# R lm simultaneous parameter tests

Using R, I'd like to test whether multiple parameters in a regression model are equal to specific values (by default, are multiple parameters equal to 0).

For example, in this regression model:

score ~ beta0 + beta1*i1 + beta2*i2 + beta3*age + beta4*i1*age + beta5*i2*age

I want to test H0: (beta2 = 0) and (beta5 = 0)

SAS can do this in PROC REG using the TEST statement.

SAS Program editor contents:

proc reg data=tolerate;
model score=i1 i2 age i1age i2age;
test i2=0, i2age=0;    * do assc prof have same reg line as asst? ;
run;


SAS Output window contents:

       Test 1 Results for Dependent Variable score
Mean
Source             DF         Square    F Value    Pr > F
Numerator           2        0.15581       0.38    0.6859
Denominator        24        0.40678


Here's code in R that starts the analysis:

# data description: http://statacumen.com/teach/ADA2/ADA2_HW_07_S13.pdf
tolerate <- read.csv("http://statacumen.com/teach/ADA2/ADA2_HW_07_tolerate.csv")
tolerate$rank <- factor(tolerate$rank)
tolerate$rank <- relevel(tolerate$rank, "3")
str(tolerate)

tolerate.manual <- data.frame(score = tolerate$score , i1 = (tolerate$rank==1)
, i2 = (tolerate$rank==2) , age = tolerate$age
, i1age = tolerate$age * (tolerate$rank==1)
, i2age = tolerate$age * (tolerate$rank==2)
)
lm.man <- lm(score ~ i1 + i2 + age + i1age + i2age, data = tolerate.manual)
summary(lm.man)


I have been unable to find a solution using library multcomp, contrast, or C(). Ideally, I could do this without creating separate terms in the model, but directly from this lm() statement:

lm.s.a.r.ar <- lm(score ~ age*rank, data = tolerate)


This gets close using a Wald test, but I'm looking for the same F-test SAS uses.

summary(lm.s.a.r.ar)
library(aod) # for wald.test()
coef.test.values <- rep(0, length(coef(lm.s.a.r.ar))) # typically, this will be all 0s
wald.test(b = coef(lm.s.a.r.ar) - coef.test.values
, Sigma = vcov(lm.s.a.r.ar)
, Terms = c(4,6))

Wald test:
----------
Chi-squared test:
X2 = 0.77, df = 2, P(> X2) = 0.68


Thanks for considering this question.

## 2 Answers

Do a full and reduced test by fitting a model with all the parameters, then another model with the reduced model (leave out the terms that you want to test with 0). Then do anova(fit1,fit2) to compute the F test.

If you want to test for values other than 0 then use the offset function in the reduced formula.

What Greg said... with exact code following from OP's example:

lm.base <- update(lm.man, ~ . - i2 - i2age)
# or if you prefer to fully specify the formula rather than using update()...
# lm.base <- lm(score ~ i1 + age + i1age, data = tolerate.manual)
anova(lm.base,lm.man)


P.S.

If you tell wald.test() the denominator df (this is stored in lm under $df.residual), it will give you an F statistic. This example follows again from OP's, but is wrapped in a print statement so we can confirm that our p-value matches what has been given above: print(wald.test(b = coef(lm.s.a.r.ar) - coef.test.values , Sigma = vcov(lm.s.a.r.ar) , Terms = c(4,6),df=lm.s.a.r.ar$df.residual),digits=4)