R vs SAS ANCOVA

Summary

Goal

The goal of this comparison is to evaluate whether ANCOVA produces equivalent results in R and SAS using the same dataset and model specification. Results from the R stats::lm() function, the sasLM::GLM() function, and SAS PROC GLM are compared for sums of squares and least-squares means.

Scope

Methodologies

Analysis of covariance (ANCOVA)
Type I sums of squares
Type III sums of squares
Least-squares means

Technical implementations

SAS: PROC GLM
R: stats::lm()
R: sasLM::GLM() with EMEANS=TRUE

Prerequisites

R packages

library(stats)   # lm()
library(sasLM)   # GLM()
library(tibble) # tibble()
library(tidyverse) # tidyverse functions

Data

The same dataset is used for the R and SAS analyses.

df_sas <- tibble( 
  drug = factor(c( "A", "A", "A", "A", "A", "A", "A", "A", "A", "A", 
                   "D", "D", "D", "D", "D", "D", "D", "D", "D", "D", 
                   "F", "F", "F", "F", "F", "F", "F", "F", "F", "F" 
                   )), 
  pre = c( 
    11, 8, 5, 14, 19, 6, 10, 6, 11, 3, 
    6, 6, 7, 8, 18, 8, 19, 8, 5, 15, 
    16, 13, 11, 9, 21, 16, 12, 12, 7, 12 
    ), 
  post = c( 6, 0, 2, 8, 11, 4, 13, 1, 8, 0, 
            0, 2, 3, 1, 18, 4, 14, 9, 1, 9, 
            13, 10, 18, 5, 23, 12, 5, 16, 1, 20 
            ) 
  )

SAS:

data df_sas;
    input drug $ pre post;
    datalines;
A 11 6
A 8 0
A 5 2
A 14 8
A 19 11
A 6 4
A 10 13
A 6 1
A 11 8
A 3 0
D 6 0
D 6 2
D 7 3
D 8 1
D 18 18
D 8 4
D 19 14
D 8 9
D 5 1
D 15 9
F 16 13
F 13 10
F 11 18
F 9 5
F 21 23
F 16 12
F 12 5
F 12 16
F 7 1
F 12 20
;
run;

The ANCOVA model includes drug as the categorical treatment variable and pre as the continuous covariate.

The general ANCOVA model is:

\[ \text{post} = \text{drug} + \text{pre} \]

where:

post is the response variable
drug is the treatment variable
pre is the continuous covariate.

ANCOVA Comparison

The following table shows the types of One Sample t-test analysis, the capabilities of each language, and whether or not the results from each language match.

Analysis	Supported in R	Supported in SAS	Results Match	Notes
ANCOVA using general linear model and lsmeans	Yes	Yes	Yes	`GLM()` function from sasLM with `EMEANS=TRUE` is the easiest to use and matches SAS
Type I Sum of Squares	Yes	Yes	Yes	Sequential sums of squares
Type II Sum of Squares	Yes	Yes	Yes	`sasLM::GLM()` provides SAS-style output
Type III Sum of Squares	Yes	Yes	Yes	`sasLM::GLM()` with `EMEANS=TRUE` matches SAS `LSMEANS`

Comparison Results

Here is a table of comparison values between lm() from the stats package, GLM() from the sasLM package, and SAS PROC GLM:

Statistic	lm()	GLM()	PROC GLM	Match
Type I, Sum sq, drug	293.6000	293.6000	293.6000	Yes
Type I, Sum sq, pre	577.897	577.8974	577.8974	Yes
Type III, Sum sq, drug	68.554	68.55371	68.55371	Yes
Type III, Sum sq, pre	577.897	577.89740	577.89740	Yes
LSmean drugA	6.71	6.714963	6.714963	Yes
LSmean drugD	6.82	6.823935	6.823935	Yes
LSmean drugF	10.16	10.161102	10.161102	Yes

Summary and Recommendation

The R ANCOVA analysis is comparable to SAS. Comparison between SAS and R show identical results for the datasets tried. The sasLM package GLM() function is very similar to SAS in the output produced. You can also match SAS using the stats package with the lm() function and various modification functions. See the R page for further information.

References

R lm() documentation: https://www.rdocumentation.org/packages/stats/versions/3.6.2/topics/lm

R GLM() documentation: https://cran.r-project.org/web/packages/sasLM/sasLM.pdf

SAS PROC GLM documentation: https://documentation.sas.com/doc/en/statug/15.2/statug_glm_syntax01.htm