加载中…Matlab 4 parameters logistic regression 四参数逻辑回归分析
(2013-11-21 09:18:50)
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Matlab
4参数的逻辑回归分析
The Four Parameters Logistic Regression or 4PL
nonlinear regression model is commonly used for curve-fitting
analysis in bioassays or immunoassays such as ELISAs or
dose-response curves.
It is characterized by it classic or sigmoidal
shape that fits the bottom and top plateaus of the curve, the EC50,
and the slope factor (Hill slope). This curve is symmetrical around
its inflection point.
The 4PL equation
is:
F(x) =
D+(A-D)/(1+(x/C)^B)
where:
A = Minimum
asymptote. In a bioassay where you have a standard
curve,
this can be
thought of as the response value at 0 standard
concentration.
B = Hill's
slope. The Hill's slope refers to the steepness of the
curve.
It could
either be positive or negative.
C =
Inflection point. The inflection point is defined as the point on
the
curve where
the curvature changes direction or signs. C is the
concentration of analyte where y=(D-A)/2.
D = Maximum
asymptote. In an bioassay where you have a standard
curve,
this can be
thought of as the response value for infinite standard
concentration.
Syntax: [cf
G]=L4P(x,y,st,L,U)
Inputs:
X and Y (mandatory) - data
points.
X is a Nx1 column vector and
Y must have the same rows number
of X. If Y is a NxM matrix (N
points and M replicates), L5P
will generate a
column vector computing means for each
row.
The standard deviations of
the rows will be used as weights of
regression.
st = starting points. This is
a 1x4 vector of starting points
that have to be used to start
the process of not linear
fitting. If this vector is
not provided, L4P will set the
starting points on the basis
of x and y data.
L = Lower bounds of
parameters. This is a 1x4 vector of lower
bounds of the 4 parameters.
If this vector is not provided, L4P
will set it on the basis of x
and y data.
U = Upper bounds of
parameters. This is a 1x4 vector of upper
bounds of the 4 parameters.
If this vector is not provided, L4P
will set it on the basis of x
and y data.
Outputs:
cf = the FIT
object
G = goodness-of-fit measures,
for the given inputs, in the
structure G. G includes the
fields:
-- SSE
sum of
squares due to error
-- R2
coefficient of determination or R^2
-- adjustedR2
degree of freedom adjusted R^2
-- stdError
fit standard error or root
mean square error
x=[0 4.5
10.6 19.7 40 84 210]; y=[0.0089 0.0419 0.0873 0.2599 0.7074 1.528
2.7739];
Calling on
MatLab the function: [cf G]=L4P(x,y)
Answer is:
cf
=
General
model:
cf(x) =
D+(A-D)/(1+(x/C)^B)
Coefficients (with 95% confidence
bounds):
A = 0.001002
(-0.04594, 0.04794)
B =
1.515 (1.293,
1.738)
C =
108 (86.58,
129.4)
D =
3.784 (3.302,
4.266)
G
=
sse:
0.0012
rsquare: 0.9998
dfe:
3
adjrsquare:
0.9996
rmse: 0.0200
hold on;
plot(x,y,'ro'); plot(cf,'r'); hold off
this will
plot the curve.
Four Parameters logistic
regression
Example:
相关问题：L4P相关知识，matlab-code
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