# https://www.r-exercises.com/2018/06/21/non-linear-model-in-r-exercise/

d <- readr::read_csv("C:/Users/mahr/Downloads/mussel.csv")

## Parsed with column specification:
## cols(
##   AREA = col_double(),
##   SPECIES = col_integer(),
##   INDIV = col_integer()
## )

plot(d$AREA, d$INDIV)

m <- nls(INDIV ~ a * AREA ^ b, d, start = list(a = .01, b = 1))
summary(m)

## 
## Formula: INDIV ~ a * AREA^b
## 
## Parameters:
##   Estimate Std. Error t value Pr(>|t|)    
## a   3.0582     2.9382   1.041    0.309    
## b   0.5738     0.1005   5.711 8.14e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 212.1 on 23 degrees of freedom
## 
## Number of iterations to convergence: 20 
## Achieved convergence tolerance: 2.505e-06

plot(d$AREA, fitted(m))

plot(fitted(m), resid(m), ylim = c(-1000, 1000))

m2 <- nls(INDIV ~ SSasympOff(AREA, Asym, lrc, c0), d)
summary(m2)

## 
## Formula: INDIV ~ SSasympOff(AREA, Asym, lrc, c0)
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## Asym 1021.146    142.173   7.182 3.37e-07 ***
## lrc    -9.009      0.353 -25.521  < 2e-16 ***
## c0    491.059    645.897   0.760    0.455    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 194.5 on 22 degrees of freedom
## 
## Number of iterations to convergence: 0 
## Achieved convergence tolerance: 1.302e-06

plot(d$AREA, fitted(m2))

plot(fitted(m2), resid(m2), ylim = c(-1000, 1000))
points(fitted(m), resid(m), col = "red")

plot(d$AREA, resid(m2))
points(d$AREA, resid(m), col = "red")

anova(m, m2)

## Analysis of Variance Table
## 
## Model 1: INDIV ~ a * AREA^b
## Model 2: INDIV ~ SSasympOff(AREA, Asym, lrc, c0)
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)  
## 1     23    1034739                           
## 2     22     831976  1 202764  5.3617 0.0303 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

AIC(m, m2)

##    df      AIC
## m   3 342.7165
## m2  4 339.2640