pi0 (version 1.3-250)

parncpt: Parametric estimation of noncentrality parameter distribution

Description

Assuming normality of noncentrality parameters, the MLE of its standard deviation (and possibly mean also) is estimated from observed t-statistics

Usage

parncpt(tstat, df, zeromean = TRUE, ...)
parncpt.bfgs.0mean(tstat, df, starts, grids, approximation = "int2", ...)
parncpt.bfgs.non0mean(tstat, df, starts, grids, approximation = "int2", ...)
parncpt.momeff(tstat,n1,n2=n1,zeromean,gamma2,lower.df=6.1,upper.df=100,approx=TRUE)

Arguments

tstat

numeric vector of t-statistics

df

numeric vector of degrees of freedom

zeromean

logical; if TRUE, then mean of noncentrality parameters is assumed to be zero and is not estimated.

...

Other arguments to optim

starts

An optional vector of starting values. If missing, a grid search will be performed to get a good starting value.

grids

A list of three components (lower, upper, ngrid) defining the grids to be searched in find a good starting value. Each component is a numeric vector of the same length as the number of parameters. lower

approximation

Methods of approximating the noncentral t-density. int2 is exact for integer df, but interpolate to fractional df. 'laplace' is the laplacian approximation; 'saddlepoint' is the saddlepoint approximation; 'none' computes the (sort of) exac

n1

Treatment 1 sample size

n2

Treatment 2 sample size

gamma2

Gamma square parameter, i.e., variance of effect sizes.

lower.df

lower bound of degrees of freedom, in case of n1 is missing

upper.df

upper bound of degrees of freedom, in case of n1 is missing

approx

logical, indicating if no exact solutions are available, whether approx. solutions are returned.

Value

• a list with class attribute being c('parncpt', 'ncpest').
• pi0
  proportion of true nulls
• mu.ncp
  mean of ncp
• sd.ncp
  SD of ncp
• data
  a list of tstat and df
• logLik
  an object of class logLik. Call logLik.ncpest to extract. Similarly, AIC is callable.
• enp
  the (effective) number of parameters in the model
• par
  estimated parameters. Call coef.ncpest to extract.
• obj
  the negative loglikelihood function that is minimized
• gradiant
  analytic gradiant at the estimate
• hessian
  numeric hessian at the estimate

Details

parncpt calls either parncpt.bfgs.0mean or parncpt.bfgs.non0mean, depending whether zeromean is TRUE or FALSE. Both parncpt.bfgs.0mean and parncpt.bfgs.non0mean use the 'L-BFGS-B' algorithm by calling optim. All gradiants are analytical, but the Hessian is only numerical approximation. The first parmater is always pi0, i.e., the proportion of true null hypotheses; the last parameter is always the standard deviation of noncentrality parameters; for parncpt.bfgs.non0mean the middle parameter is the mean of noncentrality parameters, whereas for parncpt.bfgs.0mean the mean is set to 0 a priori.

References

Qu L, Nettleton D, Dekkers JCM. (2012) Improved Estimation of the Noncentrality Parameter Distribution from a Large Number of $t$-statistics, with Applications to False Discovery Rate Estimation in Microarray Data Analysis. Biometrics (in press).

See Also

sparncpt, nparncpt, fitted.parncpt, plot.parncpt, summary.parncpt, coef.ncpest, logLik.ncpest, vcov.ncpest, AIC, dncp

Examples

data(simulatedTstat)
(npfit=nparncpt(tstat=simulatedTstat, df=8)); 
(pfit=parncpt(tstat=simulatedTstat, df=8, zeromean=FALSE)); plot(pfit)
(pfit0=parncpt(tstat=simulatedTstat, df=8, zeromean=TRUE)); plot(pfit0)
(spfit=sparncpt(npfit,pfit)); plot(spfit)