Plot diagnostics of nonlinear regression model
h = plotDiagnostics(...)
h = plotDiagnostics(mdl,plottype,Name,Value)
diagnostics from the
mdl linear model using leverage
as the plot type.
handles to the lines in the plot.
h = plotDiagnostics(...)
For many plots, the Data Cursor tool in the figure window displays the x and y values for any data point, along with the observation name or number.
Nonlinear regression model, constructed by
Character vector specifying the type of plot:
Specify optional comma-separated pairs of
Name is the argument
Value is the corresponding
Name must appear
inside single quotes (
You can specify several name and value pair
arguments in any order as
The plot property name-value pairs apply to the first returned
Width of the line or edges of filled area, in points, a positive scalar. One point is 1/72 inch.
Size of the marker in points, a strictly positive scalar. One point is 1/72 inch.
Vector of handles to lines or patches in the plot.
The hat matrix H is defined in terms of the data matrix X and the Jacobian matrix J:
Here f is the nonlinear model function, and β is the vector of model coefficients.
The Hat Matrix H is
H = J(JTJ)–1JT.
The diagonal elements Hii satisfy
where n is the number of observations (rows of X), and p is the number of coefficients in the regression model.
The leverage of observation i is the value of the ith diagonal term, hii, of the hat matrix H. Because the sum of the leverage values is p (the number of coefficients in the regression model), an observation i can be considered to be an outlier if its leverage substantially exceeds p/n, where n is the number of observations.
The Cook's distance Di of observation i is
is the jth fitted response value.
is the jth fitted response value, where the fit does not include observation i.
MSE is the mean squared error.
p is the number of coefficients in the regression model.
Cook's distance is algebraically equivalent to the following expression:
where ei is the ith residual.
Create a leverage plot of a fitted nonlinear model, and find the points with high leverage.
Load the reaction data and fit a model of the reaction rate as a function of reactants.
load reaction mdl = fitnlm(reactants,rate,@hougen,[1 .05 .02 .1 2]);
Create a leverage plot of the fitted model.
To examine the observation with high leverage, activate the Data Cursor and click the observation.
Alternatively, find the high-leverage observation at the command line.
find(mdl.Diagnostics.Leverage > 0.8)
ans = 6
 Neter, J., M. H. Kutner, C. J. Nachtsheim, and W. Wasserman. Applied Linear Statistical Models, Fourth Edition. Irwin, Chicago, 1996.