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Variable Transformations

Variance Stabilizing Transformations

Figure 32.13 shows the transformations that are available when you select Variance stabilizing from the Family list. Variance stabilizing transformations are often used to transform a variable whose variance depends on the value of the variable. For example, the variability of a variable might increase as increases. Equations for these transformations are given in Table 32.3.

Figure 32.13 Variance Stabilizing Transformations
Variance Stabilizing Transformations

Table 32.3 Description of Variance Stabilizing Transformations
 

Default

Name of

 

Transformation

Parameter

New Variable

Equation

log(Y+a)

Log_Y

log10(Y+a)

Log10_Y

sqrt(Y+a)

Sqrt_Y

1 / Y

 

Inv_Y

arcsinh(Y)

 

Arcsinh_Y

generalized log(Y; a)

GLog_Y

log-linear hybrid(Y; a)

LogLin_Y

See text.

The log-linear hybrid transformation is defined for as follows:

     

The function is linear for , logarithmic for , and continuously differentiable.

The generalized log and the log-linear hybrid transformations were introduced in the context of gene-expression microarray data by Rocke and Durbin (2003).

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