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retrieving p-values in lm

4 messages · Patrick Kuss, Christian Ritz, Marc Schwartz +1 more

Patrick Kuss
# 
Dear list,

I want to retrieve the p-value of a two-polynomial regression. For a
one-polynomial lm I can easily do this with:
summary(lm(b~a, data=c)[[4]][[8]].

But how do I find the final p-value in the two-polynomial regression? Under
$coefficients I don't find it

Any suggestions?

Patrick

alt <-(2260,2183,2189,1930,2435,
2000,2100,2050,2020,2470,
1700,2310,2090,1560,2060,
1790,1940,2100,2250,2010)

H <- c(0.2034,0.1845,0.2053,0.1788,0.2196,
0.2037,0.1655,0.2176,0.1844,0.2033,
0.1393,0.2019,0.1975,0.1490,0.1917,
0.2180,0.2064,0.1943,0.2139,0.1320)

X <- data.frame(alt,H)

lm.res <- summary(lm(H~alt,data=X))
lm.res
p1 <- lm.res[[4]][[8]]
p1

lm.res.2 <- summary(lm(H~alt+I(alt^2),data=X))
lm.res.2
str(lm.res.2) # where is p

p2 <- lm.res.2[[???]][[????]]

--
Patrick Kuss
PhD-student
Institute of Botany
University of Basel
Sch??nbeinstr. 6
CH-4056 Basel
+41 61 267 2976
Christian Ritz
# 
Hi Patrick,

try:

lm.res.2$coefficients

which I found by looking at the content of the function 'summary.lm'.

Christian
Marc Schwartz
#
On Fri, 2005-12-09 at 14:19 +0100, Patrick Kuss wrote:
First, you might want to review Chapter 11: Statistical Models in R in
An Introduction to R, which is available with your R installation or
from the main R web site under Documentation. Specifically, page 53
describes the extractor functions to be used for getting model
information.

In this case using coef() will extract the model coefficients in both
cases:
Estimate   Std. Error  t value   Pr(>|t|)
(Intercept) 6.245371e-02 4.713400e-02 1.325024 0.20173833
alt         6.179038e-05 2.261665e-05 2.732074 0.01368545
Estimate   Std. Error    t value  Pr(>|t|)
(Intercept) -9.433748e-02 3.133627e-01 -0.3010488 0.7670283
alt          2.178857e-04 3.091330e-04  0.7048283 0.4904618
I(alt^2)    -3.838002e-08 7.579576e-08 -0.5063610 0.6191070


In both models, the coefficients are present if you review the structure
as you have in your code above:
[1] "call"          "terms"         "residuals"     "coefficients" 
 [5] "aliased"       "sigma"         "df"            "r.squared"    
 [9] "adj.r.squared" "fstatistic"    "cov.unscaled"
[1] "call"          "terms"         "residuals"     "coefficients" 
 [5] "aliased"       "sigma"         "df"            "r.squared"    
 [9] "adj.r.squared" "fstatistic"    "cov.unscaled" 


So, you can get the term p values by using:
(Intercept)         alt 
 0.20173833  0.01368545
(Intercept)         alt    I(alt^2) 
  0.7670283   0.4904618   0.6191070 


In terms of the overall model p value, this is actually calculated when
you display (print) the model. It is not stored as part of the model
object itself. If you review the code for print.summary.lm() using:
...
   pf(x$fstatistic[1], x$fstatistic[2], x$fstatistic[3],
      lower.tail = FALSE)
...


Where the first argument is the F statistic and the other two are the
degrees of freedom:
value     numdf     dendf 
 7.464231  1.000000 18.000000
value     numdf     dendf 
 3.706139  2.000000 17.000000 


So, in the case of your two models:
lower.tail = FALSE)
     value 
0.01368545
lower.tail = FALSE)
    value 
0.0461472 


HTH,

Marc Schwartz
Gavin Simpson
#
On Fri, 2005-12-09 at 14:19 +0100, Patrick Kuss wrote:
Judging from your code, you mean p-value of the F-statistic for the
whole model - this isn't stored anywhere, see:

getAnywhere(print.summary.lm)

In particular this section:

 cat("\nResidual standard error:", format(signif(x$sigma,
        digits)), "on", rdf, "degrees of freedom\n")
    if (!is.null(x$fstatistic)) {
        cat("Multiple R-Squared:", formatC(x$r.squared, digits = digits))
        cat(",\tAdjusted R-squared:", formatC(x$adj.r.squared,
            digits = digits), "\nF-statistic:", formatC(x$fstatistic[1],
            digits = digits), "on", x$fstatistic[2], "and", x$fstatistic[3],
            "DF,  p-value:", format.pval(pf(x$fstatistic[1],
                x$fstatistic[2], x$fstatistic[3], lower.tail = FALSE),
                digits = digits), "\n")
    }

The relevant bit being:

format.pval(pf(x$fstatistic[1],
                x$fstatistic[2], x$fstatistic[3], lower.tail = FALSE)

The reason this works for the first model is that with one covariate the
value in $coefficients is the overall model p-value, in that case. With
two covariates, the things in $coefficients relate to these, not to the
overall model - your assumption was wrong in the first usage, you just
lucked out that it gave the same result.

So,

p1 <- pf(lm.res$fstatistic[1],
         lm.res$fstatistic[2], lm.res$fstatistic[3], 
         lower.tail = FALSE)

p2 <- pf(lm.res.2$fstatistic[1],
         lm.res.2$fstatistic[2], lm.res.2$fstatistic[3], 
         lower.tail = FALSE)

Gives you the p-values:
value
0.01368545
value
0.0461472

HTH

G