coefCI

Confidence intervals of coefficient estimates for censored linear regression model

Since R2025a

Syntax

ci = coefCI(mdl)

ci = coefCI(mdl,alpha)

Description

ci = coefCI(mdl) returns 95% confidence intervals for the coefficients in mdl.

ci = coefCI(mdl,alpha) returns confidence intervals using the confidence level 1 – alpha.

Examples

Find Confidence Intervals for Model Coefficients

Load the readmissiontimes sample data.

load readmissiontimes

The variables Age, Weight, Smoker, and ReadmissionTime contain data for patient age, weight, smoking status, and time of readmission. The Censored variable contains censoring information for ReadmissionTime.

Save Age, Weight, Smoker, and ReadmissionTime in a table, and fit a censored linear regression model to the data.

tbl = table(Age,Weight,Smoker,ReadmissionTime);
mdl = fitlmcens(tbl,Censoring=Censored);

View the names of the coefficients.

mdl.CoefficientNames

ans = 1×4 cell
    {'(Intercept)'}    {'Age'}    {'Weight'}    {'Smoker'}

Calculate the confidence intervals for the model coefficients.

ci = coefCI(mdl)

ci = 4×2

   20.9887   34.4918
   -0.1716    0.0647
   -0.1444   -0.0776
   -4.1938   -0.4971

Specify Confidence Level

Load the readmissiontimes sample data.

load readmissiontimes

The variables Age, Weight, Smoker, and ReadmissionTime contain data for patient age, weight, smoking status, and time of readmission. The Censored variable contains censoring information for ReadmissionTime.

Save Age, Weight, Smoker, and ReadmissionTime in a table, and fit a censored linear regression model to the data.

tbl = table(Age,Weight,Smoker,ReadmissionTime);
mdl = fitlmcens(tbl,Censoring=Censored);

Find the 99% confidence intervals for the coefficients.

ci = coefCI(mdl,.01)

ci = 4×2

   18.8009   36.6796
   -0.2099    0.1030
   -0.1552   -0.0668
   -4.7928    0.1019

The confidence intervals are wider than the default 95% confidence intervals in the example Find Confidence Intervals for Model Coefficients.

Input Arguments

mdl — Censored linear regression model

CensoredLinearModel object | CompactCensoredLinearModel object

Censored linear regression model, specified as a CensoredLinearModel object created using fitlmcens, or a CompactCensoredLinearModel object created using fitlmcens and compact.

alpha — Significance level

0.05 (default) | numeric value in the range [0,1]

Significance level for the confidence interval,s 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 intervals do 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 Intervals

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

$$b_i\pm t_{\left(1-\alpha /2,n-p\right)}SE\left(b_i\right),$$

where b_i is the coefficient estimate, SE(b_i) 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.

Version History

Introduced in R2025a