intermediate r - nonlinear regression in r
TRANSCRIPT
Nonlinear Regression in R
Violeta I. Bartolome
Senior Associate Scientist
PBGB-CRIL
Nonlinear Regression
• An extended linear regression technique in which a nonlinear mathematical model is used to describe the relationship between the response variable and the predictor variables.
• A nonlinear regression model is a model that contains at least one of the parameters in a nonlinear form
• Example
εεεε++++αααα==== ββββXY ),0(~2σσσσεεεε N
Linearized Nonlinear Model
• The linearized form of the example is:
XY logloglog ββββ++++αααα====
• The normality assumption for the error term
will not be appropriate for the linearized
form.
• Hence, if a nonlinear model is assumed to
be appropriate for the data, the nonlinear
model should be used for the analysis
instead of the linearized form.
Parameter Estimation
• Iterative procedures are used
• May require users to supply initial estimates of parameters
• User should know the biological interpretation of the parameters to provide intelligent initial values.
• The function getInitial() may also be used.
Logistic growth curve
• Sample data
Severity represents the number
of lesions on the leaf surface,
standardized as a proportion of
the maximum.
Read and Plot Data
Graph shows a logistic
relationship.
Logistic model:
rtey −−−−ββββ++++
αααα====1
Initial values
scal
inputxmid
e
Asymy −−−−
++++
====
1
rtey −−−−ββββ++++
αααα====1
SSlogis creates initial estimates of the parameters Asym,
xmid, and scal from the model:
The model that we are estimating is: inputtscal
r
scal
xmidAsym
========
====ββββ====αααα
1
Estimate Parameters
Check fit of data
Other Non-linear Models
• Exponential
εεεε++++==== rxeyy 0
Other Non-linear Models
• Monomolecular
(((( )))) εεεε++++−−−−−−−−==== −−−−rxeyy 011
Other Non-linear Models
• Logistic
rxey
yy
−−−−
−−−−++++
====
0
011
1
Other Non-linear Models
• Gompertz
rxyeey −−−−==== 0log
Other Non-linear Models
• Weibull
c
b
ax
ey
−−−−−−−−
−−−−==== 1 Thank you!