# Set wroking directory 
setwd("C:\\Users\\User\\Desktop\\Current paper drafts\\Pheasants and inverts")

search()

library(glmmTMB)
library(arm)
library(MuMIn)
library(MCS)
library(lme4)
library(lmtest)
library(nlme)
library(mgcv)
library(sjPlot)
library(influence.ME)
library(nlme)
library(lmerTest)
library(psych)
library(car)
library(LMERConvenienceFunctions)
library(influence.ME)
library(glmmTMB)
library(sjPlot)
library(effects)
library(lsmeans)


citation()
citation(package =  lme4, lib.loc = lib.loc)

Shifted_Invert_Data <- read.csv("Invert_Data_For_Publishing.csv")

Shifted_Invert_Data$Year<-as.factor(Shifted_Invert_Data$Year)
Shifted_Invert_Data$Survey.number <- as.factor(as.character(Shifted_Invert_Data$Survey.number))
Shifted_Invert_Data$Percentage.Enhnaced<-as.numeric(Shifted_Invert_Data$Percentage.Enhnaced)




detach(Shifted_Invert_Data)
attach(Shifted_Invert_Data)


# Each heading contains the Base, Density, and Enhanced models for each category. The Invertebrate-Habitat models are at the bottom, 
# but only the first of the Invertebrate-Habitat models has the predframe for predicting % change as only the first one showed any significance.


##----------------------------- Total Biomass -----------------------------------------

#####

##Potential DVs
Dep_Var <-Shifted_Invert_Data$Matched.Total.Biomass.in

Dep_Var <-Shifted_Invert_Data$Matched.Total.Number.in

Dep_Var <- Shifted_Invert_Data$Slug.Number.in
Dep_Var <- Dep_Var + 0.000001

Dep_Var <- Shifted_Invert_Data$Beetle.Number
Dep_Var <- Dep_Var + 0.000001

Dep_Var <- Shifted_Invert_Data$Arachnid.Number
Dep_Var <- Dep_Var + 0.000001

Dep_Var <- Shifted_Invert_Data$Detritivore.Number
Dep_Var <- Dep_Var + 0.000001



##For this equation, I've assigned pen as random terms but specified a full model

Tot.Count_Base <- glmer( Dep_Var ~ Year + Survey.number + Trap.Location 
                       + Survey.number:Trap.Location ##+ Year:Survey.number + Year:Trap.Location  
                       ##+ Year:Survey.number:Trap.Location
                       + (1 |Pen.names.Yr) 
                       , family = Gamma (link = log)
                       , data = Shifted_Invert_Data
                       , na.action = na.fail
                       , control=glmerControl(optimizer="bobyqa", optCtrl=list(maxfun=2e5))
                      )
summary(Tot.Count_Base) 
drop1(Tot.Count_Base, test = "Chisq")


##Check residuals etc
qqPlot(residuals(Tot.Count_Base))
plot(residuals(Tot.Count_Base)~fitted(Tot_Bio_Base))
##Dharma package for checking model residuals by simulation


require(lsmeans)
lsm <- lsmeans(Tot.Count_Base, ~ Survey.number*Trap.Location)
summary(lsm, type = "response")

lsmip(lsm, Trap.Location ~ Survey.number, type = "response")

##Top answer from https://stats.stackexchange.com/questions/181034/post-hoc-test-of-interaction-factor-in-binomial-glmm-with-proportions
##Produce model output table
tab_model(Tot.Count_Base)

theme_set(theme_sjplot2())
+ labs(x="Task", y= "Pecks")
plot_model(Tot.Count_Base, type = "pred", terms = c( "Survey.number", "Trap.Location"), xlab = "Start and end of training", ylab = "%correct choices")

##Potential DVs
Dep_Var <-Shifted_Invert_Data$Matched.Total.Biomass.in

Dep_Var <-Shifted_Invert_Data$Matched.Total.Number.in

Dep_Var <- Shifted_Invert_Data$Slug.Number.in
Dep_Var <- Dep_Var + 0.000001

Dep_Var <- Shifted_Invert_Data$Beetle.Number
Dep_Var <- Dep_Var + 0.000001

Dep_Var <- Shifted_Invert_Data$Arachnid.Number
Dep_Var <- Dep_Var + 0.000001

Dep_Var <- Shifted_Invert_Data$Detritivore.Number
Dep_Var <- Dep_Var + 0.000001

##Analysis of enhanced bird contribution models excluding Year as a fixed factor
Tot.Count_Enh <- glmer (Dep_Var ~ Survey.number + Trap.Location + Percentage.Enhnaced
                        + Survey.number:Trap.Location + Survey.number:Percentage.Enhnaced + Trap.Location:Percentage.Enhnaced
                        +Survey.number:Trap.Location:Percentage.Enhnaced
                        + (1 |Pen.names.Yr) + (1 |Year)
                        , family = Gamma (link = log)
                        , data = Shifted_Invert_Data
                        , na.action = na.fail
                        ##, nAGQ=0
                        , control=glmerControl(optimizer="bobyqa", optCtrl=list(maxfun=2e5))
)
summary(Tot.Count_Enh)
drop1(Tot.Count_Enh, test = "Chisq")

##Produce model output table
tab_model(Tot.Count_Enh)


##Analysis of released bird density models excluding Year as a fixed factor
Tot.Count_Den <- glmer (Dep_Var ~ Survey.number + Trap.Location + True.Density
                        + Survey.number:Trap.Location + Survey.number:True.Density + Trap.Location:True.Density
                        +Survey.number:Trap.Location:True.Density
                        + (1 |Pen.names.Yr) + (1 |Year)
                        , family = Gamma (link = log)
                        , data = Shifted_Invert_Data
                        , na.action = na.fail
                        , control=glmerControl(optimizer="bobyqa", optCtrl=list(maxfun=2e5))
)
summary(Tot.Count_Den)
drop1(Tot.Count_Den, test = "Chisq")

##Produce model output table
tab_model(Tot.Count_Den)






##to change reference catefgory [relevel(survey.number,ref=2)



##library(multcomp)
##pairwise<-glht(Tot_Bio_Base,mcp(Survey.number="Tukey"))
##pairwise
theme_set(theme_sjplot2())
plot_model(Tot.Count_Base, type = "pred", terms = c( "Survey.number", "Trap.Location", "Year"))


require(lsmeans)
lsm <- lsmeans(Tot_Bio_Base, ~ Survey.number*Trap.Location)
summary(lsm, type = "response")

lsmip(lsm, Trap.Location ~ Survey.number, type = "response")

##Top answer from https://stats.stackexchange.com/questions/181034/post-hoc-test-of-interaction-factor-in-binomial-glmm-with-proportions





##Generate means for each category
pdat <- expand.grid(Trap.Location = c("Exterior", "Interior"), Survey.number = c("1","2","3"))
pred <- predict (Tot_Bio_Base, newdata = expand.grid(Trap.Location = c("Exterior", "Interior"), Survey.number = c("1","2","3")), re.form = ~0, type = "response",se.fit=T)
predframe <- data.frame (pdat, preds = pred)


predframe





















Tot.Bio_Den <- glmer(Dep_Var ~ Survey.number 
                       
                       + Survey.number:Year
                       + True.Density:Survey.number
                       
                       
                       + Survey.number:Trap.Location:Year
                       + Trap.Location:Survey.number:True.Density
                       
                       + (1 |Pen.names.Yr)
                       , family = Gamma (link = log)
                       , nAGQ=0 
                       , data = Shifted_Invert_Data
                       , na.action = na.fail)
summary(Tot.Bio_Den) 


Tot.Bio_Enh <- glmer( (Dep_Var) ~ Survey.number 
                        
                        
                        + Survey.number:Year
                        + Percentage.Enhnaced:Survey.number
                        
                        
                        + Survey.number:Trap.Location:Year
                        + Trap.Location:Survey.number:Percentage.Enhnaced
                        
                        + (1 |Pen.names.Yr)
                        , family = Gamma (link = log)
                        , nAGQ=0 
                        , data = Shifted_Invert_Data
                        , na.action = na.fail)
summary(Tot.Bio_Enh)


# Values for % results
## For this equation, I've removed year
pdat <- expand.grid(Trap.Location = c("Exterior", "Interior"), Survey.number = c("1","2","3"))
pred <- predict (Tot_Bio_Base, newdata = expand.grid(Trap.Location = c("Exterior", "Interior"), Survey.number = c("1","2","3")), re.form = ~0, type = "response",se.fit=T)
predframe <- data.frame (pdat, preds = pred)


predframe



# For density specific results
pdat <- expand.grid(Trap.Location = c("Exterior", "Interior"), Survey.number = c("1","2","3"), True.Density = c(0.2,0.3), Year = c("1","2"))
pred <- predict (Tot.Bio_Den, newdata = expand.grid(Trap.Location = c("Exterior", "Interior"), Survey.number = c("1","2","3"), True.Density = c(0.2,0.3), Year = c("1","2")), re.form = ~0, type = "response",se.fit=T)
predframe <- data.frame (pdat, preds = pred)


predframe


# For Enhanced specific results


pdat <- expand.grid(Trap.Location = c("Exterior", "Interior"), Survey.number = c("1","2","3"), Percentage.Enhnaced = c(0,50), Year = c("1","2"))
pred <- predict (Tot.Bio_Enh, newdata = expand.grid(Trap.Location = c("Exterior", "Interior"), Survey.number = c("1","2","3"), Percentage.Enhnaced = c(0,50), Year = c("1","2")), re.form = ~0, type = "response",se.fit=T)
predframe <- data.frame (pdat, preds = pred)


predframe



# ------------------------------ Total Count ----------------------------------------------------------------

#####

Dep_Var <- Shifted_Invert_Data$Matched.Total.Number.in


Tot.Count_Base <- glmer( Dep_Var ~ Survey.number 
                         
                         
                         
                         + Survey.number:Year
                         
                         + Survey.number:Trap.Location:Year
                         + (1 |Pen.names.Yr)
                         , family = Gamma (link = log)
                         , nAGQ=0 
                         , data = Shifted_Invert_Data
                         , na.action = na.fail)
summary(Tot.Count_Base) 



Tot.Count_Den <- glmer(Dep_Var ~ Survey.number 
                       
                       + Survey.number:Year
                       + True.Density:Survey.number
                       
                       
                       + Survey.number:Trap.Location:Year
                       + Trap.Location:Survey.number:True.Density
                       
                       + (1 |Pen.names.Yr)
                       , family = Gamma (link = log)
                       , nAGQ=0 
                       , data = Shifted_Invert_Data
                       , na.action = na.fail)
summary(Tot.Count_Den) 


Tot.Count_Enh <- glmer( (Dep_Var) ~ Survey.number 
                        
                        
                        + Survey.number:Year
                        + Percentage.Enhnaced:Survey.number
                        
                        
                        + Survey.number:Trap.Location:Year
                        + Trap.Location:Survey.number:Percentage.Enhnaced
                        
                        + (1 |Pen.names.Yr)
                        , family = Gamma (link = log)
                        , nAGQ=0 
                        , data = Shifted_Invert_Data
                        , na.action = na.fail)
summary(Tot.Count_Enh)



# Values for % results

pdat <- expand.grid(Trap.Location = c("Exterior", "Interior"), Year = c("1","2"), Survey.number = c("1","2","3"))
pred <- predict (Tot.Count_Base, newdata = expand.grid(Trap.Location = c("Exterior", "Interior"), Year = c("1","2"), Survey.number = c("1","2","3")), re.form = ~0, type = "response",se.fit=T)
predframe <- data.frame (pdat, preds = pred)


predframe



# For density specific results
pdat <- expand.grid(Trap.Location = c("Exterior", "Interior"), Survey.number = c("1","2","3"), True.Density = c(0.2,0.3), Year = c("1","2"))
pred <- predict (Tot.Count_Den, newdata = expand.grid(Trap.Location = c("Exterior", "Interior"), Survey.number = c("1","2","3"), True.Density = c(0.2,0.3), Year = c("1","2")), re.form = ~0, type = "response",se.fit=T)
predframe <- data.frame (pdat, preds = pred)


predframe


# For Enhanced specific results


pdat <- expand.grid(Trap.Location = c("Exterior", "Interior"), Survey.number = c("1","2","3"), Percentage.Enhnaced = c(0,50), Year = c("1","2"))
pred <- predict (Tot.Count_Enh, newdata = expand.grid(Trap.Location = c("Exterior", "Interior"), Survey.number = c("1","2","3"), Percentage.Enhnaced = c(0,50), Year = c("1","2")), re.form = ~0, type = "response",se.fit=T)
predframe <- data.frame (pdat, preds = pred)


predframe


#--------------------------------Slug Count--------------------------

#####



Dep_Var <- Shifted_Invert_Data$Slug.Number.in
Dep_Var <- Dep_Var + 0.000001


Slug_Count_Base <- glmer( sqrt (Dep_Var) ~ Survey.number 
                          
                          + Survey.number:Year
                          
                          + Survey.number:Trap.Location:Year
                          + (1 |Pen.names.Yr)
                          , family = Gamma (link = log)
                          , nAGQ=0 
                          , data = Shifted_Invert_Data
                          , na.action = na.fail)
summary(Slug_Count_Base) 





Slug_Count_Den <- glmer(sqrt (Dep_Var) ~ Survey.number 
                        
                        
                        + Survey.number:Year
                        + True.Density:Survey.number
                        
                        
                        + Survey.number:Trap.Location:Year
                        + Trap.Location:Survey.number:True.Density
                        
                        + (1 |Pen.names.Yr)
                        , family = Gamma (link = log)
                        , nAGQ=0 
                        , data = Shifted_Invert_Data
                        , na.action = na.fail)
summary(Slug_Count_Den) 




Slug_Count_Enh <- glmer( sqrt (Dep_Var) ~ Survey.number 
                         
                         
                         + Survey.number:Year
                         + Percentage.Enhnaced:Survey.number
                         
                         
                         + Survey.number:Trap.Location:Year
                         + Trap.Location:Survey.number:Percentage.Enhnaced
                         
                         + (1 |Pen.names.Yr)
                         , family = Gamma (link = log)
                         , nAGQ=0 
                         , data = Shifted_Invert_Data
                         , na.action = na.fail)
summary(Slug_Count_Enh) 


# Values for % results

pdat <- expand.grid(Trap.Location = c("Exterior", "Interior"), Year = c("1","2"), Survey.number = c("1","2","3"))
pred <- predict (Slug_Count_Base, newdata = expand.grid(Trap.Location = c("Exterior", "Interior"), Year = c("1","2"), Survey.number = c("1","2","3")), re.form = ~0, type = "response",se.fit=T)
predframe <- data.frame (pdat, preds = pred)


predframe



# For density specific results
pdat <- expand.grid(Trap.Location = c("Exterior", "Interior"), Survey.number = c("1","2","3"), True.Density = c(0.2,0.3), Year = c("1","2"))
pred <- predict (Slug_Count_Den, newdata = expand.grid(Trap.Location = c("Exterior", "Interior"), Survey.number = c("1","2","3"), True.Density = c(0.2,0.3), Year = c("1","2")), re.form = ~0, type = "response",se.fit=T)
predframe <- data.frame (pdat, preds = pred)


predframe


# For Enhanced specific results
# For Enhanced specific results


pdat <- expand.grid(Trap.Location = c("Exterior", "Interior"), Survey.number = c("1","2","3"), Percentage.Enhnaced = c(0,50), Year = c("1","2"))
pred <- predict (Slug_Count_Enh, newdata = expand.grid(Trap.Location = c("Exterior", "Interior"), Survey.number = c("1","2","3"), Percentage.Enhnaced = c(0,50), Year = c("1","2")), re.form = ~0, type = "response",se.fit=T)
predframe <- data.frame (pdat, preds = pred)


predframe



#-----------------------------Beetle Count-------------------------------------

#####


Dep_Var <- Shifted_Invert_Data$Beetle.Number
Dep_Var <- Dep_Var + 0.000001


Beetle_Count_Base <- glmer(Dep_Var ~ Survey.number 
                           
                           
                           + Survey.number:Year
                           
                           + Survey.number:Trap.Location:Year
                           + (1 |Pen.names.Yr)
                           , family = Gamma (link = log)
                           , nAGQ=0 
                           , data = Shifted_Invert_Data
                           , na.action = na.fail)
summary(Beetle_Count_Base) 





Beetle_Count_Den <- glmer(Dep_Var ~ Survey.number 
                          
                          
                          + Survey.number:Year
                          + True.Density:Survey.number
                          
                          
                          + Survey.number:Trap.Location:Year
                          + Trap.Location:Survey.number:True.Density
                          
                          + (1 |Pen.names.Yr)
                          , family = Gamma (link = log)
                          , nAGQ=0 
                          , data = Shifted_Invert_Data
                          , na.action = na.fail)
summary(Beetle_Count_Den) 




Beetle_Count_Enh <- glmer( (Dep_Var) ~ Survey.number 
                           
                           
                           + Survey.number:Year
                           + Percentage.Enhnaced:Survey.number
                           
                           
                           + Survey.number:Trap.Location:Year
                           + Trap.Location:Survey.number:Percentage.Enhnaced
                           
                           + (1 |Pen.names.Yr)
                           , family = Gamma (link = log)
                           , nAGQ=0 
                           , data = Shifted_Invert_Data
                           , na.action = na.fail)
summary(Beetle_Count_Enh) 


# Values for % results

pdat <- expand.grid(Trap.Location = c("Exterior", "Interior"), Year = c("1","2"), Survey.number = c("1","2","3"))
pred <- predict (Beetle_Count_Base, newdata = expand.grid(Trap.Location = c("Exterior", "Interior"), Year = c("1","2"), Survey.number = c("1","2","3")), re.form = ~0, type = "response",se.fit=T)
predframe <- data.frame (pdat, preds = pred)


predframe



# For density specific results
pdat <- expand.grid(Trap.Location = c("Exterior", "Interior"), Survey.number = c("1","2","3"), True.Density = c(0.2,0.3), Year = c("1","2"))
pred <- predict (Beetle_Count_Den, newdata = expand.grid(Trap.Location = c("Exterior", "Interior"), Survey.number = c("1","2","3"), True.Density = c(0.2,0.3), Year = c("1","2")), re.form = ~0, type = "response",se.fit=T)
predframe <- data.frame (pdat, preds = pred)


predframe


# For Enhanced specific results


pdat <- expand.grid(Trap.Location = c("Exterior", "Interior"), Survey.number = c("1","2","3"), Percentage.Enhnaced = c(0,50), Year = c("1","2"))
pred <- predict (Beetle_Count_Enh, newdata = expand.grid(Trap.Location = c("Exterior", "Interior"), Survey.number = c("1","2","3"), Percentage.Enhnaced = c(0,50), Year = c("1","2")), re.form = ~0, type = "response",se.fit=T)
predframe <- data.frame (pdat, preds = pred)


predframe


#-----------------------------Arachnid Count-----------------------------------------

#####


Dep_Var <- Shifted_Invert_Data$Arachnid.Number
Dep_Var <- Dep_Var + 0.000001


Arachnid_Count_Base <- glmer(sqrt (Dep_Var) ~ Survey.number 
                             
                             
                             
                             + Survey.number:Year
                             
                             + Survey.number:Trap.Location:Year
                             + (1 |Pen.names.Yr)
                             , family = Gamma (link = log)
                             , nAGQ=0 
                             , data = Shifted_Invert_Data
                             , na.action = na.fail)
summary(Arachnid_Count_Base) 







Arachnid_Count_Den <- glmer( sqrt (Dep_Var) ~ Survey.number 
                             
                             
                             + Survey.number:Year
                             + True.Density:Survey.number
                             
                             
                             + Survey.number:Trap.Location:Year
                             + Trap.Location:Survey.number:True.Density
                             
                             + (1 |Pen.names.Yr)
                             , family = Gamma (link = log)
                             , nAGQ=0 
                             , data = Shifted_Invert_Data
                             , na.action = na.fail)
summary(Arachnid_Count_Den) 




Arachnid_Count_Enh <- glmer( sqrt(Dep_Var) ~ Survey.number 
                             
                             
                             + Survey.number:Year
                             + Percentage.Enhnaced:Survey.number
                             
                             
                             + Survey.number:Trap.Location:Year
                             + Trap.Location:Survey.number:Percentage.Enhnaced
                             
                             + (1 |Pen.names.Yr)
                             , family = Gamma (link = log)
                             , nAGQ=0 
                             , data = Shifted_Invert_Data
                             , na.action = na.fail)
summary(Arachnid_Count_Enh) 


# Values for % results

pdat <- expand.grid(Trap.Location = c("Exterior", "Interior"), Year = c("1","2"), Survey.number = c("1","2","3"))
pred <- predict (Arachnid_Count_Base, newdata = expand.grid(Trap.Location = c("Exterior", "Interior"), Year = c("1","2"), Survey.number = c("1","2","3")), re.form = ~0, type = "response",se.fit=T)
predframe <- data.frame (pdat, preds = pred)


predframe



# For density specific results
pdat <- expand.grid(Trap.Location = c("Exterior", "Interior"), Survey.number = c("1","2","3"), True.Density = c(0.2,0.3), Year = c("1","2"))
pred <- predict (Arachnid_Count_Den, newdata = expand.grid(Trap.Location = c("Exterior", "Interior"), Survey.number = c("1","2","3"), True.Density = c(0.2,0.3), Year = c("1","2")), re.form = ~0, type = "response",se.fit=T)
predframe <- data.frame (pdat, preds = pred)


predframe


# For Enhanced specific results


pdat <- expand.grid(Trap.Location = c("Exterior", "Interior"), Survey.number = c("1","2","3"), Percentage.Enhnaced = c(0,50), Year = c("1","2"))
pred <- predict (Arachnid_Count_Enh, newdata = expand.grid(Trap.Location = c("Exterior", "Interior"), Survey.number = c("1","2","3"), Percentage.Enhnaced = c(0,50), Year = c("1","2")), re.form = ~0, type = "response",se.fit=T)
predframe <- data.frame (pdat, preds = pred)


predframe


#--------------------------Detritivore Count---------------------------------------

#####


Dep_Var <- Shifted_Invert_Data$Detritivore.Number
Dep_Var <- Dep_Var + 0.000001


Det_Count_Base <- glmer( sqrt (Dep_Var) ~ Survey.number 
                         
                         
                         + Survey.number:Year
                         
                         + Survey.number:Trap.Location:Year
                         + (1 |Pen.names.Yr)
                         , family = Gamma (link = log)
                         , nAGQ=0 
                         , data = Shifted_Invert_Data
                         , na.action = na.fail)
summary(Det_Count_Base) 





Det_Count_Den <- glmer( sqrt (Dep_Var) ~ Survey.number 
                        
                        
                        + Survey.number:Year
                        + True.Density:Survey.number
                        
                        
                        + Survey.number:Trap.Location:Year
                        + Trap.Location:Survey.number:True.Density
                        
                        + (1 |Pen.names.Yr)
                        , family = Gamma (link = log)
                        , nAGQ=0 
                        , data = Shifted_Invert_Data
                        , na.action = na.fail)
summary(Det_Count_Den) 




Det_Count_Enh <- glmer( sqrt (Dep_Var) ~ Survey.number 
                        
                        
                        + Survey.number:Year
                        + Percentage.Enhnaced:Survey.number
                        
                        
                        + Survey.number:Trap.Location:Year
                        + Trap.Location:Survey.number:Percentage.Enhnaced
                        
                        + (1 |Pen.names.Yr)
                        , family = Gamma (link = log)
                        , nAGQ=0 
                        , data = Shifted_Invert_Data
                        , na.action = na.fail)
summary(Det_Count_Enh) 


# Values for % results

pdat <- expand.grid(Trap.Location = c("Exterior", "Interior"), Year = c("1","2"), Survey.number = c("1","2","3"))
pred <- predict (Det_Count_Base, newdata = expand.grid(Trap.Location = c("Exterior", "Interior"), Year = c("1","2"), Survey.number = c("1","2","3")), re.form = ~0, type = "response",se.fit=T)
predframe <- data.frame (pdat, preds = pred)


predframe



# For density specific results
pdat <- expand.grid(Trap.Location = c("Exterior", "Interior"), Survey.number = c("1","2","3"), True.Density = c(0.2,0.3), Year = c("1","2"))
pred <- predict (Det_Count_Den, newdata = expand.grid(Trap.Location = c("Exterior", "Interior"), Survey.number = c("1","2","3"), True.Density = c(0.2,0.3), Year = c("1","2")), re.form = ~0, type = "response",se.fit=T)
predframe <- data.frame (pdat, preds = pred)


predframe



# For Enhanced specific results


pdat <- expand.grid(Trap.Location = c("Exterior", "Interior"), Survey.number = c("1","2","3"), Percentage.Enhnaced = c(0,50), Year = c("1","2"))
pred <- predict (Det_Count_Enh, newdata = expand.grid(Trap.Location = c("Exterior", "Interior"), Survey.number = c("1","2","3"), Percentage.Enhnaced = c(0,50), Year = c("1","2")), re.form = ~0, type = "response",se.fit=T)
predframe <- data.frame (pdat, preds = pred)


predframe