proc for log-ratio transformation

[SASdevAnneMarie]

Hello Experts,

I would like to apply a log-ratio transformation to compositional variables before performing PCA analysis. I'm wondering if there is a dedicated proc in sas for this?

Thank you!

[sbxkoenk]

Compositional data are nonnegative multivariate data where the absolute values of the data carry only relative meaning.
Compositional data are often data with a constant-sum constraint: that is, ...

• the values for each multivariate sample are either observed as summing to a constant (usually 1 or 100%)
• or are expressed as values relative to a total that is irrelevant to the research objective (f.e. the composition of a chemical sample).

Since compositional data lies in a constrained simplex (sum to 1 or 100), it cannot be analyzed directly with standard linear models. Use the SAS DATA step to create transformed variables, such as:

• Additive Log-Ratio (ALR)
• Centered Log-Ratio (CLR)
• Isometric Log-Ratio (ILR)

Those ratios may be the by-product of some procedure (I am not aware of this), but it is actually easy to calculate them in a data step.

If you encounter difficulties in the calculation, please let us know... we will try to help you further with sample code.

BR, Koen

[sbxkoenk]

By the way,

if you can reduce the dimensionality to three using PCA,

you can then use a ternary plot (trilinear plots / triplot) to visualize.

BR, Koen

[sbxkoenk · Accepted solution]

Here's an example of the centered log-ratio (CLR) transformation.

Remark the CLR requires positive, non-zero values in the composition.

/* 1. Define sample data (5 parts: aa, bb, cc, dd, ee) */
data raw_data0;
    input id aa bb cc dd ee;

    datalines;
1 0.1 0.3 0.3 0.1 0.2
2 0.1 0.1 0.4 0.2 0.2
3 0.2 0.3 0.2 0.1 0.2
;
run;

data raw_data1;
 set raw_data0;
 array parts[5]     aa bb cc dd ee; /* List all components */
 mygeomean=geomean(of parts[*]);
 mysum    =    sum(of parts[*]);
run;

data raw_data2;
 set raw_data1;
 array parts[5]     aa bb cc dd ee; /* List all components */
 array clr_parts[5] 
clr_aa clr_bb clr_cc clr_dd clr_ee; 
 do i=1 to dim(parts);
  clr_parts[i] = log(parts[i]/mygeomean);
              /* log = ln (natural log with base e) */
 end;
 drop i;
run;
/* end of program */

BR, Koen

[SASdevAnneMarie]

Thank you, Koen !