# glht-methods

##### Methods for General Linear Hypotheses

Simultaneous tests and confidence intervals for general linear hypotheses.

##### Usage

```
## S3 method for class 'glht':
summary(object, test = adjusted(), ...)
## S3 method for class 'glht':
confint(object, parm, level = 0.95, ...)
## S3 method for class 'glht':
coef(object, rhs = FALSE, ...)
## S3 method for class 'glht':
vcov(object, ...)
univariate()
adjusted(type = c("free", "Shaffer", "Westfall", p.adjust.methods),
...)
Ftest()
Chisqtest()
```

##### Arguments

- object
- an object of class
`glht`

. - test
- a function for computing p values.
- parm
- additional parameters, currently ignored.
- level
- the confidence level required.
- rhs
- logical, indicating whether the linear function
$K \hat{\beta}$ or the right hand side
$m$ (
`rhs = TRUE`

) of the linear hypothesis should be returned. - type
- the multiplicity adjustment (
`adjusted`

) to be applied. See below and`p.adjust`

. - ...
- additional arguments, such as
`maxpts`

,`abseps`

or`releps`

to`pmvnorm`

in`adjusted`

or

##### Details

The methods for general linear hypotheses as described by objects returned
by `glht`

can be used to actually test the global
null hypothesis, each of the partial hypotheses and for
simultaneous confidence intervals for the linear function $K `coef`

and `vcov`

methods compute the linear
function $K

The `test`

argument to `summary`

takes a function specifying
the type of test to be applied. Classical Chisq (Wald test) or F statistics
for testing the global hypothesis $H_0$ are implemented in functions
`Chisqtest`

and `Ftest`

. Several approaches to multiplicity adjusted p
values for each of the linear hypotheses are implemented
in function `adjusted`

. The `type`

argument to `adjusted`

specifies the method to be applied:
`"free"`

implements adjusted p values based on the joint
normal or $t$ distribution of the linear function, and
`"Shaffer"`

and `"Westfall"`

implement logically constraint
multiplicity adjustments (Shaffer, 1986; Westfall, 1997).
In addition, all adjustment methods
implemented in `p.adjust`

are available as well.

Simultaneous confidence intervals for linear functions can be computed
using method `confint`

. Univariate confidence intervals
can be computed by specifying the additional argument `adjusted = FALSE`

to `confint`

.

All simultaneous inference procedures implemented here control
the family-wise error rate (FWER). Multivariate
normal and $t$ distributions, the latter one only for models of
class `lm`

, are evaluated using the procedures
implemented in package `mvtnorm`

.

`summary`

computes (adjusted) p values for general linear hypotheses,
`confint`

computes (adjusted) confidence intervals.
`coef`

returns estimates of the linear function $K `vcov`

its covariance.*Journal of the American Statistical Association*,

**81**, 826--831.

Peter H. Westfall (1997),
Multiple testing of general contrasts using logical constraints
and correlations. *Journal of the American Statistical Association*,
**92**, 299--306.

### set up all-pair comparisons for factor `tension' wht <- glht(amod, linfct = mcp(tension = "Tukey"))

### 95% simultaneous confidence intervals plot(print(confint(wht)))

### the same (for balanced designs only) TukeyHSD(amod, "tension")

### corresponding adjusted p values summary(wht)

### confidence bands for a simple linear model, `cars' data plot(cars, xlab = "Speed (mph)", ylab = "Stopping distance (ft)", las = 1)

### fit linear model and add regression line to plot lmod <- lm(dist ~ speed, data = cars) abline(lmod)

### a grid of speeds speeds <- seq(from = min(cars$speed), to = max(cars$speed), length = 10)

### linear hypotheses: 10 selected points on the regression line != 0 K <- cbind(1, speeds)

### set up linear hypotheses cht <- glht(lmod, linfct = K)

### confidence intervals, i.e., confidence bands, and add them plot cci <- confint(cht) lines(speeds, cci$confint[,"lwr"], col = "blue") lines(speeds, cci$confint[,"upr"], col = "blue")

### simultaneous p values for parameters in a Cox model if (require("survival") && require("MASS")) { data("leuk", package = "MASS") leuk.cox <- coxph(Surv(time) ~ ag + log(wbc), data = leuk)

### set up linear hypotheses lht <- glht(leuk.cox, linfct = diag(length(coef(leuk.cox))))

### adjusted p values print(summary(lht)) }

*Documentation reproduced from package multcomp, version 0.991-1, License: GPL*