er1: Analysis of regression

Description

The function performs analysis of some linear and nonlinear models

Usage

er1(data, model = 1, start = c(a = 1, b = 1, c = 1, d = 1, e = 1), 
mixed=FALSE, digits=6, alpha=0.05)

Arguments

data

data is a data.frame

The first column should contain the treatments (explanatory variable) and the remaining columns the response variables.

model

define the model

1 = "y~a+b*x" linear

2 = "y~a+b*x+c*x^2" quadratic

3 = "y ~ a + b * (x - c) * (x <= c)" linear plateau

4 = "y ~ (a + b * x + c * I(x^2)) * (x <= -0.5 * b/c) + (a + I(-b^2/(4 * c))) * (x > -0.5 * b/c)" quadratic plateau

5 = "ifelse(x>=d,(a-c*d)+(b+c)*x, a+b*x)" two linear

6 = "y~a*exp(b*x)" exponential

7 = "y~a*(1+b*(exp(-c*x)))^-1" logistic

8 = "y~a*(1-b*(exp(-c*x)))^3" van bertalanffy

9 = "y~a*(1-b*(exp(-c*x)))" brody

10 = "y~a*exp(-b*exp(-c*x)" gompertz

11 = "y~(a*x^b)*exp(-c*x)" lactation curve

12 = "y ~ a + b * (1 - exp(-c * x))" ruminal degradation curve

13 = "y~(a/(1+exp(2-4*c*(x-e))))+(b/(1+exp(2-4*d*(x-e))))" logistic bi-compartmental

14 = "y~a*(x^b)" exponential (allometric model)

15 = "y~a+b*x+c*x^2+d*x^3" cubic

16 = "y~a/(1+b*(exp(-c*x)))^d" richards

17 = "y~(a^d+ ((b^d)-(a^d) )*((1-exp(-c*(x-t1)))/ (1-exp(-c*(t2-t1)))))^(1/d)" schnute

start

start values of the iteration process

mixed

FALSE/defalt for fixed model or TRUE for mixed model

digits

number of digits in results (default=6)

alpha

significant level of the confident intervals for parameters in the models

Value

Returns coefficients of the models, t test for coefficients, R squared, adjusted R squared, AIC, BIC, and residuals of the model

References

KAPS, M. and LAMBERSON, W. R. Biostatistics for Animal Science: an introductory text. 2nd Edition. CABI Publishing, Wallingford, Oxfordshire, UK, 2009. 504p.

TERRANCE J. QUINN II and RICHARD B. DERISO. Quantitative Fish Dynamics, New York, Oxford, Oxford University Press, 1999.

Examples

Run this code

# NOT RUN {
# weights of an Angus cow at ages from 8 to 108 months (Kaps and Lamberson, 2009)

weight=c(280,340,430,480,550,580,590,600,590,600)
age=c(8,12,24,36,48,60,72,84,96,108)

data1=data.frame(age, weight)

# linear
er1(data1, model=1)

# quadratic
er1(data1, model=2)

# linear plateau
er1(data1, model=3)

# quadratic plateau
er1(data1, model=4)

# two linear
er1(data1, model=5, start=c(250,6,2,50))

# exponential
er1(data1, model=6, start=c(250,0.05))

# logistic
er1(data1, model=7, start=c(600,4,0.05))

# van bertalanffy
er1(data1, model=8, start=c(600,2,0.05))

# brody
er1(data1, model=9, start=c(600,4,0.05))

# gompertz
er1(data1, model=10, start=c(600,4,0.05))

# richards
er1(data1, model=16, start=c(600,2,0.05,1.4))

# allometric
er1(data1, model=14)

# cubic
er1(data1, model=15)



# growth of Zagorje turkeys (Kaps and Lamberson, 2009)


weight=c(44,66,100,150,265,370,455,605,770)
age=c(1,7,14,21,28,35,42,49,56)

data2=data.frame(age,weight)

# two linear
er1(data2, model=5, start=c(25,6,10,20))

# gain weight measurements of turkey poults (Kaps and Lamberson, 2009)

methionine=c(80,85,90,95,100,105,110,115,120)
gain=c(102,115,125,133,140,141,142,140,142)

data3=data.frame(methionine, gain)

# linear
er1(data3, model=1)

# quadratic
er1(data3, model=2)

# linear plateau
er1(data3, model=3)

# quadratic plateau
er1(data3, model=4)

# lactation curve
 milk=c(25,24,26,28,30,31,27,26,25,24,23,24,22,21,22,
20,21,19,18,17,18,18,16,17,15,16,14)
 days=c(15,15,15,75,75,75,135,135,135,195,
195,195,255,255,255,315,315,315,375,375,375,435,435,435,495,495,495)
    
 data4=data.frame(days,milk)
	

er1(data4, model=11, start=c(16,0.25,0.004))

# ruminal degradation 
time=c(2,6,9,24,48,72,96)
deg=c(20,33,46,55,66,72,76)

data5=data.frame(time,deg)

er1(data5, model=12)

# logistic bi-compartmental (gas production)
time=c(0,12,24,36,48,60,72,84,96,108,120,144,168,192)
gas=c(0.002,3.8,8,14.5,16,16.5,17,17.4,17.9,18.1,18.8,19,19.2,19.3)
    
data6=data.frame(time,gas)

er1(data6, model=13, start=c(19,4,0.025,0.004,5))

# Schnute model
#pacific halibut weight-age data of females (Terrance and Richard, 1999)
 
age=c(4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
19,20,21,22,23,24,28)
weight=c(1.7,2,3.9, 4.2,6.4,7.6,10.9,14.9,18.2,21.6,
25.4,28.8,30.9,	35.6,37.9,34.7,44.8,52.6,49.1,56.7,58.6,54.1)

halibut=data.frame(age,weight)


t1=min(halibut[,2])
t2=max(halibut[,2])

er1(halibut,model=17, start=c(a=t1,b=t2,c=0.15,d=-0.50))


# }