BC_model: Analysis: Logistic regression Brain-Cousens hormesis models

Description

The 'BC.4' and 'BC.5' logistical models provide Brain-Cousens' modified logistical models to describe u-shaped hormesis. This model was extracted from the 'drc' package and adapted for temperature analysis in seed germination

Usage

BC_model(
  trat,
  resp,
  npar = "BC.4",
  error = "SE",
  ylab = "Germination (%)",
  xlab = expression("Temperature ("^"o" * "C)"),
  theme = theme_classic(),
  legend.position = "top",
  cardinal = 0,
  r2 = "all",
  width.bar = NA,
  scale = "none",
  textsize = 12,
  pointsize = 4.5,
  linesize = 0.8,
  pointshape = 21,
  font.family = "sans"
)

Value

Coefficients: Coefficients and their p values

Optimum temperature

Optimum temperature (equivalent to the maximum point)

Optimum temperature response

Response at the optimal temperature (equivalent to the maximum point)

Minimal temperature

Temperature that has the lowest response

Minimal temperature response

Lowest predicted response

Predicted maximum basal value

Lower basal limit temperature based on the value set by the user (default is 0)

Predicted minimum basal value

Upper basal limit temperature based on the value set by the user (default is 0)

AIC

Akaike information criterion

BIC

Bayesian Inference Criterion

r-squared

Determination coefficient

RMSE

Root mean square error

grafico

Graph in ggplot2 with equation

Arguments

trat: Numerical or complex vector with treatments
resp: Numerical vector containing the response of the experiment.
npar: Number of model parameters (default is BC.4)
error: Error bar (It can be SE - default, SD or FALSE)
ylab: Variable response name (Accepts the expression() function)
xlab: Treatments name (Accepts the expression() function)
theme: ggplot2 theme (default is theme_bw())
legend.position: Legend position (default is c(0.3,0.8))
cardinal: Defines the value of y considered extreme (default considers 0 germination)
r2: Coefficient of determination of the mean or all values (default is all)
width.bar: bar width
scale: Sets x scale (default is none, can be "log")
textsize: Font size
pointsize: shape size
linesize: line size
pointshape: format point (default is 21)
font.family: Font family (default is sans)

Author

Model imported from the drc package (Ritz et al., 2016)

Gabriel Danilo Shimizu

Leandro Simoes Azeredo Goncalves

Details

The model function for the Brain-Cousens model (Brain and Cousens, 1989) is $$ f(x, b,c,d,e,f) = c + \frac{d-c+fx}{1+\exp(b(\log(x)-\log(e)))}$$ and it is a five-parameter model, obtained by extending the four-parameter log-logistic model (LL.4 to take into account inverse u-shaped hormesis effects. Fixing the lower limit at 0 yields the four-parameter model $$f(x) = 0 + \frac{d-0+fx}{1+\exp(b(\log(x)-\log(e)))}$$ used by van Ewijk and Hoekstra (1993).

References

Seber, G. A. F. and Wild, C. J (1989) Nonlinear Regression, New York: Wiley and Sons (p. 330).

Ritz, C.; STREBIG, J.C. and RITZ, M.C. Package ‘drc’. Creative Commons: Mountain View, CA, USA, 2016.

Examples

Run this code

library(seedreg)
data("aristolochia")
attach(aristolochia)

#================================
# Germination
#================================
BC_model(trat,germ)

#================================
# Germination speed
#================================
BC_model(trat, vel, ylab=expression("v"~(dias^-1)))

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