# Permutation test for difference in slopes
# Author: Rose Keith
# Calculates the difference in slopes between estimates for two variables for the observed model and 1000
# permuted data sets.
# Input file: a tab-delimited .txt file with a header

library(car)
library(dplyr)
library(lme4)


datafile <- read.table('/Users/rosekeith 1/Documents/Biology/Field_data/Field_2014/field_using/KW_complete_checked_noald.txt', header=T, sep='\t', quote='')

# fit linear model with the original data:

observed.model<-lmer(trans_Actual_fr~Site + Veg + trans_rosPctDam + trans_cauPctDam + 
                       trans_frPctDam + Stg + (1|Site:Block) + (1|Genotype), data=datafile)

# look at the results using Type III SS
Anova(observed.model,Type='III')

plot(observed.model)

coef(summary(observed.model))%>% as.data.frame %>%
  filter(row.names(.)=='trans_cauPctDam') %>% # filter out everything but caudam
  select(`Estimate`) -> obs.cau.est  # save only the Estimate for caudam

coef(summary(observed.model))%>% as.data.frame %>%
  filter(row.names(.)=='trans_frPctDam')%>% #filter out everything but frdam
  select(`Estimate`)->obs.fr.est #save only the estimate for frdam

obs.slope.diff <- obs.fr.est-obs.cau.est



###### Permutation Test #######

# set random number generator
set.seed(777)
# set number of permutations:
nperm<-2000 # set number of permutations
numrows<-length(datafile$Plant_ID)

for (i in 1:nperm) {
  # copy the data frame to a new object for permuting
  data.perm<-datafile
  if (i==1) { # initialize empty data frame to store results
    perm.results<-data.frame('Permutation'=integer(),'Cau_est'=numeric(), 'Fr_est'=numeric(), 'Slope_diff'=numeric())
  }
  for (n in 1:numrows){
    data.perm[n,25:26]<-sample(data.perm[n,25:26])
    
  }
  print(paste0("Beginning simulation number ",as.character(i)))
  perm.model<-lmer(trans_Actual_fr~Site + Veg + trans_rosPctDam + trans_cauPctDam + 
                         trans_frPctDam + Stg + (1|Site:Block) + (1|Genotype), data=data.perm)
  
  coef(summary(perm.model))%>% as.data.frame %>%
    filter(row.names(.)=='trans_cauPctDam') %>% # filter out everything but caudam
    select(`Estimate`) -> perm.cau.est  # save only the Estimate for caudam
  
  coef(summary(perm.model))%>% as.data.frame %>%
    filter(row.names(.)=='trans_frPctDam')%>% #filter out everything but frdam
    select(`Estimate`) -> perm.fr.est #save only the estimate for frdam
  
  perm.slope.diff <- perm.fr.est-perm.cau.est
  
  perm.results<- rbind(perm.results,data.frame('Permutation'=i,'Cau_est'=perm.cau.est, "FR_est"=perm.fr.est, "Slope_diff"=perm.slope.diff))
    
}

# View results:
summary(perm.results)
hist(perm.results$Estimate.2)

# Divide number of larger t-values by number of permutations to get P-value.