# simplesimint: Simultaneous confidence intervals from raw estimates In BSagri: Statistical methods for safety assessment in agricultural field trials

## 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``` ```simplesimint(coef, vcov, cmat, df = NULL, conf.level = 0.95, alternative = c("two.sided", "less", "greater")) ```

## Arguments

 `coef` a single numeric vector, specifying the point estimates of the parameters of interest `vcov` the variance-covariance matrix corresponding to `coef`, should be of dimension P-times-P, when `coef` is of P `cmat` the contrasts matrix specifying the comparisons of interest with respect to `coef`, should have P columns, when `coef` is of length p `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, `"two.sided"` for intervals, `"less"` for upper limits, and `"greater"` for lower limits

## 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 `?coef` and `?vcov` for extracting of parameter vectors and corresponding variance covariance matrices from various model fits.
 ``` 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 ```