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(...)
Character vector specifying the type of plot:
comma-separated pairs of
the argument name and
Value is the corresponding value.
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 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.
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.
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.