William Dunlap wdunlap at tibco.com
Tue Jun 25 21:01:29 CEST 2013

```Should the F statistic be the same when using add1() on models created by lm and glm(family=gaussian)?
They are in the single-degree-of-freedom case but not in the multiple-degree-of-freedom case.
MASS:addterm shows the same discrepancy.  It looks like the deviance (==residual sum of squares) gets
divided by the number of degrees of freedom for the term twice in add1.glm.  Using anova() on the output
of lm and glm(family=gaussian) gives the save F statistic as add1.lm gives.

> # factor(carb) consumes 5 degrees of freedom, am 1, compare their F values.
> fit <- lm(mpg ~ hp, data=mtcars) ; add1(fit, ~ hp + factor(carb) + am, test="F")

Model:
mpg ~ hp
Df Sum of Sq    RSS    AIC F value   Pr(>F)
<none>                    447.67 88.427
factor(carb)  5    103.54 344.13 90.009  1.5044   0.2241
am            1    202.24 245.44 71.194 23.8952 3.46e-05 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> fit <- glm(mpg ~ hp, data=mtcars) ; add1(fit, ~ hp + factor(carb) + am, test="F")

Model:
mpg ~ hp
Df Deviance    AIC F value   Pr(>F)
<none>            447.67 181.24
factor(carb)  5   344.13 182.82  0.3009   0.9077
am            1   245.44 164.01 23.8952 3.46e-05 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Bill Dunlap
Spotfire, TIBCO Software
wdunlap tibco.com

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