# tPoly.newton: Fits hierarchical global polynomial regression model to... In hisemi: Hierarchical Semiparametric Regression of Test Statistics

## Description

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

## Usage

 ```1 2 3 4 5 6 7``` ```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 [email protected]

## 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

`penLik.EMNewton`, `plot.hisemit`, `fitted.hisemit`, `coef.hisemit`, `vcov.hisemit`, `residuals.hisemit`, `logLik.hisemit`, `confint.hisemit`, `plot.hisemit` , `hisemi-package`, `pi0-package`
 `1` ```# See the example for the package. ```