# coefCI

Class: GeneralizedLinearModel

Confidence intervals of coefficient estimates of generalized linear model

## Syntax

`ci = coefCI(mdl)ci = coefCI(mdl,alpha)`

## Description

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

`ci = coefCI(mdl,alpha)` returns confidence intervals with confidence level `1 - alpha`.

## Input Arguments

 `mdl` Generalized linear model, as constructed by `fitglm` or `stepwiseglm`. `alpha` Scalar from `0` to `1`, the probability that the confidence interval does not contain the true value. Default: `0.05`

## Output Arguments

 `ci` `k`-by-`2` matrix of confidence intervals. The `j`th row of `ci` is the confidence interval of coefficient `j` of `mdl`. The name of coefficient `j` of `mdl` is in `mdl``.CoefficientNames`.

## Definitions

### Confidence Interval

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.

## Examples

collapse all

### Confidence Interval for Coefficients of a Generalized Linear Model

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```