Growth Model

new7 <- read.csv(file="N:/DaheeKim/April/Reef/reef.csv", header=TRUE, sep=",")
data1 <- new7
head(data1)

####################################################################################################
library(dplyr)
percent3 <- percent2
this <- c(1:9)
for(x in 1:9){
  data1 <- mutate(data1, overX = ifelse(value> x,"Pass","fail"))
  
  #change Character to Factor (for counting 0 frequency)
  data1[sapply(data1, is.character)]  <- lapply(data1[sapply(data1, is.character)],as.factor)
  
  #Relative Frequency table
  
  percent <-   data1 %>%
    group_by(Date,Tank,overX, .drop = FALSE) %>%
    summarise(count = n()) %>%
    mutate(relfreq= count / sum(count)*100) 
  
  percent2 <-  percent %>%
    filter(overX=="Pass") %>%
    select(Date,Tank, relfreq)%>%
    rename(Percent =relfreq)
  
  data1 <- na.omit(data1)
  table2<- data1 %>%
    group_by(Date,Tank) %>%
    summarise(Average = mean(value))
  
  percent2 <- as.data.frame(percent2)
  table2 <- as.data.frame(table2)
  
  #Add column from other dataframe
  percent2["Average"] <- table2["Average"]
  percent3[ , paste0("Percent", x)]<-  percent2$Percent
  #print(head(percent2))
}
head(percent3)

head(percent2)

#############################################################################################################
#package easynls(nonlinear model )
#############################################################################################################
library(easynls)
percent2$time <- as.numeric(percent2$Date)
new <-cbind(percent2$time, percent2$Percent)
new <- as.data.frame(new)
colnames(new) <- c("time","Percent")
# linear
nlsfit(new, model=1)

$Model
[1] "y~a+b*x"

$Parameters

# quadratic
nlsfit(new, model=2)

$Model
[1] "y~a+b*x+c*x^2"

$Parameters

# linear plateau
nlsfit(new, model=3)

$Model
[1] "y ~ a + b * (x - c) * (x <= c)"

$Parameters

# quadratic plateau
nlsfit(new, model=4)

$Model
[1] "y ~ (a + b * x + c * I(x^2)) * (x <= -0.5 * b/c) + (a + I(-b^2/(4 * c))) * (x > -0.5 * b/c)"

$Parameters

# two linear
#nlsfit(new, model=5, start=c(50,5,2,50))
# exponential
nlsfit(new, model=6, start=c(50,0.03))

$Model
[1] "y~a*exp(b*x)"

$Parameters

# logistic
nlsfit(new, model=7, start=c(98.20,1.4,0.03))

$Model
[1] "y~a*(1+b*(exp(-c*x)))^-1"

$Parameters

# van bertalanffy
nlsfit(new, model=8, start=c(118,1.4,0.03))

$Model
[1] "y~a*(1-b*(exp(-c*x)))^3"

$Parameters

# brody
nlsfit(new, model=9, start=c(118,4,0.05))

$Model
[1] "y~a*(1-b*(exp(-c*x)))"

$Parameters

# gompertz
nlsfit(new, model=10, start=c(100,4,0.05))

$Model
[1] "y~a*exp(-b*exp(-c*x)"

$Parameters

# linear
nlsplot(new, model=1)

# quadratic
nlsplot(new, model=2)

# linear plateau
nlsplot(new, model=3)

# quadratic plateau
nlsplot(new, model=4)

# two linear
#nlsplot(new, model=5, start=c(50,5,2,50))
# exponential
nlsplot(new, model=6, start=c(50,0.03))

# logistic
#nlsplot(new, model=7, start=c(118,1.4,0.03))
# van bertalanffy
nlsplot(new, model=8, start=c(118,1.4,0.03))

# brody
nlsplot(new, model=9, start=c(118,4,0.05))

# gompertz
nlsplot(new, model=10, start=c(100,4,0.05))

reg.Gompertz= nls("Percent~A*exp(-exp(mu*exp(1)/A*(lambda-time)+1))", percent3, start=list(A=100,mu=7.185374,lambda=21.000000))

Error in nls("Percent~A*exp(-exp(mu*exp(1)/A*(lambda-time)+1))", percent3,  : 
  singular gradient

SS<-getInitial(Percent~SSlogis(time,alpha,xmid,scale),percent2)
fm1 <- nls(Percent ~ SSlogis(time, Asym, xmid, scal), data = percent2)
summary(fm1)

Formula: Percent ~ SSlogis(time, Asym, xmid, scal)

Parameters:
     Estimate Std. Error t value Pr(>|t|)    
Asym 97.73746    0.70410  138.81   <2e-16 ***
xmid  7.42913    0.06600  112.56   <2e-16 ***
scal  1.38983    0.05683   24.45   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 3.446 on 57 degrees of freedom

Number of iterations to convergence: 0 
Achieved convergence tolerance: 2.448e-06

reg.Logistic= nls(Percent~(Asym)/(1+exp((xmid-time)/scal)),data=percent2, start=list(Asym=98.1750,xmid=24.3177,scal=4.9204))

Error in nls(Percent ~ (Asym)/(1 + exp((xmid - time)/scal)), data = percent2,  : 
  singular gradient

#############################################################################################################
# Nonlinear Regression for (Richards) function
#############################################################################################################
#install.packages("NRAIA", repos="http://R-Forge.R-project.org")
library(NRAIA)

Loading required package: lattice
Registered S3 methods overwritten by 'NRAIA':
  method           from 
  plot.nls         nlme 
  plot.profile.nls stats

reg.Richards <- nls(Percent ~ SSRichards(time, Asym, xmid, scal, lpow), percent2)
summary(reg.Richards <- nls(Percent ~ SSRichards(time, Asym, xmid, scal, lpow), percent2))

Formula: Percent ~ SSRichards(time, Asym, xmid, scal, lpow)

Parameters:
     Estimate Std. Error t value Pr(>|t|)    
Asym  99.1846     0.7688 129.017   <2e-16 ***
xmid   3.0067     2.6619   1.130   0.2635    
scal   1.9750     0.1642  12.028   <2e-16 ***
lpow  -1.8813     1.1107  -1.694   0.0959 .  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 3.005 on 56 degrees of freedom

Number of iterations to convergence: 0 
Achieved convergence tolerance: 3.004e-06

reg.Richards=  nls(Percent ~ A*(1+exp((xmid-time)/scal))^(-exp(-lpow)),data=percent2,start=list(A=99.4454,xmid=6.2748,scal=7.0667,lpow=-2.1747))

Error in nls(Percent ~ A * (1 + exp((xmid - time)/scal))^(-exp(-lpow)),  : 
  singular gradient

#############################################################################################################
# Nonlinear Regression for (van bertalanffy) function
#############################################################################################################
reg.van=  nls(Percent ~ a*(1-b*(exp(-c*time)))^3,data=percent2,start=list(a=103.6684,b=2.3165,c=0.083))
#compare graph
AIC(reg.Logistic, reg.Richards,reg.Gompertz,reg.van)

Error in AIC(reg.Logistic, reg.Richards, reg.Gompertz, reg.van) : 
  object 'reg.Logistic' not found

#############################################################################################################  
#table 
library(knitr)
kable(new2, format = "rst")

Error in kable(new2, format = "rst") : object 'new2' not found