R help - Jul 2003 - Comparing two regression slopes

Hello,
I've written a simple (although probably overly roundabout) function to 
test whether two regression slope coefficients from two linear models on 
independent data sets are significantly different. I'm a bit concerned, 
because when I test it on simulated data with different sample sizes and 
variances, the function seems to be extremely sensitive both of these. I am 
wondering if I've missed something in my function? I'd be very grateful
for
any tips.


Thanks!

Martin


TwoSlope <-function(lm1, lm2) {

## lm1 and lm2 are two linear models on independent data sets

coef1 <-summary(lm1)$coef
coef2 <-summary(lm2)$coef

sigma <-(sum(lm1$residuals^2)+sum(lm2$residuals^2))/(lm1$df.residual + 
lm2$df.residual-4)
SSall <-sum(lm1$model[,2]^2) + sum(lm2$model[,2]^2)
SSprod <-sum(lm1$model[,2]^2) * sum(lm2$model[,2]^2)

F.val <-(as.numeric(coefficients(lm1)[2]) - as.numeric(coefficients(lm2) 
[2]))^2/((SSall/SSprod)*sigma)

p.val <-1-pf(F.val, 1, (lm1$df.residual + lm2$df.residual-4))

cat("\n\nTest for equality between two regression slopes\n\n")
cat("\nCoefficients model 1:\n\n")
print(coef1)

cat("\nCoefficients model 2:\n\n")
print(coef2)

cat("\nF-value on 1 and", lm1$df.residual + lm2$df.residual-4,
"degrees of
freedom:" ,F.val, "\n")
cat("p =", ifelse(p.val>=0.0001, p.val, "< 0.0001"),
"\n")

}

I'm afraid of your manual ANOVA.  It may be correct, but it won't easily
generalize.  Instead, how about the following:

 > df1 <- data.frame(x=1:3, y=1:3+rnorm(3))
 > df2 <- data.frame(x=1:3, y=1:3+rnorm(3))
 >
 > fit1 <- lm(y~x, df1)
 > s1 <- summary(fit1)$coefficients
 > fit2 <- lm(y~x, df2)
 > s2 <- summary(fit2)$coefficients
 >
 > db <- (s2[2,1]-s1[2,1])
 > sd <- sqrt(s2[2,2]^2+s1[2,2]^2)
 > df <- (fit1$df.residual+fit2$df.residual)
 > td <- db/sd
 > 2*pt(-abs(td), df)
[1] 0.9510506

The function "attributes" helped me figure this out.

hope this helps.  spencer graves

Martin Biuw wrote:
> Hello,
> I've written a simple (although probably overly roundabout) function to
> test whether two regression slope coefficients from two linear models on 
> independent data sets are significantly different. I'm a bit concerned,
> because when I test it on simulated data with different sample sizes and 
> variances, the function seems to be extremely sensitive both of these. I 
> am wondering if I've missed something in my function? I'd be very 
> grateful for any tips.
> 
> 
> Thanks!
> 
> Martin
> 
> 
> TwoSlope <-function(lm1, lm2) {
> 
> ## lm1 and lm2 are two linear models on independent data sets
> 
> coef1 <-summary(lm1)$coef
> coef2 <-summary(lm2)$coef
> 
> sigma <-(sum(lm1$residuals^2)+sum(lm2$residuals^2))/(lm1$df.residual + 
> lm2$df.residual-4)
> SSall <-sum(lm1$model[,2]^2) + sum(lm2$model[,2]^2)
> SSprod <-sum(lm1$model[,2]^2) * sum(lm2$model[,2]^2)
> 
> F.val <-(as.numeric(coefficients(lm1)[2]) - as.numeric(coefficients(lm2)
> [2]))^2/((SSall/SSprod)*sigma)
> 
> p.val <-1-pf(F.val, 1, (lm1$df.residual + lm2$df.residual-4))
> 
> cat("\n\nTest for equality between two regression slopes\n\n")
> cat("\nCoefficients model 1:\n\n")
> print(coef1)
> 
> cat("\nCoefficients model 2:\n\n")
> print(coef2)
> 
> cat("\nF-value on 1 and", lm1$df.residual + lm2$df.residual-4,
"degrees
> of freedom:" ,F.val, "\n")
> cat("p =", ifelse(p.val>=0.0001, p.val, "<
0.0001"), "\n")
> 
> }
> 
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://www.stat.math.ethz.ch/mailman/listinfo/r-help

Sorry, I sent this without a subject at first......

Hello,
Is there a simple function that calculates standard errors and confidence 
limits of response values (Y) in a linear model, where parameter estimates 
have been arrived at by bootstrapping (e.g. according to the first example 
in Angelo Canty's prsentation of the "boot" package in R-News, Dec
2002)?
Or does anyone have any ideas as to the simplest way to write such a 
function, incorporating enough flexibility in terms of model structure etc?

Thanks!

Martin