Documentation |
Class: GeneralizedLinearModel
Linear hypothesis test on generalized linear regression model coefficients
p = coefTest(mdl)
p = coefTest(mdl,H)
p = coefTest(mdl,H,C)
[p,F] =
coefTest(mdl,...)
[p,F,r]
= coefTest(mdl,...)
p = coefTest(mdl) computes the p-value for an F test that all coefficient estimates in mdl are zero, except for the intercept term.
p = coefTest(mdl,H) performs an F test that H*B = 0, where B represents the coefficient vector.
p = coefTest(mdl,H,C) performs an F test that H*B = C.
[p,F] = coefTest(mdl,...) returns the F test statistic.
[p,F,r] = coefTest(mdl,...) returns the numerator degrees of freedom for the test.
mdl |
Generalized linear model, as constructed by fitglm or stepwiseglm. |
H |
Numeric matrix having one column for each coefficient in the model. When H is an input, the output p is the p-value for an F test that H*B = 0, where B represents the coefficient vector. |
C |
Numeric vector with the same number of rows as H. When C is an input, the output p is the p-value for an F test that H*B = C, where B represents the coefficient vector. |
p |
p-value of the F test (see Definitions). |
F |
Value of the test statistic for the F test (see Definitions). |
r |
Numerator degrees of freedom for the F test (see Definitions). The F statistic has r degrees of freedom in the numerator and mdl.DFE degrees of freedom in the denominator. |
The p-value, F statistic, and numerator degrees of freedom are valid under these assumptions:
The data comes from a model represented by the formula mdl.Formula.
The observations are independent conditional on the predictor values.
Suppose these assumptions hold. Let β represent the (unknown) coefficient vector of the linear regression. Suppose H is a full-rank matrix of size r-by-s, where s is the number of terms in β. Let v be a vector the same size as β. The following is a test statistic for the hypothesis that Hβ = v:
$$F={\left(H\widehat{\beta}-v\right)}^{\prime}{\left(HC{H}^{\prime}\right)}^{-1}\left(H\widehat{\beta}-v\right).$$
Here $$\widehat{\beta}$$ is the estimate of the coefficient vector β in mdl.Coefs, and C is the estimated covariance of the coefficient estimates in mdl.CoefCov. When the hypothesis is true, the test statistic F has an F Distribution with r and u degrees of freedom.