# Simultaneous confidence intervals from raw estimates

### Description

Calculates simultaneous confidence intervals for multiple contrasts based on a parameter vector, its variance-covariance matrix and (optionally) the degrees of freedom, using quantiles of the multivar

### Usage

1 2 |

### Arguments

`coef` |
a single numeric vector, specifying the point estimates of the parameters of interest |

`vcov` |
the variance-covariance matrix corresponding to |

`cmat` |
the contrasts matrix specifying the comparisons of interest with respect to |

`df` |
optional, the degree of freedom for the multivariate t-distribution; if specified, quantiles from the multivariate t-distribution are used for confidence interval estimation, if not specified (default), quantiles of the multivariate normal distribution are used |

`conf.level` |
a single numeric value between 0.5 and 1.0; the simultaneous confidence level |

`alternative` |
a single character string, |

### Details

Implements the methods formerly available in package multcomp, function `csimint`

.
Input values are a vector of parameter estimates *mu* of length *P*,
a corresponding estimate for its variance-covariance matrix *Sigma* (P times P), and a
contrast matrix *C* of dimension *M times P*. The contrasts *L = C * mu* are computed,
the variance-covariance matrix (being a function of *C* and *Sigma*) and the corresponding correlation matrix *R* are computed.
Finally, confidence intervals for *L* are computed: if df is given, quantiles of an M-dimensional t distribution with correlation matrix R are used,
otherwise quantiles of an M-dimensional standard normal distribution with correlation matrix R are used.

### Value

An object of class "simplesimint"

`estimate ` |
the estimates of the contrasts |

`lower ` |
the lower confidence limits |

`upper ` |
the upper confidence limits |

`cmat` |
the contrast matrix, as input |

`alternative` |
a character string, as input |

`conf.level` |
a numeric value, as input |

`quantile` |
a numeric value, the quantile used for confidence interval estimation |

`df` |
a numeric value or NULL, as input |

`stderr` |
the standard error of the contrasts |

`vcovC` |
the variance covariance matrix of the contrasts |

### Note

This is a testversion and has not been checked extensively.

### Author(s)

Frank Schaarschmidt

### See Also

See `?coef`

and `?vcov`

for extracting of parameter vectors and corresponding variance covariance matrices from various model fits.

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 | ```
# For the simple case of Gaussian response
# variables with homoscedastic variance,
# see the following example
library(mratios)
data(angina)
boxplot(response ~ dose, data=angina)
# Fit a cell means model,
fit<-lm(response ~ 0+dose, data=angina)
# extract cell means, the corresponding
# variance-covariance matrix and the
# residual degree of freedom,
cofi<-coef(fit)
vcofi<-vcov(fit)
dofi<-fit$df.residual
# define an appropriate contrast matrix,
# here, comparisons to control
n<-unlist(lapply(split(angina$response, f=angina$dose), length))
names(n)<-names(cofi)
cmat<-contrMat(n=n, type="Dunnett")
cmat
#
test<-simplesimint(coef=cofi, vcov=vcofi, df=dofi, cmat=cmat, alternative="greater" )
test
summary(test)
plotCI(test)
### Note, that the same result can be achieved much more conveniently
### using confint.glht in package multcomp
``` |