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Are Scaled Estimates Unitless

vince_faller

Maybe I'm just having a stroke. Was hoping for someone to confirm/deny this to me.

Accepted answers

Mark_Bailey

The standardization is such that the numerator and the denominator have the same units, so the units 'cancel' and the result is 'unitless' or 'scale invariant.'

That is a YES.

All comments

Byron_JMP

https://community.jmp.com/t5/Discussions/What-s-the-difference-between-scaled-estimates-and-standardized/td-p/1176

vince_faller

Saw that, still asked. So that's a yes right?

Mark_Bailey

The standardization is such that the numerator and the denominator have the same units, so the units 'cancel' and the result is 'unitless' or 'scale invariant.'

That is a YES.

vince_faller

Thanks @Mark_Bailey and @Byron_JMP

I have someone that won't believe me. Y'all have any way that I can prove this to them?

To give a little context they're trying to divide scaled estimates by RMSE to create a pseudo "Z-score".

*Edit* did this and made them amtch, so doesn't that mean that each scaled estimate is in the units of Y (height in this case)?

Names default to here( 1 );
dt = open("$SAMPLE_DATA\Big Class.jmp");

dt << New Column("Scaled height", 
	<<Formula((:height-ColMean(:height))/((:ColMax(:height)-ColMin(:weight))/2))
);

dt << New Column("Scaled weight", 
	<<Formula((:weight-ColMean(:weight))/((:ColMax(:weight)-ColMin(:weight))/2))
);

dt << Fit Model(
	Y( :height ),
	Effects( :Scaled weight ),
	Personality( "Standard Least Squares" ),
	Emphasis( "Effect Leverage" ),
	Run()
);

dt << Fit Model(
	Y( :height ),
	Effects( :weight ),
	Personality( "Standard Least Squares" ),
	Emphasis( "Effect Leverage" ),
	Run(Scaled Estimates(1))
);