coefCI
Confidence intervals of coefficient estimates of generalized linear regression model
Description
Examples
Find Confidence Intervals for Model Coefficients
Find the confidence intervals for the coefficients of a fitted generalized linear regression model.
Generate sample data 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','Distribution','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 for the coefficients of the model.
ci = coefCI(mdl)
ci = 3×2
0.9966 1.0844
0.9901 1.0035
1.9744 1.9996
Find 99% confidence intervals for the coefficients.
alpha = 0.01; ci = coefCI(mdl,alpha)
ci = 3×2
0.9824 1.0986
0.9880 1.0056
1.9703 2.0036
Input Arguments
mdl
— Generalized linear regression model
GeneralizedLinearModel
object | CompactGeneralizedLinearModel
object
Generalized linear regression model, specified as a GeneralizedLinearModel
object created using fitglm
or stepwiseglm
, or a CompactGeneralizedLinearModel
object created using compact
.
alpha
— Significance level
0.05 (default) | numeric value in the range [0,1]
Significance level for the confidence interval, specified as a numeric value in the
range [0,1]. The confidence level of ci
is equal to 100(1 – alpha
)%. alpha
is the probability that the confidence
interval does not contain the true value.
Example: 0.01
Data Types: single
| double
Output Arguments
ci
— Confidence intervals
numeric matrix
Confidence intervals, returned as a k-by-2 numeric matrix, where
k is the number of coefficients. The jth row
of ci
is the confidence interval of the jth
coefficient of mdl
. The name of coefficient j is
stored in the CoefficientNames
property of
mdl
.
Data Types: single
| double
More About
Confidence Interval
The coefficient confidence intervals provide a measure of precision for regression coefficient estimates.
A 100(1 – α)% confidence interval gives the range for the corresponding regression coefficient with 100(1 – α)% confidence, meaning that 100(1 – α)% of the intervals resulting from repeated experimentation will contain the true value of the coefficient.
The software finds confidence intervals using the Wald method. The 100(1 – α)% confidence intervals for regression coefficients are
where bi is the coefficient estimate, SE(bi) is the standard error of the coefficient estimate, and t(1–α/2,n–p) is the 100(1 – α/2) percentile of the t-distribution with n – p degrees of freedom. n is the number of observations and p is the number of regression coefficients.
Extended Capabilities
GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.
This function fully supports GPU arrays. For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).
Version History
Introduced in R2012a
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