Plot diagnostics of nonlinear regression model
h = plotDiagnostics(___)
plotDiagnostics( creates a leverage plot of the
nonlinear regression model (
mdl) observations. A dotted line in
the plot represents the recommended threshold values.
specifies the graphical properties of diagnostic data points using one or more
name-value arguments. For example, you can specify the marker symbol and size for the
graphics objects for the lines or contour in the plot using any of the input argument
combinations in the previous syntaxes. Use
h = plotDiagnostics(___)
h to modify the
properties of a specific line or contour after you create the plot. For a list of
properties, see Line Properties and Contour Properties.
Nonlinear regression model, constructed by
Character vector or string scalar specifying the type of plot:
comma-separated pairs of
the argument name and
Value is the corresponding value.
Name must appear inside quotes. You can specify several name and value
pair arguments in any order as
The graphical properties listed here are only a subset. For a complete list, see Line Properties. The specified properties determine the appearance of diagnostic data points.
Color of the line or marker, specified as an RGB triplet, hexadecimal color code, color name, or short name for one of the color options listed in the following table.
For a custom color, specify an RGB triplet or a hexadecimal color code.
Alternatively, you can specify some common colors by name. This table lists the named color options, the equivalent RGB triplets, and hexadecimal color codes.
Here are the RGB triplets and hexadecimal color codes for the default colors MATLAB® uses in many types of plots.
Width of the line or edges of filled area, in points, a positive scalar. One point is 1/72 inch.
Marker symbol, specified as one of the values in this table.
Marker outline color, specified as an RGB triplet, hexadecimal color code, color name, or
short name for one of the color options listed in the
Fill color for filled markers, specified as an RGB triplet, hexadecimal color code, color
name, or short name for one of the color options listed in the
Size of the marker in points, a strictly positive scalar. One point is 1/72 inch.
Graphics objects corresponding to the lines or contour in the plot, returned as a graphics array. Use dot notation to query and set properties of the graphics objects. For details, see Line Properties and Contour Properties.
You can use name-value arguments to specify the appearance of
diagnostic data points corresponding to the first graphics object
Nonlinear Model Leverage 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.
Use data tips to examine the observation with high leverage. A data tip appears when you hover over a data point.
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.
Leverage is a measure of the effect of a particular observation on the regression predictions due to the position of that observation in the space of the inputs.
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 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.
The data cursor displays the values of the selected plot point in a data tip (small text box located next to the data point). The data tip includes the x-axis and y-axis values for the selected 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.