# Solved – 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.

Contents

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.