Type: Package
Title: Easy Regression
Version: 4.0
Date: 2019-10-13
Author: Emmanuel Arnhold
Maintainer: Emmanuel Arnhold <emmanuelarnhold@yahoo.com.br>
Description: Performs analysis of regression in simple designs with quantitative treatments, including mixed models and non linear models.
Depends: R (≥ 3.0.0)
Imports: nlme
License: GPL-2
NeedsCompilation: no
Packaged: 2019-09-13 12:29:52 UTC; emmanuel
Repository: CRAN
Date/Publication: 2019-09-13 13:30:02 UTC

Easy Regression

Description

Performs analysis of regression in simple designs with quantitative treatments, including mixed models ans non linear models

Details

Package: easyreg
Type: Package
Version: 4.0
Date: 2019-10-13
License: GPL (>= 2)

Author(s)

Emmanuel Arnhold <emmanuelarnhold@yahoo.com.br>

References

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

SAMPAIO, I. B. M. Estatistica aplicada a experimentacao animal. 3nd Edition. Belo Horizonte: Editora FEPMVZ, Fundacao de Ensino e Pesquisa em Medicina Veterinaria e Zootecnia, 2010. 264p.

Examples

# analysis in completely randomized design
data(data1)
r1=er2(data1)
names(r1)
r1
r1[1]

# analysis in randomized block design
data(data2)
r2=er2(data2, design=2)
r2

# analysis in latin square design
data(data3)
r3=er2(data3, design=3)
r3

# analysis in several latin squares
data(data4)
r4=er2(data4, design=4)
r4

# the 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
regplot(data2, model=5, start=c(25,6,10,20))

regplot(data2, model=5, start=c(25,6,10,20), digits=2)

# in other function
bl(data2)

Analysis of broken line regression

Description

The function performs analysis of broken line regression

Usage

bl(data, model=1, alpha=0.05, xlab = "Explanatory Variable", ylab = "Response Variable", 
    position = 1, digits = 6, mean = TRUE, sd=FALSE, legend = TRUE, lty=2, 
col="dark blue", pch=20, xlim="default.x",ylim="default.y", ...)

Arguments

data

data is a data.frame The first column contain the treatments (explanatory variable) and the second column the response variable

model

model for analysis: 1=two linear; 2=linear plateau (LRP); 3= model 1 with blocks random; 4 = model 2 with blocks random

alpha

significant level for cofidence intervals (parameters estimated)

xlab

name of explanatory variable

ylab

name of response variable

position

position of equation in the graph

top=1

bottomright=2

bottom=3

bottomleft=4

left=5

topleft=6 (default)

topright=7

right=8

center=9

digits

number of digits (default=6)

mean

mean=TRUE (plot mean of data) mean=FALSE (plot all data)

sd

sd=FALSE (plot without standard deviation) sd=TRUE (plot with standard deviation)

legend

legend=TRUE (plot legend) legend=FALSE (not plot legend)

lty

line type

col

line color

pch

point type

xlim

limits for x

ylim

limits for y

...

others graphical parameters (see par)

Value

Returns coefficients of the models, t test for coefficients, knot (break point), R squared, adjusted R squared, AIC, BIC, residuals and shapiro-wilk test for residuals.

Author(s)

Emmanuel Arnhold <emmanuelarnhold@yahoo.com.br>

References

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

See Also

lm, ea1(easyanova package), er1

Examples


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

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

data2=data.frame(age,weight)

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

bl(data2, digits=2)


#linear and quadratic plateau
x=c(0,1,2,3,4,5,6)
y=c(1,2,3,6.1,5.9,6,6.1)

data=data.frame(x,y)

bl(data,model=2, lty=1, col=1, digits=2, position=8)


# effect os blocks
x=c(1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8)
y=c(4,12,9,20,16,25,21,31,28,42,33,46,33,46,34,44)
blocks=rep(c(1,2),8)

dat=data.frame(x,blocks,y)

bl(dat, 3)

bl(dat,4, sd=TRUE)

bl(dat,4, mean=FALSE)

data1: Sampaio (2010): page 134

Description

Quantitative treatments in completely randomized design.

Usage

data(data1)

Format

A data frame with 24 observations on the following 2 variables.

treatment

a numeric vector

gain

a numeric vector

References

SAMPAIO, I. B. M. Estatistica aplicada a experimentacao animal. 3nd Edition. Belo Horizonte: Editora FEPMVZ, Fundacao de Ensino e Pesquisa em Medicina Veterinaria e Zootecnia, 2010. 264p.

Examples

data(data1)
summary(data1)

data2: Kaps and Lamberson (2009): page 434

Description

Quantitative treatments in randomizad block design.

Usage

data(data2)

Format

A data frame with 25 observations on the following 3 variables.

protein_level

a numeric vector

litter

a factor with levels l1 l2 l3 l4 l5

feed_conversion

a numeric vector

References

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

Examples

data(data2)
summary(data2)

data3: fictional example

Description

Quantitative treatments in latin square design.

Usage

data(data3)

Format

A data frame with 25 observations on the following 4 variables.

treatment

a numeric vector

animal

a factor with levels a1 a2 a3 a4 a5

period

a factor with levels p1 p2 p3 p4 p5

milk_fat

a numeric vector

Examples

data(data3)
summary(data3)

data4: fictional example

Description

Quantitative treatments in several latin squares design.

Usage

data(data4)

Format

A data frame with 50 observations on the following 5 variables.

treatment

a numeric vector

square

a numeric vector

animal

a factor with levels a1 a2 a3 a4 a5

period

a factor with levels p1 p2 p3 p4 p5

milk_fat

a numeric vector

Examples

data(data4)
summary(data4)

data5: fictional example

Description

Quantitative treatments and three response variable.

Usage

data(data5)

Format

A data frame with 24 observations on the following 4 variables.

treatments

a numeric vector

variable1

a numeric vector

variable2

a numeric vector

variable3

a numeric vector

Examples

data(data5)
summary(data5)

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

Author(s)

Emmanuel Arnhold <emmanuelarnhold@yahoo.com.br>

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.

See Also

nls, nls2

Examples

# 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))

Analysis of polynomial regression

Description

The function performs analysis of polynomial regression in simple designs with quantitative treatments.

Usage

er2(data, design = 1, list = FALSE, type = 2)

Arguments

data

data is a data.frame

data frame with two columns, treatments and response (completely randomized design)

data frame with three columns, treatments, blocks and response (randomized block design)

data frame with four columns, treatments, rows, cols and response (latin square design)

data frame with five columns, treatments, square, rows, cols and response (several latin squares)

design

1 = completely randomized design

2 = randomized block design

3 = latin square design

4 = several latin squares

list

FALSE = a single response variable

TRUE = multivariable response

type

type is form of obtain sum of squares

1 = a sequential sum of squares

2 = a partial sum of squares

Details

The response and the treatments must be numeric. Other variables can be numeric or factors.

Value

Returns analysis of variance, models, t test for coefficients and R squared and adjusted R squared.

Author(s)

Emmanuel Arnhold <emmanuelarnhold@yahoo.com.br>

References

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

SAMPAIO, I. B. M. Estatistica aplicada a experimentacao animal. 3nd Edition. Belo Horizonte: Editora FEPMVZ, Fundacao de Ensino e Pesquisa em Medicina Veterinaria e Zootecnia, 2010. 264p.

See Also

lm, lme(package nlme), ea1(package easyanova), er1

Examples

# analysis in completely randomized design
data(data1)
r1=er2(data1)
names(r1)
r1
r1[1]

# analysis in randomized block design
data(data2)
r2=er2(data2, design=2)
r2

# analysis in latin square design
data(data3)
r3=er2(data3, design=3)
r3

# analysis in several latin squares
data(data4)
r4=er2(data4, design=4)
r4

# data
treatments=rep(c(0.5,1,1.5,2,2.5,3), c(3,3,3,3,3,3))
r1=rnorm(18,60,3)
r2=r1*1:18
r3=r1*18:1
r4=r1*c(c(1:10),10,10,10,10,10,10,10,10)
data6=data.frame(treatments,r1,r2,r3, r4)

# use the argument list = TRUE
er2(data6, design=1, list=TRUE)

Plot data and equation

Description

The function plot data and equation

Usage

regplot(data, model=1, start=c(a=1,b=1,c=1,d=1,e=1), xlab="Explanatory Variable", 
ylab="Response Variable", position=1, digits=6, mean=TRUE, sd=FALSE, 
legend = TRUE, lty=2, col="dark blue", pch=20,  xlim="defalt.x",ylim="defalt.y",...)

Arguments

data

data is a data.frame The first column contain the treatments (explanatory variable) and the remaining column the response variable

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 (iterations) values of model

xlab

names of variable x

ylab

names of variable y

position

position of equation in the graph

top=1

bottomright=2

bottom=3

bottomleft=4

left=5

topleft=6 (default)

topright=7

right=8

center=9

digits

number of digits (defalt=6)

mean

mean=TRUE (plot mean of data) mean=FALSE (plot all data)

sd

sd=FALSE (plot without standard deviation) sd=TRUE (plot with standard deviation)

legend

legend=TRUE (plot legend) legend=FALSE (not plot legend)

lty

line type

col

line color

pch

point type

xlim

limits for x

ylim

limits for y

...

others graphical parameters (see par)

Author(s)

Emmanuel Arnhold <emmanuelarnhold@yahoo.com.br>

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.

See Also

nls,er1,er2,bl

Examples

# weights of 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
regplot(data1, model=1, digits=3, position=3, ylab="weight", xlab="age")

# quadratic
regplot(data1, model=2, digits=3, position=3, col=1, ylim=c(200,700))

# linear plateau
regplot(data1, model=3,ylab="weight", xlab="age", lty=5, col="dark green",
position=3, ylim=c(200,700), xlim=c(0,150), lwd=2)

# quadratic plateau
regplot(data1, model=4,ylab="weight", xlab="age")

# two linear
regplot(data1, model=5, start=c(250,6,2,50),digits=3, position=3 )

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

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

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

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

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

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

# allometric
regplot(data1, model=14)

# cubic
regplot(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
regplot(data2, model=5, start=c(25,6,10,20))


# weight gain 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
regplot(data3, model=1)

# quadratic
regplot(data3, model=2)

# linear plateau
regplot(data3, model=3)

# quadratic plateau
regplot(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)
	

regplot(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)

regplot(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)

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

# multiple curves
time=c(0,12,24,48,64,72,96)
t1=c(36,48,59,72,85,86,87)
t2=c(14,25,36,49,59,65,72)
t3=c(55,78,86,87,86,87,88)

data=data.frame(time,t1,t2,t3)

regplot(data, model=12)
regplot(data, model=4)

# include standard deviation in graph
data(data1)

regplot(data1, sd=TRUE)

# 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])

regplot(halibut,model=17,start=c(t1,t2,0.22,-0.63), ylim=c(0,100))

Test of models and parameters

Description

This function performs test of models and parameters

Usage

regtest(data, model = 1, start = c(a = 1, b = 1, c = 1, d = 1,e = 1))

Arguments

data

data is a data.frame The first column contain explanatory variable, second column contain treatments and the third column contain the response variable

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 iterations

Value

Returns coefficients of the models, test for coefficients, AIC and BIC.

Author(s)

Emmanuel Arnhold <emmanuelarnhold@yahoo.com.br>

See Also

lm, ea1(easyanova package), pr2, regplot

Examples

x=c(1,1,1,2,2,2,3,3,3,4,4,4)
y=c(5,5.3,6,8,8.9,12,14,18,25,25,29,32)
t=c("t1","t2","t3","t1","t2","t3","t1","t2","t3","t1","t2","t3")
data=data.frame(x,t,y)
# linear
regtest(data, model=1)
# quadratic
regtest(data, model=2)
# exponential
regtest(data, model=6)
# ... etc