Fits hierarchical global polynomial regression model to t-statistics

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Description

Fits hierarchical global polynomial regression model to t-statistics through Newtonian algorithms.

Usage

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tPoly.newton(tstat, x, df, starts, 
        pen.order=1,
        optim.method = c("nlminb", "BFGS", "CG", 
        "L-BFGS-B", "Nelder-Mead", "SANN", "NR"), 
        newton.iter.max = 1500, 
        scale.conv = 0.001, lfdr.conv = 0.001, NPLL.conv = 0.001, 
        debugging = FALSE, plotit = TRUE, ...)

Arguments

tstat

A numeric vector t-statistics

x

A numeric matrix of covariates, with nrow(x) being length(tstat)

df

A numeric scalar or vector of degrees of freedom

starts

An optional numeric vector of starting values. The first element is the r, i.e. log(scale-1). The second parameter is the intercept. The remaining elements are the starting values for the B-spline coefficients (removing the first basis) for each x. When thist argument is not provided, the code starts with a global constant model that is easiest to fit, and then increase the order gradually using the warm starts from lower order fits.

pen.order

A numeric scalar of the order of derivatives of which squared integration will be used as roughness penalty. Note: The final order of the global polynomial is always pen.order-1.

optim.method

A character scalar specifying the method of optimization.

newton.iter.max

A numeric scalar specifying the maximum number of iterations in Newton method.

scale.conv

A small numeric scalar specifying the convergence criterion for the scale parameter.

lfdr.conv

A small numeric scalar specifying the convergence criterion for the local false discovery rates.

NPLL.conv

A small numeric scalar specifying the convergence criretion for the negative penalized log likelhood.

debugging

A logical scalar. If TRUE, then dump.frame will be called whenever error occurs.

plotit

A locgical scalr specifying whether a plot should be generated.

...

Currently not used.

Value

An list of class hisemit:

lfdr:

A numeric vector of local false discovery rates.

model

A list of tstat, df and x, which are the same as arguments

scale.fact:

A list with

  • scale.fact: Scale factor

  • sd.ncp: Equivalent standard deviation of noncentrality parameters

  • r: A reparameterization of scale.fact

  • t.cross: sqrt(df*(s^(2/(df+1))-1)/(1-s^(-2*df/(df+1))))

where s is the scale.fact

pi0:

A numeric vector of mixing proportions for the central t component

tuning:

A list with

  • mean: Mean criterion

  • var: Variance of criterion across observations

  • grp: Cross-validation group membership

  • method: The tuning.method used.

  • final: The minimum mean criterion

spar:

A list with

  • all: All smoothing parameters searched

  • final: The smoothing parameter used

  • final.idx: The index of the final spar

enp:

A list with

  • raw: Raw effective number of parameters

  • logistic: Effective number of parameters after fitting logistic curve as a correction

  • final: The effective nubmer of parameters in the final model

  • good.idx: The index of the selected effective number of parameters

fit:

A list with

  • intercept: The fitted intercept

  • covariate.idx: The index of covariates

  • f.covariate: Each additive smooth function evaluated at the covariates

  • f: Fitted smoothing funciton

  • beta: Estimated regression coefficients

  • H: Expanded design matrix

  • asym.vcov: Asymptotic variance-covariance matrix for estimated parameters

NPLL:

A list with

  • NPLL: Negative penalized log likelihood

  • logLik: Log likelihood

  • penalty: Penalty term

  • saturated.ll: Saturated log likelihood

Author(s)

Long Qu long.qu@wright.edu

References

Long Qu, Dan Nettleton, Jack Dekkers (2012) A hierarchical semiparametric model for incorporating inter-gene relationship information for analysis of genomic data. Biometrics, 68(4):1168-1177

See Also

penLik.EMNewton, plot.hisemit, fitted.hisemit, coef.hisemit, vcov.hisemit, residuals.hisemit, logLik.hisemit, confint.hisemit, plot.hisemit , hisemi-package, pi0-package

Examples

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# See the example for the package.