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(...)
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.
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
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.
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.
 Neter, J., M. H. Kutner, C. J. Nachtsheim, and W. Wasserman. Applied Linear Statistical Models, Fourth Edition. Irwin, Chicago, 1996.