| Title: | Tools for Data Analyses in Biology |
|---|---|
| Description: | It is associated to the blog 'Fixing the bridge between biologists and statisticians" and contains several tools for nonlinear regression analyses and general data analysis in biology and agriculture. Several datasets are also included for practicing and teaching purposes. |
| Authors: | Andrea Onofri <[email protected]> |
| Maintainer: | Andrea Onofri <[email protected]> |
| License: | GPL-3 |
| Version: | 0.9.9 |
| Built: | 2024-10-22 05:40:56 UTC |
| Source: | https://github.com/onofriandreapg/statforbiology |
This function performs the AMMI (Addittive Main effects Multiplicative Interaction) analysis, according to Zobel et al (1988). The function has been described in Onofri and Ciriciofolo (2007).
AMMI(yield, genotype, environment, block = NULL, PC = 2, MSE = NULL, dfr = NULL)AMMI(yield, genotype, environment, block = NULL, PC = 2, MSE = NULL, dfr = NULL)
yield |
a vector containing yield levels |
genotype |
a vector containing genotype codings |
environment |
a vector containing environment codings |
block |
a vector containing block codes for each environment |
PC |
the number of PCs that one wants to extract |
MSE |
Mean Squared Error |
dfr |
Residual Degrees of Freedom |
Returns a list of class 'AMMIobject' with the following components
genotype_means |
The overall least squares genotype means |
environment_means |
The overall least squares environment means |
interaction_means |
The least squares means for the genotype by environment combinations |
interaction_effect |
a two-way table of interaction effects |
additive_ANOVA |
an ANOVA table for the additive model |
mult_Interaction |
an ANOVA table for multiplicative model |
MSE |
Mean Square Error |
dfr |
Degrees of freedom for the MSE |
environment_scores |
a table of environment scores |
genotype_scores |
a table of genotype scores |
stability |
AMMI stability value (ASV; Mohammadi and Amri, 2008) |
Andrea Onofri
Mohammadi, R., Amri, A., 2008. Comparison of parametric and non-parametric methods for selecting stable and adapted durum wheat genotypes in varibale environments. Euphytica 159, 419–432.
Onofri, A., Ciriciofolo, E., 2007. Using R to perform the AMMI analysis on agriculture variety trials. R NEWS 7, 14–19.
Zobel, R. W., Wright, M.J., and Gauch, H. G., 1988. Statistical analysis of a yield trial. Agronomy Journal, 388-393.
WinterWheat <- getAgroData("WinterWheat") tab <- with(WinterWheat, AMMI(Yield, Genotype, Year, Block, PC = 2)) tabWinterWheat <- getAgroData("WinterWheat") tab <- with(WinterWheat, AMMI(Yield, Genotype, Year, Block, PC = 2)) tab
Angular transformation for percentages
angularTransform(percentage)angularTransform(percentage)
percentage |
A number. |
A number.
angularTransform(25) angularTransform(35.2)angularTransform(25) angularTransform(35.2)
A wrapper for the 'summary' method for objects of class 'aovlist'.
## S3 method for class 'aovlist' anova(object, ...)## S3 method for class 'aovlist' anova(object, ...)
object |
An object of class |
... |
Other additional arguments |
An object of class "summary.aovlist". It is a list (one object
per error stratum) of ANOVA tables (class "anova") with a row for
each term in the model, plus one for "Residuals" if there
are any.
aov, summary, model.tables,
TukeyHSD
# A split-plot design rm(list=ls()) data(oats) oats.aov <- aov(Y ~ N*V + Error(B/V), data = oats) anova(oats.aov) emmeans::emmeans(oats.aov, ~N)# A split-plot design rm(list=ls()) data(oats) oats.aov <- aov(Y ~ N*V + Error(B/V), data = oats) anova(oats.aov) emmeans::emmeans(oats.aov, ~N)
These functions provide the asymptotic regression model (asymReg), the asymptotic regression function with self-starter for the nls function and the asymptotic regression function with self-starter for the drm function in the drc package. The 'DRC.SSasymp()' function provides the self-starter for drc, to fit the same function as in the 'SSasymp()' function in the 'nlme' package. The asymptotic regression model is also known as the Mitscherlich law in agriculture and as the von Bertalanffy law in fisheries research.
asymReg.fun(predictor, init, m, plateau) NLS.asymReg(predictor, init, m, plateau) DRC.asymReg(fixed = c(NA, NA, NA), names = c("init", "m", "plateau")) DRC.SSasymp(fixed = c(NA, NA, NA), names = c("Asym", "R0", "lrc"))asymReg.fun(predictor, init, m, plateau) NLS.asymReg(predictor, init, m, plateau) DRC.asymReg(fixed = c(NA, NA, NA), names = c("init", "m", "plateau")) DRC.SSasymp(fixed = c(NA, NA, NA), names = c("Asym", "R0", "lrc"))
predictor |
a numeric vector of values at which to evaluate the model |
init |
model parameter |
m |
model parameter |
plateau |
model parameter |
fixed |
numeric vector. Specifies which parameters are fixed and at what value they are fixed. NAs for parameter that are not fixed. |
names |
a vector of character strings giving the names of the parameters. The default is reasonable. |
The asymptotic model is given by the following function:
A similar parameterisation where 'm' is replaced by exp(lrc) is provided in the 'nlme' package, with self-starter for the 'nls' function. Here, we provide the self-starter for the 'drm' function in the 'drc' package:
asymReg.fun and NLS. asymReg return a numeric value, while DRC.asymReg and DRC.SSasymp return a list containing the nonlinear function, the self starter function and the parameter names.
DRC.asymReg and DRC.SSasymp are for use with the function drm.
Andrea Onofri
Ratkowsky, DA (1990) Handbook of nonlinear regression models. New York (USA): Marcel Dekker Inc.
Onofri, A. (2020). A collection of self-starters for nonlinear regression in R. See: https://www.statforbiology.com/2020/stat_nls_usefulfunctions/
X <- c(1, 3, 5, 7, 9, 11, 13, 20) Y <- c(8.22, 14.0, 17.2, 16.9, 19.2, 19.6, 19.4, 19.6) # nls fit model <- nls(Y ~ NLS.asymReg(X, init, m, plateau) ) # drm fit model <- drm(Y ~ X, fct = DRC.asymReg()) summary(model) model2 <- drm(Y ~ X, fct = DRC.SSasymp()) summary(model2)X <- c(1, 3, 5, 7, 9, 11, 13, 20) Y <- c(8.22, 14.0, 17.2, 16.9, 19.2, 19.6, 19.4, 19.6) # nls fit model <- nls(Y ~ NLS.asymReg(X, init, m, plateau) ) # drm fit model <- drm(Y ~ X, fct = DRC.asymReg()) summary(model) model2 <- drm(Y ~ X, fct = DRC.SSasymp()) summary(model2)
A data frame with 18 observations on the following 3 variables:
data("beetGrowth")data("beetGrowth")
A data frame with 18 rows and 3 variables
DAE. numeric: Days After Emergence
weightInf. numeric: weight of crop biomass on the weed infested plots
weightFree. numeric: weight of crop biomass on the weed free plots
Covarelli, G., Onofri, A., 1998. Effects of timing of weed removal and emergence in sugarbeet, in: Proceedings 6th EWRS Mediterranean Symposium, Montpellier, 13-15 May 1998. EWRS, pp. 65–72.
data(beetGrowth) mod3 <- nls(weightInf ~ NLS.L3(DAE, b, c, d), data = beetGrowth)data(beetGrowth) mod3 <- nls(weightInf ~ NLS.L3(DAE, b, c, d), data = beetGrowth)
This method is reserved for the classes 'AMMIobject' and 'GGEobject' as obtained from the 'AMMI()' and 'GGE()' functions in the 'aomisc' package. It draws swift biplots of two types: type 1 plots PC1 against the average yield of genotypes across environments, while type 2 plots PC2 against PC1. The former type of biplot is reserved for 'AMMI' objects, while the second one is for AMMI and GGE objects.
## S3 method for class 'AMMIobject' biplot(x, biplot = 1, xlim=NULL, ylim=NULL, elabels=NULL, glabels=NULL, quad=FALSE, cexG=0.9, cexE=0.9, xlab=NULL, ylab=NULL, font=1, ...) ## S3 method for class 'GGEobject' biplot(x, biplot = 1, xlim=NULL, ylim=NULL, elabels=NULL, glabels=NULL, quad=FALSE, cexG=0.9, cexE=0.9, xlab=NULL, ylab=NULL, font=1, ...)## S3 method for class 'AMMIobject' biplot(x, biplot = 1, xlim=NULL, ylim=NULL, elabels=NULL, glabels=NULL, quad=FALSE, cexG=0.9, cexE=0.9, xlab=NULL, ylab=NULL, font=1, ...) ## S3 method for class 'GGEobject' biplot(x, biplot = 1, xlim=NULL, ylim=NULL, elabels=NULL, glabels=NULL, quad=FALSE, cexG=0.9, cexE=0.9, xlab=NULL, ylab=NULL, font=1, ...)
x |
a 'AMMIobject' or 'GGEobject' objects |
biplot |
Numeric: either 1 or 2, to request on of the two available types of biplots (see description). |
xlim |
graphical parameter as in the 'plot' method |
ylim |
graphical parameter as in the 'plot' method |
elabels |
labels for the environments |
glabels |
labels for the genotypes |
quad |
logical. If TRUE, plots the axes |
cexG |
graphical parameter: the 'cex' for the genotype labels |
cexE |
graphical parameter: the 'cex' for the environment labels |
xlab |
graphical parameter as in the 'plot' method |
ylab |
graphical parameter as in the 'plot' method |
font |
graphical parameter as in the 'plot' method. Relating to the genotype labels |
... |
Other additional arguments |
It only returns a graph
Andrea Onofri
WinterWheat <- getAgroData("WinterWheat") tab <- with(WinterWheat, AMMI(Yield, Genotype, Year, Block, PC = 2)) biplot(tab)WinterWheat <- getAgroData("WinterWheat") tab <- with(WinterWheat, AMMI(Yield, Genotype, Year, Block, PC = 2)) biplot(tab)
Finds the optimal Box-Cox transformation for non-linear regression models.
## S3 method for class 'nls' boxcox(object, lambda = seq(-2, 2, 1/10), plotit = TRUE, start, eps = 1/50, bcAdd = 0, level = 0.95, xlab = expression(lambda), ylab = "log-likelihood", ...) ## S3 method for class 'nlsbc' summary(object, ...)## S3 method for class 'nls' boxcox(object, lambda = seq(-2, 2, 1/10), plotit = TRUE, start, eps = 1/50, bcAdd = 0, level = 0.95, xlab = expression(lambda), ylab = "log-likelihood", ...) ## S3 method for class 'nlsbc' summary(object, ...)
object |
object of class |
lambda |
numeric vector of lambda values; the default is (-2, 2) in steps of 0.1. |
plotit |
logical which controls whether the result should be plotted. |
start |
a list of starting values (optional). |
eps |
numeric value: the tolerance for lambda = 0; defaults to 0.02. |
bcAdd |
numeric value specifying the constant to be added on both sides prior to Box-Cox transformation. The default is 0. |
level |
numeric value: the confidence level required. |
xlab |
character string: the label on the x axis, defaults to "lambda". |
ylab |
character string: the label on the y axis, defaults to "log-likelihood". |
... |
additional graphical parameters. |
boxcox.nls is very similar to the boxcox in its
arguments.
The optimal lambda value is determined using a profile likelihood approach:
For each lambda value the non-linear regression model is fitted and the lambda
value resulting in thre largest value of the log likelihood function is picked.
If a self starter model was used in the model fit, then gradient information
will be used in the profiling.
An object of class nls (returned invisibly).
If plotit = TRUE a plot of loglik vs lambda is shown indicating a confidence interval (by default 95%) about
the optimal lambda value.
Christian Ritz, modified by Andrea Onofri
Carroll, R. J. and Ruppert, D. (1988) Transformation and Weighting in Regression, New York: Chapman and Hall (Chapter 4).
For linear regression the analogue is boxcox.
## Fitting log-logistic model without transformation ryegrass.m1 <- nls(rootl ~ NLS.L4(conc, b, c, d, e), data=ryegrass) summary(ryegrass.m1) ## Fitting the same model with optimal Box-Cox transformation ryegrass.m2 <- boxcox(ryegrass.m1, plotit = TRUE) summary(ryegrass.m2)## Fitting log-logistic model without transformation ryegrass.m1 <- nls(rootl ~ NLS.L4(conc, b, c, d, e), data=ryegrass) summary(ryegrass.m1) ## Fitting the same model with optimal Box-Cox transformation ryegrass.m2 <- boxcox(ryegrass.m1, plotit = TRUE) summary(ryegrass.m2)
This function takes a linear model object as an argument and checks whether the residuals are homoscedastic, in relation to a stratification variable or covariate, that is given as an argument.
check.hom(obj, var, alternative)check.hom(obj, var, alternative)
obj |
a linear model object fitted with lm() |
var |
a vector containing a stratification variable. If missing, the fitted values from obj are taken as a covariate |
alternative |
The null (homogeneous variances) is tested against the alternative, that is (i) different variances for each level of the stratification variable given as argument ("varIdent"), (ii) variance is a power function of a covariate, that is given as argument ("varPower"; the fitted values are taken as the covariate, in case the argument 'var' is missing and (iii) the variance is an exponential function of a covariate, that is given as argument ("varExp"; the fitted values are taken as the covariate, in case the argument 'var' is missing) |
The function fits a gls with same structure as the input model, together with a heteroscedastic gls, where residuals are allowed to be heteroscedastic, according to the 'alternative' argument. The two models are compared by a LRT
LRT |
the value of LRT |
LRT |
the P-value of LRT |
aovtable |
a summary table for the LRT |
modHet |
the gls object containing the heteroscedastic fit |
Andrea Onofri
fileName <- "https://www.casaonofri.it/_datasets/FGP_rape.csv" library(statforbiology) dataset <- read.csv(fileName) dataset[,1:5] <- lapply(dataset[,1:5], factor) mod <- lm(FGP ~ Genotype * Run, data = dataset) check <- check.hom(mod, Run) check$aovtablefileName <- "https://www.casaonofri.it/_datasets/FGP_rape.csv" library(statforbiology) dataset <- read.csv(fileName) dataset[,1:5] <- lapply(dataset[,1:5], factor) mod <- lm(FGP ~ Genotype * Run, data = dataset) check <- check.hom(mod, Run) check$aovtable
With models containing covariates and factors, we may be interested in fitting nonlinear regression models in a groupwise fashion, according to the levels of the experimental factor(s). This function permits pairwise comparison procedures of model parameters; parameters can be compared by means of either ratios or differences. It works very much like the function 'compParm' in the package 'drc', but it is to be used with 'nls' objects.
compCoefs(object, parameterNames, operator = "-", display = "pairwise", adjust = "holm", reversed = FALSE, level = 0.05, Letters = c(letters, LETTERS))compCoefs(object, parameterNames, operator = "-", display = "pairwise", adjust = "holm", reversed = FALSE, level = 0.05, Letters = c(letters, LETTERS))
object |
an object of class 'nls' |
parameterNames |
The name of parameters to compare. It must corresponds to the names of parameters in coefs(object) |
operator |
a character. If equal to "/" parameter ratios are compared. If equal to "-" (default) parameter differences are compared. |
display |
a character. If equal to "pairwise" (default), pairwise comparisons are displayed. Otherwise, a compact letter display is returned, according to the argument in 'level'. |
adjust |
A multiplicity adjustment method as in p.adjust. Defaults to "holm". |
reversed |
logical. Should the order of means/letters be decreasing? Defaults to FALSE, which means that the means and letters are in increasing order. |
level |
Protection level for compact letter display |
Letters |
Vector of distinct characters (or character strings) used to connect levels that are not significantly different. They should be recogizable when concatenated. The default behaviour is to use the small letters, followed by the capital letters. See help for 'multcompView::multcompLetters()' for futher detail) |
returns a dataframe, containing the results
Andrea Onofri
data(metamitron) modNlin <- nls(Conc ~ A[Herbicide] * exp(-k[Herbicide] * Time), start=list(A=rep(100, 4), k=rep(0.06, 4)), data=metamitron) tab <- summary(modNlin) pn <- c("k1", "k2", "k3", "k4") compCoefs(modNlin, pn) # Holm multiplicity adjustment compCoefs(modNlin, pn, adjust = "none") # Displaying letters (P = 0.05 is default) compCoefs(modNlin, pn, adjust = "none", display = "cld") # Calculate ratios compCoefs(modNlin, pn, adjust = "none", display = "pairwise", operator = "/")data(metamitron) modNlin <- nls(Conc ~ A[Herbicide] * exp(-k[Herbicide] * Time), start=list(A=rep(100, 4), k=rep(0.06, 4)), data=metamitron) tab <- summary(modNlin) pn <- c("k1", "k2", "k3", "k4") compCoefs(modNlin, pn) # Holm multiplicity adjustment compCoefs(modNlin, pn, adjust = "none") # Displaying letters (P = 0.05 is default) compCoefs(modNlin, pn, adjust = "none", display = "cld") # Calculate ratios compCoefs(modNlin, pn, adjust = "none", display = "pairwise", operator = "/")
For regression models containing grouping factors and fitted with the 'drm' function in the 'drc' package, this function compares the different curves for each factor level in a pairwise fashion, according to a series of F tests for the extra-sum-of-squares. Works only with 'drc' objects
compCurves( obj, adjusted = c("none", "holm", "hochberg", "hommel", "bonferroni", "BH", "BY", "fdr") )compCurves( obj, adjusted = c("none", "holm", "hochberg", "hommel", "bonferroni", "BH", "BY", "fdr") )
obj |
a drc object |
adjusted |
a character string, for selecting the method of multiplicity correction. Must be one of: c("none", "holm", "hochberg", "hommel", "bonferroni", "BH", "BY", "fdr") |
returns a list with two slots: (i) Pairs: the list of peirwise comparisons, with F values and P-values; (ii) Letters: letter display for the different curves
Andrea Onofri
metamitron <- getAgroData("metamitron") head(metamitron) tail(metamitron) mod1 <- drm(Conc ~ Time, fct = DRC.expoDecay(), curveid = Herbicide, data = metamitron) summary(mod1) compCurves(mod1, adjusted = "bonferroni")metamitron <- getAgroData("metamitron") head(metamitron) tail(metamitron) mod1 <- drm(Conc ~ Time, fct = DRC.expoDecay(), curveid = Herbicide, data = metamitron) summary(mod1) compCurves(mod1, adjusted = "bonferroni")
Returns a matrix of Tukey-type contrasts (all-pairwise)
contr.Tukey(n, names = NULL)contr.Tukey(n, names = NULL)
n |
an integer: the number of levels, corresponding to the number of columns in the output matrix |
names |
a vector of names with same length as n |
This functions is used for creating contrast matrices for use with glht or other methods for fitting linear contrasts. The rows of the resulting matrices contain the coefficients of contrasts relating to a factor with n levels. The names of the levels can be optionally given with the argument 'names', other wise they default to the numbers from 1 to n.
A matrix with n columns and n(n-1)/2 rows
Andrea Onofri
contr.Tukey(8, LETTERS[1:8])contr.Tukey(8, LETTERS[1:8])
This function performs canonical variate analysis as a descriptive visualisation tool. It is close to the 'lda()' function in the MASS package but it is not meant to be used for discriminant analyses.
CVA(dataset, groups, scale = TRUE, constraint = 3)CVA(dataset, groups, scale = TRUE, constraint = 3)
dataset |
dataset is a multidimensional matrix of observations |
groups |
groups is a vector coding for groupings |
scale |
whether the data needs to be standardised prior to analysis. Defaults to TRUE |
constraint |
It is the type of scaling for eigenvectors, so that canonical variates have: 1 = unit within-group standard deviations (most common); 2 = unit total standard deviations; 3 = unit within group norms; 4 = unit total norms. It defaults to 3 |
More detail can be found in a blog page, at 'https://www.statforbiology.com/2023/stat_multivar_cva/'. Please, note that preliminary data transformations (e.g.: standardisation) are left to the user and must be performed prior to analyses (see example below).
TOT |
matrix of total variances-covariances |
B |
matrix of 'between-groups' variances-covariances |
W |
matrix of 'within-group' variances-covariances |
B/W |
matrix of W^{-1} B |
eigenvalues |
vector of eigenvalues |
eigenvectors |
matrix of eigenvectors |
proportion |
a vector containing the proportion of total discriminating ability captured by each canonical variate |
correlation |
vector of canonical correlations |
squared.canonical.correlation |
vector of squared canonical correlations |
coefficients |
matrix of canonical coefficients |
scores |
matrix of canonical scores |
centroids |
matrix of scores for centroids |
total.structure |
matrix of total canonical structure |
between.structure |
matrix of between-groups canonical structure |
within.structure |
matrix of within-groups canonical structure |
class.fun |
matrix of classifications functions |
class.val |
matrix of classification values |
within.structure |
matrix of within-groups canonical structure |
class |
vector of predicted classes |
Andrea Onofri
https://www.statforbiology.com/2023/stat_multivar_cva/
dataset <- getAgroData("WheatQuality4years") dataset$Year <- factor(dataset$Year) head(dataset) # Standardise the data groups <- dataset$Genotype Z <- apply(dataset[,3:6], 2, scale, center = TRUE, scale = TRUE) head(Z) # Performs CVA cvaobj <- CVA(Z, groups) cvaobjdataset <- getAgroData("WheatQuality4years") dataset$Year <- factor(dataset$Year) head(dataset) # Standardise the data groups <- dataset$Genotype Z <- apply(dataset[,3:6], 2, scale, center = TRUE, scale = TRUE) head(Z) # Performs CVA cvaobj <- CVA(Z, groups) cvaobj
A data frame with 24 observations on the following 2 variables:
data("degradation")data("degradation")
A data frame with 24 rows and 2 variables
Time. numeric: Days from start of incubation
Conc. numeric: residual concentration
data("degradation") degradationdata("degradation") degradation
Calculate the sum of squared residuals from a non-linear regression fit with the 'drm()' function in the 'drc()' package.
## S3 method for class 'drc' deviance(object, ...)## S3 method for class 'drc' deviance(object, ...)
object |
a 'drc' object, for which the deviance is required |
... |
Other additional arguments, if necessary |
The value of the deviance extracted from the object object.
Andrea Onofri
X <- c(1, 3, 5, 7, 9, 11, 13, 20) Y <- c(8.22, 14.0, 17.2, 16.9, 19.2, 19.6, 19.4, 19.6) # nls fit model <- nls(Y ~ NLS.asymReg(X, init, m, plateau) ) deviance(model) # drm fit model2 <- drm(Y ~ X, fct = DRC.asymReg()) deviance(model2)X <- c(1, 3, 5, 7, 9, 11, 13, 20) Y <- c(8.22, 14.0, 17.2, 16.9, 19.2, 19.6, 19.4, 19.6) # nls fit model <- nls(Y ~ NLS.asymReg(X, init, m, plateau) ) deviance(model) # drm fit model2 <- drm(Y ~ X, fct = DRC.asymReg()) deviance(model2)
These functions provide the exponential decay function (expoDecay), the exponential decay function with self-starter for the nls function and the exponential decay function with self-starter for the drm function in the drc package.
expoDecay.fun(predictor, C0, k) NLS.expoDecay(predictor, C0, k) DRC.expoDecay(fixed = c(NA, NA), names = c("C0", "k"))expoDecay.fun(predictor, C0, k) NLS.expoDecay(predictor, C0, k) DRC.expoDecay(fixed = c(NA, NA), names = c("C0", "k"))
predictor |
a numeric vector of values at which to evaluate the model. |
C0 |
model parameter |
k |
model parameter |
fixed |
numeric vector. Specifies which parameters are fixed and at what value they are fixed. NAs for parameter that are not fixed. |
names |
a vector of character strings giving the names of the parameters. The default is reasonable. |
The exponential decay is given by the following function:
expoDecay.fun and NLS.expoDecay return a numeric value, while DRC.expoDecay returns a list containing the nonlinear function, the self starter function and the parameter names.
DRC.expoDecay is for use with the function drm.
Andrea Onofri
Ratkowsky, DA (1990) Handbook of nonlinear regression models. New York (USA): Marcel Dekker Inc.
Onofri, A. (2020). A collection of self-starters for nonlinear regression in R. See: https://www.statforbiology.com/2020/stat_nls_usefulfunctions/
rm(list=ls()) data("degradation") model <- drm(Conc ~ Time, fct = DRC.expoDecay(), data = degradation) summary(model) model2 <- nls(Conc ~ NLS.expoDecay(Time, a, b), data = degradation) summary(model2)rm(list=ls()) data("degradation") model <- drm(Conc ~ Time, fct = DRC.expoDecay(), data = degradation) summary(model) model2 <- nls(Conc ~ NLS.expoDecay(Time, a, b), data = degradation) summary(model2)
These functions provide the exponential growth equation (expoGrowth), the exponential growth equation with self-starter for the nls function and the exponential growth equation with self-starter for the drm function in the drc package.
expoGrowth.fun(predictor, init, k) NLS.expoGrowth(predictor, init, k) DRC.expoGrowth(fixed = c(NA, NA), names = c("init", "k"))expoGrowth.fun(predictor, init, k) NLS.expoGrowth(predictor, init, k) DRC.expoGrowth(fixed = c(NA, NA), names = c("init", "k"))
predictor |
a numeric vector of values at which to evaluate the model. |
init |
model parameter: response at predictor = 0 |
k |
model parameter: growth rate |
fixed |
numeric vector. Specifies which parameters are fixed and at what value they are fixed. NAs for parameter that are not fixed. |
names |
a vector of character strings giving the names of the parameters. The default is reasonable. |
The exponential growth is given by the following function:
expoGrowth.fun() and NLS.expoGrowth() return a numeric value, while DRC.expoGrowth() returns a list containing the nonlinear function, the self starter function and the parameter names.
DRC.expoGrowth() is for use with the function drm.
Andrea Onofri
Ratkowsky, DA (1990) Handbook of nonlinear regression models. New York (USA): Marcel Dekker Inc.
Onofri, A. (2020). A collection of self-starters for nonlinear regression in R. See: https://www.statforbiology.com/2020/stat_nls_usefulfunctions/
library(statforbiology) Time <- 1:20 Resp <- c(0.18, 0.64, 1.14, 0.67, 0.32, 0.86, 0.70, 0.73, 0.89, 0.48, 2.20, 1.03, 1.14, 2.14, 1.31, 2.08, 1.85, 1.47, 1.98, 1.30) model <- drm(Resp ~ Time, fct = DRC.expoGrowth()) summary(model) model2 <- nls(Resp ~ NLS.expoGrowth(Time, a, b)) summary(model2)library(statforbiology) Time <- 1:20 Resp <- c(0.18, 0.64, 1.14, 0.67, 0.32, 0.86, 0.70, 0.73, 0.89, 0.48, 2.20, 1.03, 1.14, 2.14, 1.31, 2.08, 1.85, 1.47, 1.98, 1.30) model <- drm(Resp ~ Time, fct = DRC.expoGrowth()) summary(model) model2 <- nls(Resp ~ NLS.expoGrowth(Time, a, b)) summary(model2)
This function loads and returns a dataset available in an external repository and stored as '.csv' or other type of text files. all the examples.
getAgroData( fileName, where = "https://www.casaonofri.it/_datasets/", type = "csv" )getAgroData( fileName, where = "https://www.casaonofri.it/_datasets/", type = "csv" )
fileName |
character: the name of the file (with no extension) |
where |
character: the name of the web repository |
type |
character: the extension of the web file |
returns a data.frame
Andrea Onofri
getAgroData("rimsulfuron")getAgroData("rimsulfuron")
This method works on a model object and retrieves the data for plotting the observed values (average or all data) and predictions from model fit. It is mainly meant to be used with ggplot()
getPlotData(obj, ...) ## S3 method for class 'drc' getPlotData(obj, xlim = NULL, gridsize = 100, type = c("average", "all"), ...) ## S3 method for class 'nls' getPlotData(obj, xlim = NULL, gridsize = 100, type = c("average", "all"), ...) ## S3 method for class 'drcte' getPlotData( obj, xlim = NULL, gridsize = 100, npmle.type = c("interpolation", "midpoint", "right", "left", "none"), ... )getPlotData(obj, ...) ## S3 method for class 'drc' getPlotData(obj, xlim = NULL, gridsize = 100, type = c("average", "all"), ...) ## S3 method for class 'nls' getPlotData(obj, xlim = NULL, gridsize = 100, type = c("average", "all"), ...) ## S3 method for class 'drcte' getPlotData( obj, xlim = NULL, gridsize = 100, npmle.type = c("interpolation", "midpoint", "right", "left", "none"), ... )
obj |
A fitted model object. Methods are provided for drc, drcte and nls objects |
... |
Other additional arguments. |
xlim |
a vector. The interval for the predictor in which predictions are to be obtained |
gridsize |
numeric. Number of points in the grid (within xlim) used for predictions. |
type |
a character string specifying whether all the observed points should be plotted (type = "all") or whether the response should be averaged over the levels of the predictor (type = "all"). It is disregarded for drcte objects |
npmle.type |
a character string. For drcte objects, the NPMLE of the cumulative density function is only specified at the end of each inspection interval, while it is not unique within each interval. This argument specifies how the CDF increases within each interval: possible values are "interpolation" (it is assumed that the CDF increases progressively), "left" (the CDF increases at the beginning of each interval), "right" (the CDF increases at the end of each interval; it is very common in survival analysis) and "midpoint" (the CDF increases in the middle of each interval; it is very common in survival analysis). This argument is neglected with nls and drc objects. |
This function returns a list of two elements: 'plotPoints' is a dataframe containing the observed data, 'plotFits' is a dataframe containing model predictions
Andrea Onofri
fileName <- "https://www.casaonofri.it/_datasets/metamitron.csv" metamitron <- read.csv(fileName) mod <- drm(Conc ~ Time, fct = EXD.2(), data = metamitron, curveid = Herbicide) retVal <- getPlotData(mod) library(ggplot2) ggplot() + geom_point(data = retVal$plotPoints, mapping = aes(x = Time, y = Conc)) + geom_line(data = retVal$plotFits, mapping = aes(x = Time, y = Conc)) + facet_wrap(~ Herbicide)fileName <- "https://www.casaonofri.it/_datasets/metamitron.csv" metamitron <- read.csv(fileName) mod <- drm(Conc ~ Time, fct = EXD.2(), data = metamitron, curveid = Herbicide) retVal <- getPlotData(mod) library(ggplot2) ggplot() + geom_point(data = retVal$plotPoints, mapping = aes(x = Time, y = Conc)) + geom_line(data = retVal$plotFits, mapping = aes(x = Time, y = Conc)) + facet_wrap(~ Herbicide)
This function performs the GGE (Genotype plus Genotype by Environment interaction) analysis, according to Yan et al., 2000.
GGE(yield, genotype, environment, block, PC = 2)GGE(yield, genotype, environment, block, PC = 2)
yield |
a vector containing yield levels |
genotype |
a vector containing genotype codings |
environment |
a vector containing environment codings |
block |
a vector containing block codes for each environment |
PC |
the number of PCs that one wants to extract |
Returns a list of class 'GGEobject' with the following components
genotype_means |
The overall least squares genotype means |
environment_means |
The overall least squares environment means |
interaction_means |
The least squares means for the genotype by environment combinations |
ge_effect |
a two-way table of 'interaction effects'gge' effects |
additive_ANOVA |
an ANOVA table for the additive model |
GGE_summary |
a summary table for GGE analysis |
environment_scores |
a table of environment scores |
genotype_scores |
a table of genotype scores |
Andrea Onofri
Yan, W., Hunt, L.A., Sheng, Q., Szlavnics, Z., 2000. Cultivar Evaluation and Mega-Environment Investigation Based on the GGE Biplot. Crop Science 40, 597–605.
WinterWheat <- getAgroData("WinterWheat") tab <- with(WinterWheat, GGE(Yield, Genotype, Year, Block, PC = 2)) tabWinterWheat <- getAgroData("WinterWheat") tab <- with(WinterWheat, GGE(Yield, Genotype, Year, Block, PC = 2)) tab
This function calculates linear/nonlinear contrasts of model parameters and returns their estimates with delta standard errors.
## S3 method for class 'numeric' gnlht(object, func, const, vcov., parameterNames, dfr, ...) ## S3 method for class 'lm' gnlht(object, func, const, vcov., parameterNames, dfr, ...) ## S3 method for class 'nls' gnlht(object, func, const, vcov., parameterNames, dfr, ...) ## S3 method for class 'lme' gnlht(object, func, const, vcov., parameterNames, dfr, ...) ## S3 method for class 'nlme' gnlht(object, func, const, vcov., parameterNames, dfr, ...) ## S3 method for class 'drc' gnlht(object, func, const, vcov., parameterNames, dfr, ...)## S3 method for class 'numeric' gnlht(object, func, const, vcov., parameterNames, dfr, ...) ## S3 method for class 'lm' gnlht(object, func, const, vcov., parameterNames, dfr, ...) ## S3 method for class 'nls' gnlht(object, func, const, vcov., parameterNames, dfr, ...) ## S3 method for class 'lme' gnlht(object, func, const, vcov., parameterNames, dfr, ...) ## S3 method for class 'nlme' gnlht(object, func, const, vcov., parameterNames, dfr, ...) ## S3 method for class 'drc' gnlht(object, func, const, vcov., parameterNames, dfr, ...)
object |
a named vector of parameter estimates, or a model object for which there are coef and vcov methods. The estimates are assumed as asymptotically normally distributed with covariance matrix returned by vcov. or passed as an argument |
func |
a list of functions or quoted strings that are the functions of the parameter estimates to be evaluated |
const |
If necessary, a dataframe whose columns are the constants to be used in the calculations above. For each row of this dataframe, the functions above are evaluated |
vcov. |
a variance-covariance matrix, or a function to calculate it from the model object |
parameterNames |
a character vector with namings for the parameters to be combined |
dfr |
number of degrees of freedom |
... |
Additional arguments |
Methods are given for several types of model fitting objects (lm, nls, lme, nlme, drc), from where model coefficients and a variance-covariance matrix are automatically retrieved. For other cases, a named vector of model parameters and a variance-covariance matrix can be provided as arguments to the 'gnlht()' function.
Returns a data.frame
Andrea Onofri
data(metamitron) #Fit nls grouped model modNlin <- nls(Conc ~ A[Herbicide] * exp(-k[Herbicide] * Time), start=list(A=rep(100, 4), k=rep(0.06, 4)), data=metamitron) summary(modNlin) # Compare parameters funList <- list(~k1 - k2, ~k1 - k3, ~k1 - k4) gnlht(modNlin, funList) # Combine parameters funList <- list(~ -log(0.5)/k1, ~ -log(0.5)/k2, ~ -log(0.5)/k3, ~ -log(0.5)/k4) gnlht(modNlin, funList) # Combine more flexibly funList <- list(~ -log(prop)/k1, ~ -log(prop)/k2, ~ -log(prop)/k3, ~ -log(prop)/k4) gnlht(modNlin, funList, const = data.frame(prop = 0.5)) funList <- list(~ -log(prop)/k1, ~ -log(prop)/k2, ~ -log(prop)/k3, ~ -log(prop)/k4) gnlht(modNlin, funList, const = data.frame(prop = c(0.7, 0.5, 0.3))) # Other possibilities funList <- list(~ (k2 - k1)/(k1 * k2) * log(prop), ~ (k3 - k1)/(k1 * k3) * log(prop), ~ (k4 - k1)/(k1 * k4) * log(prop)) gnlht(modNlin, funList, const = data.frame(prop = c(0.7, 0.5, 0.3))) # Predictions funList <- list(~ A1 * exp (- k1 * Time), ~ A2 * exp (- k2 * Time), ~ A3 * exp (- k3 * Time), ~ A4 * exp (- k4 * Time)) propdF <- data.frame(Time = seq(0, 67, 1)) func <- funList const <- propdF pred <- gnlht(modNlin, funList, const = propdF) head(pred) tail(pred)data(metamitron) #Fit nls grouped model modNlin <- nls(Conc ~ A[Herbicide] * exp(-k[Herbicide] * Time), start=list(A=rep(100, 4), k=rep(0.06, 4)), data=metamitron) summary(modNlin) # Compare parameters funList <- list(~k1 - k2, ~k1 - k3, ~k1 - k4) gnlht(modNlin, funList) # Combine parameters funList <- list(~ -log(0.5)/k1, ~ -log(0.5)/k2, ~ -log(0.5)/k3, ~ -log(0.5)/k4) gnlht(modNlin, funList) # Combine more flexibly funList <- list(~ -log(prop)/k1, ~ -log(prop)/k2, ~ -log(prop)/k3, ~ -log(prop)/k4) gnlht(modNlin, funList, const = data.frame(prop = 0.5)) funList <- list(~ -log(prop)/k1, ~ -log(prop)/k2, ~ -log(prop)/k3, ~ -log(prop)/k4) gnlht(modNlin, funList, const = data.frame(prop = c(0.7, 0.5, 0.3))) # Other possibilities funList <- list(~ (k2 - k1)/(k1 * k2) * log(prop), ~ (k3 - k1)/(k1 * k3) * log(prop), ~ (k4 - k1)/(k1 * k4) * log(prop)) gnlht(modNlin, funList, const = data.frame(prop = c(0.7, 0.5, 0.3))) # Predictions funList <- list(~ A1 * exp (- k1 * Time), ~ A2 * exp (- k2 * Time), ~ A3 * exp (- k3 * Time), ~ A4 * exp (- k4 * Time)) propdF <- data.frame(Time = seq(0, 67, 1)) func <- funList const <- propdF pred <- gnlht(modNlin, funList, const = propdF) head(pred) tail(pred)
These functions provide the simple linear regression model (linear), the linear regression model with self-starter for the nls function (NLS.linear) and the simple linear regression function with self-starter for the drm function in the drc package (DRC.linear). For the 'nls' function, we also provide function and self starter for the simple linear regression through origin (NLS.linearOrigin). Obviously, fitting linear functions with nonlinear least square regression is sub-optimal, but it might be useful for comparing alternative models.
linear.fun(predictor, a, b) NLS.linear(predictor, a, b) NLS.linearOrigin(predictor, b) DRC.linear(fixed = c(NA, NA), names = c("a", "b"))linear.fun(predictor, a, b) NLS.linear(predictor, a, b) NLS.linearOrigin(predictor, b) DRC.linear(fixed = c(NA, NA), names = c("a", "b"))
predictor |
a numeric vector of values at which to evaluate the model. |
a |
numeric. The response when the predict is equal to 0. |
b |
numeric. The slope. |
fixed |
numeric vector. Specifies which parameters are fixed and at what value they are fixed. NAs for parameter that are not fixed. |
names |
a vector of character strings giving the names of the parameters. The default is reasonable. |
The simple linear regression model is given by the following equation:
linear.fun, NLS.linear and NLS.linearOrigin return a numeric value, while DRC.linear returns a list containing the nonlinear function, the self starter function and the parameter names.
Andrea Onofri
Ratkowsky, DA (1990) Handbook of nonlinear regression models. New York (USA): Marcel Dekker Inc.
Onofri, A. (2020). A collection of self-starters for nonlinear regression in R. See: https://www.statforbiology.com/2020/stat_nls_usefulfunctions/
# Simple linear regression X <- seq(5, 50, 5) Y <- 10 + 0.5*X + rnorm(10, 0, 0.5) model1 <- nls(Y ~ NLS.linear(X, a, b)) model2 <- nls(Y ~ NLS.linearOrigin(X, b)) # force through origin summary(model1); summary(model2) model1 <- drm(Y ~ X, fct = DRC.linear()) model2 <- drm(Y ~ X, fct = DRC.linear(fixed = c(0, NA))) summary(model1); summary(model2)# Simple linear regression X <- seq(5, 50, 5) Y <- 10 + 0.5*X + rnorm(10, 0, 0.5) model1 <- nls(Y ~ NLS.linear(X, a, b)) model2 <- nls(Y ~ NLS.linearOrigin(X, b)) # force through origin summary(model1); summary(model2) model1 <- drm(Y ~ X, fct = DRC.linear()) model2 <- drm(Y ~ X, fct = DRC.linear(fixed = c(0, NA))) summary(model1); summary(model2)
These functions provide the logarithmic model (logCurve) with self-starter for the nls function and for the drm function in the drc package.
logCurve.fun(predictor, a, b) NLS.logCurve(predictor, a, b) NLS.logCurveNI(predictor, b) DRC.logCurve(fixed = c(NA, NA), names = c("a", "b"))logCurve.fun(predictor, a, b) NLS.logCurve(predictor, a, b) NLS.logCurveNI(predictor, b) DRC.logCurve(fixed = c(NA, NA), names = c("a", "b"))
predictor |
a numeric vector of values at which to evaluate the model. |
a |
model parameter |
b |
model parameter |
fixed |
numeric vector. Specifies which parameters are fixed and at what value they are fixed. NAs for parameter that are not fixed. |
names |
a vector of character strings giving the names of the parameters. The default is reasonable. |
The logarithmic curve is given by the following function:
This curve crosses the X axis at X = a. We can force it through the origin by setting a = 0; this is possible by setting 'fixed = c(=, NA), while, in the 'nls()' function, we need to use the NLS.logCurveNI()' function.
logCurve.fun, NLS.logCurve and NLS.logCurveNI return a numeric value, while DRC.logCurve returns a list containing the nonlinear function, the self starter function and the parameter names.
DRC.logCurve() is for use with the function drm.
Andrea Onofri
Ratkowsky, DA (1990) Handbook of nonlinear regression models. New York (USA): Marcel Dekker Inc.
Onofri, A. (2020). A collection of self-starters for nonlinear regression in R. See: https://www.statforbiology.com/2020/stat_nls_usefulfunctions/
X <- c(1,2,4,5,7,12) Y <- c(1.97, 2.32, 2.67, 2.71, 2.86, 3.09) # lm fit model <- lm(Y ~ log(X) ) # nls fit model <- nls(Y ~ NLS.logCurve(X, a, b) ) # drm fit model <- drm(Y ~ X, fct = DRC.logCurve() )X <- c(1,2,4,5,7,12) Y <- c(1.97, 2.32, 2.67, 2.71, 2.86, 3.09) # lm fit model <- lm(Y ~ log(X) ) # nls fit model <- nls(Y ~ NLS.logCurve(X, a, b) ) # drm fit model <- drm(Y ~ X, fct = DRC.logCurve() )
This is a wrapper for the 'filter()' function that uses the convolution method to calculate the moving averages of the terms in a vector, i.e. a series of averages of different subsets of the full vector
ma(x, n = 5, sides = 2)ma(x, n = 5, sides = 2)
x |
a numeric vector representing a time series |
n |
an integer, representing the number of values that compose each subset to be averaged |
sides |
can be either 1 or 2. If sides = 1 the n values to be averaged are taken before the preent values; If sides = 2 the n values are taken before and after the present value; If n is odd, (n - 1)/2 values are taken before the present value and (n - 1)/2 are taken after the present value, while, if n is even, more values are taken after the present value |
This function returns a vector of moving averages
Andrea Onofri
series <- c(319, 317, 332, 271, 301, 292, 351, 358, 259, 270) ma(series, n = 4, sides = 2)series <- c(319, 317, 332, 271, 301, 292, 351, 358, 259, 270) ma(series, n = 4, sides = 2)
The dataset describes the degradation of metamitron in soil at 20°C with several co-applied herbicides. It is a synthetic dataset, that was generated by Monte Carlo methods, starting from the observed data in Vischetti et al., 1996. A data frame with 96 observations on the following 3 variables:
data("metamitron")data("metamitron")
A data frame with 96 rows and 3 variables
Time. numeric: Days from start of incubation
Herbicide. factor: M is 'metamitron', MP is 'metamitron+phenmedipham', MC is 'metamitron+chloridazon' and MPC is 'metamitron+phenmedipham+chloridazon'
Conc. numeric: residual concentration of metamitron
Vischetti, C., Marini, M., Businelli, M., Onofri, A., 1996. The effect of temperature and co-applied herbicides on the degradation rate of phenmedipham, chloridazon and metamitron in a clay loam soil in the laboratory, in: Re, A.D., Capri, E., Evans, S.P., Trevisan, M. (Eds.), “The Environmental Phate of Xenobiotics”, Proceedings X Symposium on Pesticide Chemistry, Piacenza. La Goliardica Pavese, Piacenza, pp. 287–294.
data("metamitron") metamitrondata("metamitron") metamitron
Two herbicides are used alone and in mixture. It is a data frame with 16 observations on the following 2 variables:
data("mixture")data("mixture")
A data frame with 24 rows and 2 variables
Treat. Factor: the treatment levels
Weight. numeric: the weight of weeds
data("degradation") degradationdata("degradation") degradation
These functions provide the negative exponential model (negExp.fun) with the related self-starters for the nls function (NLS.negExp) drm function in the 'drc' package (DRC.negExp) and the exponential cumulative distribution function (negExpDist.fun), with self-starters for both 'nls' (NLS.negExpDist) and 'drc' (DRC.negExpDist).
negExp.fun(predictor, a, c) negExpDist.fun(predictor, c) NLS.negExp(predictor, a, c) DRC.negExp(fixed = c(NA, NA), names = c("a", "c")) NLS.negExpDist(predictor, c) DRC.negExpDist(fixed = NA, names = c("c"))negExp.fun(predictor, a, c) negExpDist.fun(predictor, c) NLS.negExp(predictor, a, c) DRC.negExp(fixed = c(NA, NA), names = c("a", "c")) NLS.negExpDist(predictor, c) DRC.negExpDist(fixed = NA, names = c("c"))
predictor |
a numeric vector of values at which to evaluate the model. |
a |
a numeric parameter representing the higher asymptote |
c |
a numeric parameter that is proportional to the relative rate of increase of the fitted function |
fixed |
numeric vector. Specifies which parameters are fixed and at what value they are fixed. NAs for parameter that are not fixed. |
names |
a vector of character strings giving the names of the parameters. The default is reasonable. |
The negative exponential model is given by the following function:
while the exponential CDF is obtained by setting a = 1:
The ‘drc’ package contains also the function AR.2(), where c is replaced by e = 1/c. The ‘nlme’ package also contains an alternative parameterisation named 'SSasympOrig()', where c is replaced by phi3 = log(c).
negExp.fun and negExpDist.fun return a numeric value, while the self-starters return a list containing the nonlinear function, the self starter function and the parameter names.
Andrea Onofri
Ratkowsky, DA (1990) Handbook of nonlinear regression models. New York (USA): Marcel Dekker Inc. Onofri, A. (2020). A collection of self-starters for nonlinear regression in R. See: https://www.statforbiology.com/2020/stat_nls_usefulfunctions/
X <- c(1, 3, 5, 7, 9, 11, 13, 20) Y <- c(4.5, 12.0, 16.1, 16.4, 18.9, 19.5, 19.3, 19.6) model <- drm(Y ~ X, fct = DRC.negExp()) summary(model)X <- c(1, 3, 5, 7, 9, 11, 13, 20) Y <- c(4.5, 12.0, 16.1, 16.4, 18.9, 19.5, 19.3, 19.6) model <- drm(Y ~ X, fct = DRC.negExp()) summary(model)
This function provides pairwise comparisons between the element of a vector, as long as a variance-covariance matrix is also provided
pairComp(parm, vcovMat, nams = NULL, dfr = NULL, adjust = "none", level = 0.05, Letters = c(letters, LETTERS, "."), reversed = FALSE)pairComp(parm, vcovMat, nams = NULL, dfr = NULL, adjust = "none", level = 0.05, Letters = c(letters, LETTERS, "."), reversed = FALSE)
parm |
A (possibly named) vector of estimates |
vcovMat |
Variance-covariance matrix for the estimates |
nams |
A character vector of parameter names (optional). If it is not provided and if 'parm' is not a named vectors, numbers '1:length(parm)' are used. |
dfr |
An optional number of residual degrees of freedom (defaults to Inf) |
adjust |
A multiplicity adjustment method as in 'multcomp'. Defaults to "none". |
level |
Protection level for compact letter display |
Letters |
Vector of distinct characters (or character strings) used to connect levels that are not significantly different. They should be recogizable when concatenated. The default behaviour is to use the small letters, followed by the capital letters. See help for 'multcompView::multcompLetters()' for futher detail) |
reversed |
logical. Should the order of means/letters be decreasing? Defaults to FALSE, which means that the means and letters are in increasing order) |
Returns a list with the following elements
Pairs |
A dataframe of pairwise comparisons |
Letters |
A dataframe with compact letter display |
Andrea Onofri
Onofri A. (2020) The broken bridge between biologists and statisticians: a blog and R package, Statforbiology, IT, web: https://www.statforbiology.com
# library(devtools) # install_github("OnofriAndreaPG/aomisc") library(statforbiology) data(metamitron) #Fit nls grouped model modNlin <- nls(Conc ~ A[Herbicide] * exp(-k[Herbicide] * Time), start=list(A=rep(100, 4), k=rep(0.06, 4)), data=metamitron) tab <- summary(modNlin) tab # Retreive infos and make comparisons coefs <- coef(modNlin)[5:8] vcovMat <- vcov(modNlin)[5:8, 5:8] cp <- pairComp(coefs, vcovMat, dfr = tab$df[2], adjust = "none", reversed = FALSE) cp$Letters cp$pairs# library(devtools) # install_github("OnofriAndreaPG/aomisc") library(statforbiology) data(metamitron) #Fit nls grouped model modNlin <- nls(Conc ~ A[Herbicide] * exp(-k[Herbicide] * Time), start=list(A=rep(100, 4), k=rep(0.06, 4)), data=metamitron) tab <- summary(modNlin) tab # Retreive infos and make comparisons coefs <- coef(modNlin)[5:8] vcovMat <- vcov(modNlin)[5:8, 5:8] cp <- pairComp(coefs, vcovMat, dfr = tab$df[2], adjust = "none", reversed = FALSE) cp$Letters cp$pairs
nls objectThis function is aimed at providing some types of plots to assess the goodness of fit for the selected model. Three plots (selectable by the argument 'which') are currently available: a plot of residuals against fitted values (which = 1), a Normal Q-Q plot (which = 2) and a plot of predicted against expected (line) and observed (symbols). By default, type = 3 is provided. As for the third graph, we can either plot all the data (type= "all") or the group means (type = "means"; the default)
plotnls(x, type = c("average", "all"), xlim = NULL, gridsize = 100, which = 3, ...)plotnls(x, type = c("average", "all"), xlim = NULL, gridsize = 100, which = 3, ...)
x |
an object of class 'nls' |
type |
it can be either "means" or "all". In the first case, the group means are plotted for the third graph. It is only considered when which = 3 |
xlim |
The limits for the x-axis (x1, x2) |
gridsize |
For 'which = 3', it sets the resolution of the fitted line |
which |
The type of graph: can be 1, 2 or 3 (see description). It defaults to 3. |
... |
additional graphical arguments |
It mimicks the behaviour of the function plot.lm()
Andrea Onofri
degradation <- read.csv("https://www.casaonofri.it/_datasets/degradation.csv") mod <- nls(Conc ~ A*exp(-k*Time), start=list(A=100, k=0.05), data=degradation) plotnls(mod, which = 3)degradation <- read.csv("https://www.casaonofri.it/_datasets/degradation.csv") mod <- nls(Conc ~ A*exp(-k*Time), start=list(A=100, k=0.05), data=degradation) plotnls(mod, which = 3)
These functions provide the simple polynomial (second order) regression model (poly2), the polynomial regression model with self-starter for the nls function (NLS.poly2) and the polynomial regression function with self-starter for the drm function in the drc package (DRC.poly2). Fitting linear functions with nonlinear least square regression is sub-optimal, but it might be useful for comparing alternative models.
poly2.fun(predictor, a, b, c) NLS.poly2(predictor, a, b, c) DRC.poly2(fixed = c(NA, NA, NA), names = c("a", "b", "c"))poly2.fun(predictor, a, b, c) NLS.poly2(predictor, a, b, c) DRC.poly2(fixed = c(NA, NA, NA), names = c("a", "b", "c"))
predictor |
a numeric vector of values at which to evaluate the model |
a |
numeric. The response when the predictor is equal to 0. |
b |
numeric. The slope at X = 0 |
c |
numeric. Regression parameter |
fixed |
numeric vector. Specifies which parameters are fixed and at what value they are fixed. NAs for parameter that are not fixed. |
names |
a vector of character strings giving the names of the parameters. The default is reasonable. |
The simple polynomial (second order) regression model is given by the following equation:
poly2.fun and NLS.poly2 return a numeric value, while DRC.poly2 returns a list containing the nonlinear function, the self starter function and the parameter names.
Andrea Onofri
Ratkowsky, DA (1990) Handbook of nonlinear regression models. New York (USA): Marcel Dekker Inc.
Onofri, A. (2020). A collection of self-starters for nonlinear regression in R. See: https://www.statforbiology.com/2020/stat_nls_usefulfunctions/
# Polynomial regression X <- seq(5, 50, 5) Y <- c(12.6, 74.1, 157.6, 225.5, 303.4, 462.8, 669.9, 805.3, 964.2, 1169) model <- nls(Y ~ NLS.poly2(X, a, b, c)) summary(model) model <- drm(Y ~ X, fct = DRC.poly2()) summary(model)# Polynomial regression X <- seq(5, 50, 5) Y <- c(12.6, 74.1, 157.6, 225.5, 303.4, 462.8, 669.9, 805.3, 964.2, 1169) model <- nls(Y ~ NLS.poly2(X, a, b, c)) summary(model) model <- drm(Y ~ X, fct = DRC.poly2()) summary(model)
This function calculates measures of goodness of fit for nonlinear regression. It works with both 'nls' and 'drc' objects
R2nls(object)R2nls(object)
object |
A nonlinear regression fit object. It can be either a 'nls' fit or 'drm' fit. |
A list with the following slots:
R2 |
Traditional coefficient of determination, calculated as the ratio of model SS to total SS. Formula as in Schabenberger and Pierce, 5.23, pag 211. |
PseudoR2 |
Pseudo-R2, more useful for nonlinear regression with no-intercept-models. Formula Formula as in Schabenberger and Pierce, 5.24, pag 212. |
R2adj |
Adjusted R2, similar to R2 above, but penalised for higher number of parameters. |
MSE |
Mean Squared Error |
RMSE |
Root Means Squared Error |
RRMSE |
Relative Root Means Squared Error |
Andrea Onofri
Schabenberger, O., Pierce, F.J., 2002. Contemporary statistical models for the plant and soil sciences. Taylor & Francis, CRC Press, Books.
data(beetGrowth) mod3 <- nls(weightInf ~ NLS.L3(DAE, b, c, d), data = beetGrowth) R2nls(mod3) mod4 <- drm(weightInf ~ DAE, fct = L.3(), data = beetGrowth) R2nls(mod4)data(beetGrowth) mod3 <- nls(weightInf ~ NLS.L3(DAE, b, c, d), data = beetGrowth) R2nls(mod3) mod4 <- drm(weightInf ~ DAE, fct = L.3(), data = beetGrowth) R2nls(mod4)
These functions provide the beta equation, a threshold model that was derived
from the beta density function and it was adapted to describe phenomena taking place only
within a minimum and a maximum threshold value (threshold model), for example
to describe the germination rate (GR, i.e. the inverse of germination time)
as a function of temperature. These functions provide the beta
equation (beta.fun), the self-starters for the nls
function (NLS.beta) and the self-starters for
the drm function in the drc package (DRC.beta)
beta.fun(X, b, d, Xb, Xo, Xc) NLS.beta(X, b, d, Xb, Xo, Xc) DRC.beta()beta.fun(X, b, d, Xb, Xo, Xc) NLS.beta(X, b, d, Xb, Xo, Xc) DRC.beta()
X |
a numeric vector of values at which to evaluate the model |
b |
model parameter |
d |
model parameter |
Xb |
model parameter (base threshold level) |
Xo |
model parameter (optimal threshold level) |
Xc |
model parameter (ceiling threshold level) |
This equation is parameterised as:
It depicts a curve that is equal to 0 for X < Xb, grows up to a maximum, that is attained at X = Xo and decreases down to 0, that is attained at X = Xc and mantained for X > Xc.
beta.fun, NLS.beta return a numeric value, while DRC.beta returns a list containing the nonlinear function and the self starter function
Andrea Onofri
Ratkowsky, DA (1990) Handbook of nonlinear regression models. New York (USA): Marcel Dekker Inc.
Onofri, A. (2020). A collection of self-starters for nonlinear regression in R. See: https://www.statforbiology.com/2020/stat_nls_usefulfunctions/
X <- c(1, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50) Y <- c(0, 0, 0, 7.7, 12.3, 19.7, 22.4, 20.3, 6.6, 0, 0) model <- nls(Y ~ NLS.beta(X, b, d, Xb, Xo, Xc)) summary(model) modelb <- drm(Y ~ X, fct = DRC.beta()) summary(modelb) plot(modelb, log = "")X <- c(1, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50) Y <- c(0, 0, 0, 7.7, 12.3, 19.7, 22.4, 20.3, 6.6, 0, 0) model <- nls(Y ~ NLS.beta(X, b, d, Xb, Xo, Xc)) summary(model) modelb <- drm(Y ~ X, fct = DRC.beta()) summary(modelb) plot(modelb, log = "")
These functions provide the Bragg's equations, that is based on
the normal (Gaussian) distribution and it supports a maximum,
a minimum and inflection points. These functions provide the
equations with 4 (bragg.4.fun) and 3 (bragg.3.fun) parameters
with self-starters for the nls
function (NLS.bragg.4, NLS.bragg.3) and the self-starters for
the drm function in the drc package (DRC.bragg.4, DRC.bragg.3)
bragg.4.fun(X, b, c, d, e) bragg.3.fun(X, b, d, e) NLS.bragg.4(X, b, c, d, e) NLS.bragg.3(X, b, d, e) DRC.bragg.4() DRC.bragg.3()bragg.4.fun(X, b, c, d, e) bragg.3.fun(X, b, d, e) NLS.bragg.4(X, b, c, d, e) NLS.bragg.3(X, b, d, e) DRC.bragg.4() DRC.bragg.3()
X |
a numeric vector of values at which to evaluate the model |
b |
model parameter (relates to slope at inflection point) |
d |
model parameter (maximum value) |
e |
model parameter (abscissa at maximum value) |
c |
model parameter (lower asymptote) |
The Bragg's equation is parameterised as:
for the 4-parameter model. For the 3-parameter model, c is equal to 0. It depicts a bell-shaped curve
bragg.4.fun, bragg.3.fun, NLS.bragg.4 and NLS.bragg.3 return a numeric value, while DRC.bragg.4 and DRC.bragg.3 return a list containing the nonlinear function and the self starter function
Andrea Onofri
Ratkowsky, DA (1990) Handbook of nonlinear regression models. New York (USA): Marcel Dekker Inc.
Onofri, A. (2020). A collection of self-starters for nonlinear regression in R. See: https://www.statforbiology.com/2020/stat_nls_usefulfunctions/
library(statforbiology) X <- c(5, 10, 15, 20, 25, 30, 35, 40, 45, 50) Y1 <- c(0.1, 2, 5.7, 9.3, 19.7, 28.4, 20.3, 6.6, 1.3, 0.1) Y2 <- Y1 + 2 # nls fit mod.nls <- nls(Y1 ~ NLS.bragg.3(X, b, d, e) ) mod.nls2 <- nls(Y2 ~ NLS.bragg.4(X, b, c, d, e) ) # drm fit mod.drc <- drm(Y1 ~ X, fct = DRC.bragg.3() ) mod.drc2 <- drm(Y2 ~ X, fct = DRC.bragg.4() ) plot(mod.drc, ylim = c(0, 30), log = "") plot(mod.drc2, add = TRUE, col = "red")library(statforbiology) X <- c(5, 10, 15, 20, 25, 30, 35, 40, 45, 50) Y1 <- c(0.1, 2, 5.7, 9.3, 19.7, 28.4, 20.3, 6.6, 1.3, 0.1) Y2 <- Y1 + 2 # nls fit mod.nls <- nls(Y1 ~ NLS.bragg.3(X, b, d, e) ) mod.nls2 <- nls(Y2 ~ NLS.bragg.4(X, b, c, d, e) ) # drm fit mod.drc <- drm(Y1 ~ X, fct = DRC.bragg.3() ) mod.drc2 <- drm(Y2 ~ X, fct = DRC.bragg.4() ) plot(mod.drc, ylim = c(0, 30), log = "") plot(mod.drc2, add = TRUE, col = "red")
These functions provide the rectangula hyperbola that was devided by Cousens (1985)
for modelling the relationship between crop yield and weed density. The function was
derived from the yield-loss function, and contains parameters that are revelant for
competition studies. These functions provide the
equation (cousens85.fun), the self-starters for the nls
function (NLS.cousens85) and the self-starters for
the drm function in the drc package (DRC.cousens85)
cousens85.fun(predictor, Ywf, i, A) NLS.cousens85(predictor, Ywf, i, A) DRC.cousens85(fixed = c(NA, NA, NA), names = c("Ywf", "i", "A"))cousens85.fun(predictor, Ywf, i, A) NLS.cousens85(predictor, Ywf, i, A) DRC.cousens85(fixed = c(NA, NA, NA), names = c("Ywf", "i", "A"))
predictor |
a numeric vector of values at which to evaluate the model |
Ywf |
model parameter (Weed-free yield) |
i |
model parameter (initial slope) |
A |
model parameter (maximum percentage yield loss) |
fixed |
numeric vector. Specifies which parameters are fixed and at what value they are fixed. NAs for parameter that are not fixed. |
names |
a vector of character strings giving the names of the parameters. The default is usually reasonable. |
This equation is parameterised as:
It depicts a decreasing curve with no inflection point. The curve is equal to 'Ywf' when x = 0 and the lower asymptote is at 'A' multiplied by 'Ywf/100'
cousens85.fun, NLS.cousens85 return a numeric value, while DRC.cousens85 return a list containing the nonlinear function and the self starter function
Andrea Onofri
Ratkowsky, DA (1990) Handbook of nonlinear regression models. New York (USA): Marcel Dekker Inc.
Onofri, A. (2020). A collection of self-starters for nonlinear regression in R. See: https://www.statforbiology.com/2020/stat_nls_usefulfunctions/
Cousens, R., 1985. A simple model relating yield loss to weed density. Annals of Applied Biology 107, 239–252. https://doi.org/10.1111/j.1744-7348.1985.tb01567.x
library(statforbiology) dataset <- getAgroData("Sinapis") # nls fit mod.nls <- nls(yield ~ NLS.cousens85(density, Ywf, i, A), data = dataset ) summary(mod.nls) mod.nls2 <- drm(yield ~ density, fct = DRC.cousens85(), data = dataset ) summary(mod.nls2) plot(mod.nls2)library(statforbiology) dataset <- getAgroData("Sinapis") # nls fit mod.nls <- nls(yield ~ NLS.cousens85(density, Ywf, i, A), data = dataset ) summary(mod.nls) mod.nls2 <- drm(yield ~ density, fct = DRC.cousens85(), data = dataset ) summary(mod.nls2) plot(mod.nls2)
These functions provide the modified Gompertz equations with 4 (E4.fun), 3 (E3.fun)
and 2 (E2.fun) parameters with self-starter for the nls
function (NLS.E4, NLS.E3 and NLS.E2) and for the drm function
in the 'drc' package (DRC.E4, DRC.E3 and DRC.E2).
E4.fun(predictor, b, c, d, e) E3.fun(predictor, b, d, e) E2.fun(predictor, b, e) NLS.E4(predictor, b, c, d, e) NLS.E3(predictor, b, d, e) NLS.E2(predictor, b, e) DRC.E4(fixed = c(NA, NA, NA, NA), names = c("b", "c", "d", "e")) DRC.E3(fixed = c(NA, NA, NA), names = c("b", "d", "e")) DRC.E2(fixed = c(NA, NA), names = c("b", "e"))E4.fun(predictor, b, c, d, e) E3.fun(predictor, b, d, e) E2.fun(predictor, b, e) NLS.E4(predictor, b, c, d, e) NLS.E3(predictor, b, d, e) NLS.E2(predictor, b, e) DRC.E4(fixed = c(NA, NA, NA, NA), names = c("b", "c", "d", "e")) DRC.E3(fixed = c(NA, NA, NA), names = c("b", "d", "e")) DRC.E2(fixed = c(NA, NA), names = c("b", "e"))
predictor |
a numeric vector of values at which to evaluate the model |
b |
model parameter (slope at inflection point) |
c |
model parameter (lower asymptote) |
d |
model parameter (higher asymptote) |
e |
model parameter (abscissa at inflection point) |
fixed |
numeric vector. Specifies which parameters are fixed and at what value they are fixed. NAs for parameter that are not fixed. |
names |
names. A vector of character strings giving the names of the parameters. The default is reasonable. |
The modified Gompertz equation is parameterised as:
It is a sygmoidally shaped curve and it is asymmetric about its inflection point, but the type of asymmetry is different from the Gompertz equation. For the 3- and 2-parameter model c is equal to 0, while for the 2-parameter model d is equal to 1.
E4.fun, E3.fun, E2.fun, NLS.E4, NLS.E3 and NLS.E2 return a numeric value, while DRC.E4, DRC.E3 and DRC.E2 return a list containing the nonlinear function, the self starter function and the parameter names.
Andrea Onofri
data(beetGrowth) mod3 <- nls(weightInf ~ NLS.E3(DAE, b, c, d), data = beetGrowth) summary(mod3) plot(mod3)data(beetGrowth) mod3 <- nls(weightInf ~ NLS.E3(DAE, b, c, d), data = beetGrowth) summary(mod3) plot(mod3)
These functions provide the Gompertz equations with 4 (G4.fun), 3 (G3.fun)
and 2 (G2.fun) parameters with self-starter for the nls
function (NLS.G4, NLS.G3 and NLS.G2).
G4.fun(predictor, b, c, d, e) G3.fun(predictor, b, d, e) G2.fun(predictor, b, e) NLS.G4(predictor, b, c, d, e) NLS.G3(predictor, b, d, e) NLS.G2(predictor, b, e)G4.fun(predictor, b, c, d, e) G3.fun(predictor, b, d, e) G2.fun(predictor, b, e) NLS.G4(predictor, b, c, d, e) NLS.G3(predictor, b, d, e) NLS.G2(predictor, b, e)
predictor |
a numeric vector of values at which to evaluate the model |
b |
model parameter (slope at inflection point) |
c |
model parameter (lower asymptote) |
d |
model parameter (higher asymptote) |
e |
model parameter (abscissa at inflection point) |
The Gompertz equation is parameterised as:
It is a sygmoidally shaped curve and it is asymmetric about its inflection point. For the 3- and 2-parameter model c is equal to 0, while for the 2-parameter model d is equal to 1.
All these functions return a numeric value.
Andrea Onofri
data(beetGrowth) mod3 <- nls(weightInf ~ NLS.G3(DAE, b, c, d), data = beetGrowth) summary(mod3) plot(mod3)data(beetGrowth) mod3 <- nls(weightInf ~ NLS.G3(DAE, b, c, d), data = beetGrowth) summary(mod3) plot(mod3)
These functions provide the logistic equations with 4 (L4.fun), 3 (L3.fun)
and 2 (L2.fun) parameters with self-starter for the nls
function (NLS.L4, NLS.L3 and NLS.L2) and the self-starter for logistic
function with two parameters for the drm function in the
drc package (DRC.L2).
L4.fun(predictor, b, c, d, e) L3.fun(predictor, b, d, e) L2.fun(predictor, b, e) NLS.L4(predictor, b, c, d, e) NLS.L3(predictor, b, d, e) NLS.L2(predictor, b, e) DRC.L2(upper = 1, fixed = c(NA, NA), names = c("b", "e"))L4.fun(predictor, b, c, d, e) L3.fun(predictor, b, d, e) L2.fun(predictor, b, e) NLS.L4(predictor, b, c, d, e) NLS.L3(predictor, b, d, e) NLS.L2(predictor, b, e) DRC.L2(upper = 1, fixed = c(NA, NA), names = c("b", "e"))
predictor |
a numeric vector of values at which to evaluate the model |
b |
model parameter (slope at inflection point) |
c |
model parameter (lower asymptote) |
d |
model parameter (higher asymptote) |
e |
model parameter (abscissa at inflection point) |
upper |
numeric. For L.2, a upper asymptote different from 1 can be specified. |
fixed |
numeric vector. Specifies which parameters are fixed and at what value they are fixed. NAs for parameter that are not fixed. |
names |
names. A vector of character strings giving the names of the parameters. The default is reasonable. |
The logistic equation is parameterised as:
for the 3- and 2-parameter model c is equal to 0, while for the 2-parameter model d is equal to 1.
L4.fun, L3.fun, L2.fun, NLS.L4, NLS.L3 and NLS.L2 return a numeric value, while DRC.L2 returns a list containing the nonlinear function, the self starter function and the parameter names.
Andrea Onofri
data(beetGrowth) mod3 <- nls(weightInf ~ NLS.L3(DAE, b, c, d), data = beetGrowth) mod3b <- drm(weightInf ~ DAE, fct=DRC.L2(upper = 25), data = beetGrowth)data(beetGrowth) mod3 <- nls(weightInf ~ NLS.L3(DAE, b, c, d), data = beetGrowth) mod3b <- drm(weightInf ~ DAE, fct=DRC.L2(upper = 25), data = beetGrowth)
These functions provide the loglogistic equation, that has a
symmetric sygmoidal shape over the logarithm of time and it has been used
for bioassay work. These functions provide the 4-, 3- and 2-parameter
equations (LL4.fun(), LL3.fun() and LL2.fun()) as well as the self-starters
for the nls function (NLS.LL4(), NLS.LL3() and NLS.LL2() )
LL4.fun(predictor, b, c, d, e) LL3.fun(predictor, b, d, e) LL2.fun(predictor, b, e) NLS.LL4(predictor, b, c, d, e) NLS.LL3(predictor, b, d, e) NLS.LL2(predictor, b, e)LL4.fun(predictor, b, c, d, e) LL3.fun(predictor, b, d, e) LL2.fun(predictor, b, e) NLS.LL4(predictor, b, c, d, e) NLS.LL3(predictor, b, d, e) NLS.LL2(predictor, b, e)
predictor |
a numeric vector of values at which to evaluate the model |
b |
model parameter (slope at inflection point) |
c |
model parameter (lower asymptote) |
d |
model parameter (higher asymptote) |
e |
model parameter (abscissa at inflection point) |
These functions provide the log-logistic equation for bioassay work This equation (4-parameters) is parameterised as:
For the 3- and 2-parameters model, c is equal to 0, while for the 2-parameter model d is equal to 1.
All these functions return a numeric value
Andrea Onofri
Ratkowsky, DA (1990) Handbook of nonlinear regression models. New York (USA): Marcel Dekker Inc.
Onofri, A. (2020). A collection of self-starters for nonlinear regression in R. See: https://www.statforbiology.com/2020/stat_nls_usefulfunctions/
Ritz, C., Jensen, S.M., Gerhard, D., Streibig, J.C., 2019. Dose-response analysis using R, CRC Press. ed. USA.
dataset <- getAgroData("brassica") model <- nls(FW ~ NLS.LL4(Dose, b, c, d, e), data = dataset) model <- nls(FW ~ NLS.LL3(Dose, b, d, e), data = dataset) model <- nls(FW/max(FW) ~ NLS.LL2(Dose, b, e), data = dataset) summary(model)dataset <- getAgroData("brassica") model <- nls(FW ~ NLS.LL4(Dose, b, c, d, e), data = dataset) model <- nls(FW ~ NLS.LL3(Dose, b, d, e), data = dataset) model <- nls(FW/max(FW) ~ NLS.LL2(Dose, b, e), data = dataset) summary(model)
These functions provide the Lorentz equation with 3 and 4 parameters ('lorentz.3.fun()'
and 'lorentz.4.fun()' ), as well as the self-starters for the nls
function ( 'NLS.lorentz.3()' and 'NLS.lorentz.4()') and for the
drm function in the 'drc' package ('DRC.lorentz.3()' and 'DRC.lorentz.4()')
lorentz.3.fun(X, b, d, e) lorentz.4.fun(X, b, c, d, e) NLS.lorentz.3(X, b, d, e) NLS.lorentz.4(X, b, c, d, e) DRC.lorentz.3() DRC.lorentz.4()lorentz.3.fun(X, b, d, e) lorentz.4.fun(X, b, c, d, e) NLS.lorentz.3(X, b, d, e) NLS.lorentz.4(X, b, c, d, e) DRC.lorentz.3() DRC.lorentz.4()
X |
a numeric vector of values at which to evaluate the model |
b |
model parameter |
d |
model parameter |
e |
model parameter |
c |
model parameter |
These functions provide the Lorentz equation, that is a bell-shaped curve similar to a gaussian density function. It is parameterised as:
The parameter 'e' represents the abscissa of the maximum value, while c is the minimum (asymptotic) response value and d is the maximum response value. The parameter 'b' relates to the slope at inflection point. For the 3-parameters curve, c is equal to 0.
lorentz.3.fun(), lorentz.4.fun(), NLS.lorentz.3() and NLS.lorentz.4() return a numeric value, while DRC.lorentz.3() and DRC.lorentz.4() returns a list containing the nonlinear function, the self starter function and the parameter names.
Andrea Onofri
Ratkowsky, DA (1990) Handbook of nonlinear regression models. New York (USA): Marcel Dekker Inc.
Onofri, A. (2020). A collection of self-starters for nonlinear regression in R. See: https://www.statforbiology.com/2020/stat_nls_usefulfunctions/
X <- c(5, 10, 15, 20, 25, 30, 35, 40, 45, 50) Y1 <- c(0.1, 2, 5.7, 9.3, 19.7, 28.4, 20.3, 6.6, 1.3, 0.1) Y2 <- Y1 + 2 # nls fit mod.nls <- nls(Y1 ~ NLS.lorentz.3(X, b, d, e) ) mod.nls2 <- nls(Y2 ~ NLS.lorentz.4(X, b, c, d, e) ) # drm fit mod.drc <- drm(Y1 ~ X, fct = DRC.lorentz.3() ) mod.drc2 <- drm(Y2 ~ X, fct = DRC.lorentz.4() ) plot(mod.drc, ylim = c(0, 30), log = "") plot(mod.drc2, add = TRUE, col = "red")X <- c(5, 10, 15, 20, 25, 30, 35, 40, 45, 50) Y1 <- c(0.1, 2, 5.7, 9.3, 19.7, 28.4, 20.3, 6.6, 1.3, 0.1) Y2 <- Y1 + 2 # nls fit mod.nls <- nls(Y1 ~ NLS.lorentz.3(X, b, d, e) ) mod.nls2 <- nls(Y2 ~ NLS.lorentz.4(X, b, c, d, e) ) # drm fit mod.drc <- drm(Y1 ~ X, fct = DRC.lorentz.3() ) mod.drc2 <- drm(Y2 ~ X, fct = DRC.lorentz.4() ) plot(mod.drc, ylim = c(0, 30), log = "") plot(mod.drc2, add = TRUE, col = "red")
These functions provide the Power curve equation, that is also known
as the Freundlich equation and it is very used in agricultural chemistry,
e.g. to model the sorption of xenobiotics in soil. It is also used to model
the number of plant species as a function of sampling area
(Muller-Dumbois method). These functions provide the equation
('powerCurve.fun()') as well as the self-starters
for the nls function ( 'NLS.powerCurve()' ) and for the
drm function in the 'drc' package ('DRC.powerCurve()')
powerCurve.fun(predictor, a, b) NLS.powerCurve(predictor, a, b) DRC.powerCurve(fixed = c(NA, NA), names = c("a", "b"))powerCurve.fun(predictor, a, b) NLS.powerCurve(predictor, a, b) DRC.powerCurve(fixed = c(NA, NA), names = c("a", "b"))
predictor |
a numeric vector of values at which to evaluate the model |
a |
model parameter |
b |
model parameter |
fixed |
numeric vector. Specifies which parameters are fixed and at what value they are fixed. NAs for parameter that are not fixed. |
names |
names. A vector of character strings giving the names of the parameters. The default is reasonable. |
These functions provide the Power curve equation, that is parameterised as:
which is totally equivalent to an exponential curve on the logarithm of X:
We see that both parameters relate to the ‘slope’ of the curve and b dictates its shape. If 0 < b < 1, the response Y increases as X increases and the curve is convex up. If b < 0 the curve is concave up and Y decreases as X increases. Otherwise, if b > 1, the curve is concave up and Y increases as X increases.
powerCurve.fun() and NLS.powerCurve() return a numeric value, while DRC.powerCurve() returns a list containing the nonlinear function, the self starter function and the parameter names.
Andrea Onofri
Ratkowsky, DA (1990) Handbook of nonlinear regression models. New York (USA): Marcel Dekker Inc.
Onofri, A. (2020). A collection of self-starters for nonlinear regression in R. See: https://www.statforbiology.com/2020/stat_nls_usefulfunctions/
dataset <-getAgroData("speciesArea") #nls fit model <- nls(numSpecies ~ NLS.powerCurve(Area, a, b), data = dataset) summary(model) # drm fit model <- drm(numSpecies ~ Area, fct = DRC.powerCurve(), data = dataset) summary(model)dataset <-getAgroData("speciesArea") #nls fit model <- nls(numSpecies ~ NLS.powerCurve(Area, a, b), data = dataset) summary(model) # drm fit model <- drm(numSpecies ~ Area, fct = DRC.powerCurve(), data = dataset) summary(model)
These functions provide the Weibull equation (type I), that has an
asymmetric sygmoidal shape and it has been used for bioassay work.
These functions provide the 4-, 3- and 2-parameter equations
(W1.4.fun(), W1.3.fun() and W1.2.fun()) as well as the self-starters
for the nls function (NLS.W1.4(), NLS.W1.3() and NLS.W1.2()
W1.4.fun(predictor, b, c, d, e) W1.3.fun(predictor, b, d, e) W1.2.fun(predictor, b, e) NLS.W1.4(predictor, b, c, d, e) NLS.W1.3(predictor, b, d, e) NLS.W1.2(predictor, b, e)W1.4.fun(predictor, b, c, d, e) W1.3.fun(predictor, b, d, e) W1.2.fun(predictor, b, e) NLS.W1.4(predictor, b, c, d, e) NLS.W1.3(predictor, b, d, e) NLS.W1.2(predictor, b, e)
predictor |
a numeric vector of values at which to evaluate the model |
b |
model parameter (slope at inflection point) |
c |
model parameter (lower asymptote) |
d |
model parameter (higher asymptote) |
e |
model parameter (abscissa at inlection point) |
These functions provide the Weibull (Type I) equation for bioassay work This equation (4-parameters) is parameterised as:
For the 3- and 2-parameters model, c is equal to 0, while for the 2-parameter model d is equal to 1.
All these functions return a numeric value
Andrea Onofri
Ratkowsky, DA (1990) Handbook of nonlinear regression models. New York (USA): Marcel Dekker Inc.
Onofri, A. (2020). A collection of self-starters for nonlinear regression in R. See: https://www.statforbiology.com/2020/stat_nls_usefulfunctions/
Ritz, C., Jensen, S.M., Gerhard, D., Streibig, J.C., 2019. Dose-response analysis using R, CRC Press. ed. USA.
library(statforbiology) dataset <- getAgroData("brassica") model <- nls(FW ~ NLS.W1.4(Dose, b, c, d, e), data = dataset) model.2 <- nls(FW ~ NLS.W1.3(Dose, b, d, e), data = dataset) model.3 <- nls(FW/max(FW) ~ NLS.W1.2(Dose, b, e), data = dataset) summary(model)library(statforbiology) dataset <- getAgroData("brassica") model <- nls(FW ~ NLS.W1.4(Dose, b, c, d, e), data = dataset) model.2 <- nls(FW ~ NLS.W1.3(Dose, b, d, e), data = dataset) model.3 <- nls(FW/max(FW) ~ NLS.W1.2(Dose, b, e), data = dataset) summary(model)
These functions provide the Weibull equation (type II), that has an
asymmetric sygmoidal shape and it has been used for bioassay work.
These functions provide the 4-, 3- and 2-parameter equations
(W2.4.fun(), W2.3.fun() and W2.2.fun()) as well as the self-starters
for the nls function (NLS.W2.4(), NLS.W2.3() and NLS.W2.2()
W2.4.fun(predictor, b, c, d, e) W2.3.fun(predictor, b, d, e) W2.2.fun(predictor, b, e) NLS.W2.4(predictor, b, c, d, e) NLS.W2.3(predictor, b, d, e) NLS.W2.2(predictor, b, e)W2.4.fun(predictor, b, c, d, e) W2.3.fun(predictor, b, d, e) W2.2.fun(predictor, b, e) NLS.W2.4(predictor, b, c, d, e) NLS.W2.3(predictor, b, d, e) NLS.W2.2(predictor, b, e)
predictor |
a numeric vector of values at which to evaluate the model |
b |
model parameter (slope at inflection point) |
c |
model parameter (lower asymptote) |
d |
model parameter (higher asymptote) |
e |
model parameter (abscissa at inlection point) |
These functions provide the Weibull (Type I) equation for bioassay work This equation (4-parameters) is parameterised as:
For the 3- and 2-parameters model, c is equal to 0, while for the 2-parameter model d is equal to 1.
All these functions return a numeric value
Andrea Onofri
Ratkowsky, DA (1990) Handbook of nonlinear regression models. New York (USA): Marcel Dekker Inc.
Onofri, A. (2020). A collection of self-starters for nonlinear regression in R. See: https://www.statforbiology.com/2020/stat_nls_usefulfunctions/
Ritz, C., Jensen, S.M., Gerhard, D., Streibig, J.C., 2019. Dose-response analysis using R, CRC Press. ed. USA.
library(statforbiology) dataset <- getAgroData("brassica") model <- nls(FW ~ NLS.W2.4(Dose, b, c, d, e), data = dataset) model <- nls(FW ~ NLS.W2.3(Dose, b, d, e), data = dataset) model <- nls(FW/max(FW) ~ NLS.W2.2(Dose, b, e), data = dataset) summary(model)library(statforbiology) dataset <- getAgroData("brassica") model <- nls(FW ~ NLS.W2.4(Dose, b, c, d, e), data = dataset) model <- nls(FW ~ NLS.W2.3(Dose, b, d, e), data = dataset) model <- nls(FW/max(FW) ~ NLS.W2.2(Dose, b, e), data = dataset) summary(model)
These functions provide the yield loss equation, based on
a rectangular hyperbola, supporting a higher asymptote and
no inflection points. These functions provide the
equation (YL.fun), the equation
with self-starters for the nls
function (NLS.YL) and equation with self-starters for
the drm function in the drc package (DRC.YL)
YL.fun(predictor, i, A) NLS.YL(predictor, i, A) DRC.YL(fixed = c(NA, NA), names = c("i", "A"))YL.fun(predictor, i, A) NLS.YL(predictor, i, A) DRC.YL(fixed = c(NA, NA), names = c("i", "A"))
predictor |
a numeric vector of values at which to evaluate the model |
i |
model parameter (initial slope) |
A |
model parameter (maximum percentage yield loss) |
fixed |
numeric vector. Specifies which parameters are fixed and at what value they are fixed. NAs for parameter that are not fixed. |
names |
a vector of character strings giving the names of the parameters. The default is usually reasonable. |
The Yield-loss equation is parameterised as:
, it is convex and asymptotically increasing, while the predictor increases. The response is zero when the predictor is also zero and it was mainly used to describe yield losses (in percentage) due to weed competition, expressed as plant density (Cousens, 1985)
YL.fun and NLS.YL return a numeric value, while DRC.YL returns a list containing the nonlinear function and the self starter function
Andrea Onofri
Ratkowsky, DA (1990) Handbook of nonlinear regression models. New York (USA): Marcel Dekker Inc.
Onofri, A. (2020). A collection of self-starters for nonlinear regression in R. See: https://www.statforbiology.com/2020/stat_nls_usefulfunctions/
Cousens, R., 1985. A simple model relating yield loss to weed density. Annals of Applied Biology 107, 239–252. https://doi.org/10.1111/j.1744-7348.1985.tb01567.x
library(statforbiology) WeedDens <- c(0, 5, 10, 20, 25) YieldLoss <- c(0, 17.9, 21.5, 27.4, 29.5) # nls fit mod.nls <- nls(YieldLoss ~ NLS.YL(WeedDens, i, A) ) summary(mod.nls) # drm fit mod.drc <- drm(YieldLoss ~ WeedDens, fct = DRC.YL() ) summary(mod.drc)library(statforbiology) WeedDens <- c(0, 5, 10, 20, 25) YieldLoss <- c(0, 17.9, 21.5, 27.4, 29.5) # nls fit mod.nls <- nls(YieldLoss ~ NLS.YL(WeedDens, i, A) ) summary(mod.nls) # drm fit mod.drc <- drm(YieldLoss ~ WeedDens, fct = DRC.YL() ) summary(mod.drc)