This function either centers and scales a continuous variable and provides options for binary variables, or returns an untransformed variable from a centered and scaled variable.

`CenterScale(x, Binary="none", Inverse=FALSE, mu, sigma, Range, Min)`

x

This is a vector to be centered and scaled, or to be
untransformed if `Inverse=TRUE`

.

Binary

This argument indicates how binary variables will be
treated, and defaults to `"none"`

, which keeps the original
scale, or transforms the variable to the 0-1 range, if not already
there. With `"center"`

, it will center the binary variable by
subtracting the mean. With `"center0"`

, it centers the binary
variable at zero, recoding a 0 to -0.5, and a 1 to 0.5. Finally,
`"centerscale"`

will center and scale the binary variable,
subtracting the mean and dividing by two standard deviations.

Inverse

Logical. If `TRUE`

, then a centered and scaled
variable `x`

will be transformed to its original, un-centered
and un-scaled state. This defaults to `FALSE`

.

mu, sigma, Range, Min

These arguments are required only when
`Inverse=TRUE`

, where `mu`

is the mean, `sigma`

is
the standard deviation, `Range`

is the range, and `Min`

is
the minimum of the original `x`

. `Range`

and `Min`

are used only when `Binary="none"`

or `Binary="center0"`

.

The `CenterScale`

function returns a centered and scaled vector,
or the untransformed vector.

Gelman (2008) recommends centering and scaling continuous predictors
to facilitate MCMC convergence and enable comparisons between
coefficients of centered and scaled continuous predictors with
coefficients of untransformed binary predictors. A continuous
predictor is centered and scaled as follows: ```
x.cs <- (x -
mean(x)) / (2*sd(x))
```

. This is an improvement over the usual
practice of standardizing predictors, which is ```
x.z <- (x -
mean(x)) / sd(x)
```

, where coefficients cannot be validly compared
between binary and continuous predictors.

In MCMC, such as in `LaplacesDemon`

, a centered and
scaled predictor often results in a higher effective sample size
(`ESS`

), and therefore the chain mixes better. Centering
and scaling is a method of re-parameterization to improve mixing.

Griffin and Brown (2013) also assert that the user may not want to scale predictors that are measured on the same scale, since scaling in this case may increase noisy, low signals. In this case, centering (without scaling) is recommended. To center a predictor, subtract its mean.

Gelman, A. (2008). "Scaling Regression Inputs by Dividing by Two Standard
Devations". *Statistics in Medicine*, 27, p. 2865--2873.

Griffin, J.E. and Brown, P.J. (2013) "Some Priors for Sparse
Regression Modelling". *Bayesian Analysis*, 8(3), p. 691--702.

`ESS`

,
`IterativeQuadrature`

,
`LaplaceApproximation`

,
`LaplacesDemon`

, and
`PMC`

.

```
# NOT RUN {
### See the LaplacesDemon function for an example in use.
library(LaplacesDemon)
x <- rnorm(100,10,1)
x.cs <- CenterScale(x)
x.orig <- CenterScale(x.cs, Inverse=TRUE, mu=mean(x), sigma=sd(x))
# }
```

Run the code above in your browser using DataLab