
BOX COX HOMOSCEDASTICITY PLOTName:
A BoxCox homoscedasticity plot is a graphical technique for determining the BoxCox transformation that yields the most constant variance of one variable relative to the values of a second variable. The BoxCox family is essentially the powertransformation family (adjusted to include log transformations). The form of the family is:
There are various methods for measuring constant variance. The particular method Dataplot uses is to divide the first variable into groups with the same value for the second value. For a given value of lambda, the standard deviation is computed for each group. The statistic used is the ratio of the minimum standard deviation to the maximum standard deviation (this ratio will always be between 0 and 1). The plot then consists of this statistic on the vertical axis versus the lambda parameter on the horizontal axis. The lambda corresponding to the highest ratio is the appropriate transformation to use to provide the most constant variance. This command only applies if there is replication in the second response variable.
<SUBSET/EXCEPT/FOR qualification> where <y> is the first response variable; <x> is the second response variable; and where the <SUBSET/EXCEPT/FOR qualification> is optional.
<SUBSET/EXCEPT/FOR qualification> where <y> is the first response variable; <x> is the second response variable; <tag1> is a groupid variable; and where the <SUBSET/EXCEPT/FOR qualification> is optional. A BoxCox homoscedasticity plot will be generated for each distinct value of the groupid variable. These plots will be overlaid on the same plot.
<SUBSET/EXCEPT/FOR qualification> where <y> is the first response variable; <x> is the second response variable; <tag1> is a groupid variable; <tag2> is a groupid variable; and where the <SUBSET/EXCEPT/FOR qualification> is optional. The two groupid variables are crosstabulated and a BoxCox homoscedasticity plot will be generated for each distinct combination of values for the groupid variables. These plots will be overlaid on the same plot.
REPLICATED BOX COX HOMOSCED PLOT Y X TAG
2010/5: Support for REPLICATION option SKIP 25 READ NELSON.DAT Y X1 X2 . MULTIPLOT CORNER COORDINATES 0 0 100 100 MULTIPLOT SCALE FACTOR 2 MULTIPLOT 2 2 FIT Y X2 LINE SOLID BLANK CHARACTER BLANK X TITLE LINEAR FIT OF RAW DATA PLOT PRED Y VS X2 . TITLE BOXCOX HOMOSCEDASTICITY PLOT X1LABEL LAMBDA Y1LABEL CORRELATION COEFFICIENT BOXCOX HOMOSCEDASTICTY PLOT Y X2 . LET YTEMP = MAXIMUM YPLOT RETAIN XPLOT SUBSET YPLOT = YTEMP LET LAMBDA = XPLOT(1) LET Y2 = (Y**LAMBDA  1)/LAMBDA FIT Y2 X2 TITLE LINEAR FIT OF TRANSFORMED DATA X1LABEL ; Y1LABEL PLOT PRED Y2 VS X2 END OF MULTIPLOT
 
Date created: 11/30/2010 Last updated: 12/04/2023 Please email comments on this WWW page to alan.heckert@nist.gov. 