Confidence intervals of coefficient estimates of generalized linear model
ci = coefCI(mdl)
ci = coefCI(mdl,alpha)
Scalar from 0 to 1, the probability that the confidence interval does not contain the true value.
k-by-2 matrix of confidence intervals. The jth row of ci is the confidence interval of coefficient j of mdl. The name of coefficient j of mdl is in mdl.CoefficientNames.
Assume that model assumptions hold (data comes from a generalized linear model represented by the formula mdl.Formula and the specified link function, and with observations that are independent conditional on the predictor values). Then row j of the confidence interval matrix ci gives a confidence interval [ci(j,1),ci(j,2)] computed such that, with repeated experimentation, a proportion 1 - alpha of the intervals will contain the true value of the coefficient.
Find confidence intervals for the coefficients of a fitted generalized nonlinear model.
Generate artificial data for the model using Poisson random numbers with two underlying predictors X(1) and X(2).
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')
mdl = Generalized Linear regression model: log(y) ~ 1 + x1 + x2 Distribution = Poisson Estimated Coefficients: Estimate SE tStat pValue (Intercept) 1.0405 0.022122 47.034 0 x1 0.9968 0.003362 296.49 0 x2 1.987 0.0063433 313.24 0 100 observations, 97 error degrees of freedom Dispersion: 1 Chi^2-statistic vs. constant model: 2.95e+05, p-value = 0
Find 95% (default) confidence intervals on the coefficients of the model.
ci = coefCI(mdl)
ci = 0.9966 1.0844 0.9901 1.0035 1.9744 1.9996
Find 99% confidence intervals on the coefficients.
alpha = .01; ci = coefCI(mdl,alpha)
ci = 0.9824 1.0986 0.9880 1.0056 1.9703 2.0036