Plot diagnostics of generalized linear 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.
String 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 a diagonal weight matrix W:
H = X(XTWX)–1XTWT.
W has diagonal elements wi:
g is the link function mapping yi to xib.
is the derivative of the link function g.
V is the variance function.
μi is the ith mean.
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 dispersion parameter (estimated or theoretical).
ei is the linear predictor residual, , where
g is the link function.
yi is the observed response.
xi is the observation.
is the estimated coefficient vector.
p is the number of coefficients in the regression model.
hii is the ith diagonal element of the Hat Matrix H.
Create leverage and Cook's distance plots of a fitted generalized linear model.
Generate artificial data for the model, Poisson random
numbers with two underlying predictors
rng('default') % for reproducibility rndvars = randn(100,2); X = [2+rndvars(:,1),rndvars(:,2)]; mu = exp(1 + X*[1;2]); y = poissrnd(mu);
Create a generalized linear regression model of Poisson data.
mdl = fitglm(X,y,... 'y ~ x1 + x2','distr','poisson');
Create a leverage plot.
Create a contour plot with Cook's distance.
 Neter, J., M. H. Kutner, C. J. Nachtsheim, and W. Wasserman. Applied Linear Statistical Models, Fourth Edition. Irwin, Chicago, 1996.