The function performs analysis of some linear and nonlinear models

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`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 |

`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) |

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

Emmanuel Arnhold <emmanuelarnhold@yahoo.com.br>

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

nls, nls2

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# 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))
# 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))
``` |

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