max  
#-4.3587  -2.0465  -0.9864   1.5373   3.8610  
#
#Coefficients:
#                       Estimate Std. Error t value Pr(>|t|)
#(Intercept)            4.742861  11.747775   0.404    0.687
#SpeciesB               0.429462  14.153376   0.030    0.976
#Temp                  -0.118988   0.704660  -0.169    0.866
#Rel.Hum               -0.126446   0.178585  -0.708    0.481
#SpeciesB:Temp          0.070348   0.856805   0.082    0.935
#SpeciesB:Rel.Hum       0.013108   0.214611   0.061    0.951
#Temp:Rel.Hum           0.003071   0.010681   0.287    0.774
#SpeciesB:Temp:Rel.Hum -0.001318   0.012954  -0.102    0.919
#
#(Dispersion parameter for quasibinomial family taken to be 4.051934)
#
#    Null deviance: 539.72  on 95  degrees of freedom
#Residual deviance: 416.25  on 88  degrees of freedom
#AIC: NA

## Nothing is significant! The combination of temperature and relative humidity cancel out.


## look at the two species separately

m5<-glm(spA$Deaths ~ spA$Temp+spA$Rel.Hum)
plot(m5)
summary(m5)
# spA$Rel.Hum -0.11566    0.05241  -2.207   0.0325 *

# just considering spA there is a weakly significant trend to lower mortality with higher humidity, but no significant effect of temperature.


m6<-glm(spB$Deaths ~ spB$Temp+spB$Rel.Hum)
plot(m6)
summary(m6)
# spB$Rel.Hum  -0.2639     0.1036  -2.548   0.0143 *

## just considering spB there is a more significant trend to lower mortality with higher humidity, but again not with temperature.