MCPower: Function _MCPower_

In ltable: Easy to Make (Lazy) Tables

Function MCPower

Description

Performs power analyses for constructed tabulated data based on based on Gibbs sampler with NB2 posterior marginal distribution for counts

Usage

MCPower(formula, data, offset, contrasts=NULL, XLB=-100, XUB=100, a=0.1, b=0.1,
scale_min=1, scale_max=5, effect, p_alpha=0.05, draw=10000, burnin=3000)

Arguments

formula	a symbolic description of the model to be fit.
data	name of the data set; object of data.frame class
offset	variable in the data set to be used as offset.
contrasts	serves to choose types of contrasts to study effects of factors, same with glm{stats}), orthogonal polynomials by default
XLB	the vector of smallest possible values of regression effects betas; can be number if pertains to all betas.
XUB	the vector of largest possible values of regression effects betas; can be number if pertains to all betas.
a	the value of shape parameter of gamma distributed inverce dispersion parameter (phi), i.e., phi~Ga(a,b), so that mean(phi)=a/b and var(phi)=a/b^2
b	the value of rate (1/scale) parameter of gamma distributed inverce dispersion parameter (phi), i.e., phi~Ga(a,b), so that mean(phi)=a/b and var(phi)=a/b^2
scale_min	the smallest number of sample size scale range, 1 signifies the given data sample size (observed total counts).
scale_max	the max number of sample size considered in power analysis. 5 by default means 5 times augmented observed counts
effect	quoted effect tested by hypothesis; it should be one from the model formula, of second or higher order, introduced by * delimiter, i.e., "y*x", "y1*y2*x1*x2", etc.
p_alpha	serves to signify Z to check simulated z-scores against in power analysis, 0.05 by default
draw	indicates requested number of samples
burnin	indicates requested number of initial samples to discard

Details

• Performs power analysis in a given range of sample sizes (scale_min - scale_max).

• Creates object of S4 class PowerClass with accessing methods

Value

returns object of S4 class PowerClass

Note

The inspected sample size range defined by scale_min - scale_max automatically is divided into 11 consecutive values investigated by function. Given the results one can change sample size range, for example to scrutinize some particular interval to ensure power and p-value.
Function provides better conditioned variance matrix estimates against function stats::glm by the auspicity of NB2 dispersion parameter, coping with overdispersion in counts distribution, which is particular important for high order effects and power analysis. Particularly suggestive is to check the model fit first. Jacobian reciprocal condition number near zero indicates solution instability. If chisq/n >> 1, the error estimates obtained from the covariance matrix will be too small and should be multiplied by square root of chisq/dof. Poor fit will result from the use of an inappropriate model and jeopardizes the validity of power analysis.
The drawback is failure to tackle singularity of order 5 or higher of Hessian matrix. Code returns error "Sorry, can't proceed with singular Hessian matrix." On such rare occasions please use ltable v.2.0.1 available for Unix (MacOS) machines. Function PowerPoisson performs log-linear and power analyses based on Levenberg-Marquardt algorithm which is distribution-free (so, Poisson in name of function is misleading). The only inconvenience is that GSL: GNU Scientific Library has to be installed first.
See-saw dynamic of either power or test curves is caused by Jacobian singularity, that indicates solution instability.
Flat profiles given low test or power values are indicative for insignificance of tested effect.
Flat profiles with z-values above 2 or power values that exceed 0.8 are indicative for significance of tested effect. On such occasions decrease both scale parameters to inspect smaller samples.

Author(s)

Ocheredko Oleksandr [e-mail]

See Also

glm

Examples

require(ltable)
data(tdata, package="ltable")
## For better illustration You should increase draw and burnin pars
pres1<-MCPower(Counts~smoker +contraceptive +tromb +contraceptive*tromb,
scale_min=0.5, scale_max=1.5, effect="contraceptive*tromb", data=tdata, 
draw=1000, burnin=300)
print(pres1, "model")
print(pres1)
plot(pres1, stencil=3)

ltable documentation built on Aug. 17, 2023, 1:06 a.m.