[R] degrees of freedom
Ben Bolker
bbolker at gmail.com
Thu Jan 23 23:34:35 CET 2014
Iain Gallagher <iaingallagher <at> btopenworld.com> writes:
>
> Hello List
>
> I have been asked to analyse some data for a colleague.
> The design consists of a two sets of animals
>
> First set of three - one leg is treated and the
> other is not under two different conditions (control &
> overload are the same animals - control leg is control
> (!) for treated leg;
>
> Second set of three - one leg is treated and the other
> is not under two different conditions (high_fat and
> high_fat_overload are the same animals with high_fat
> being control leg for high_fat_overload).
>
> Ideally I'd like to find differences between the treatments.
bip <- structure(list(group = structure(c(1L, 1L, 1L, 2L, 2L, 2L, 3L,
3L, 3L, 4L, 4L, 4L), .Label = c("control", "overload", "high_fat",
"high_fat_overload"), class = "factor"), variable = structure(c(1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L), .Label = "BiP", class = "factor"),
animal = structure(c(1L, 3L, 5L, 1L, 3L, 5L, 2L, 4L, 6L,
2L, 4L, 6L), .Label = c("rat1_c", "rat1_hf", "rat2_c", "rat2_hf",
"rat3_c", "rat3_hf"), class = "factor"), value = c(404979.65625,
783511.8125, 677277.625, 1576900.375, 1460101.875, 1591022,
581313.75, 992724.1875, 1106941.5, 996600.375, 1101696.5,
1171004.375)), .Names = c("group", "variable", "animal",
"value"), row.names = c(NA, 12L), class = "data.frame")
>
> I chose to analyse this as a mixed effects model with treatment
> as a fixed effect and animal as random.
>
library(lme4)
model1 <- lmer(value~group + (1|animal), data=bip)
summary(model1)
> And then compare this to no treatment with:
anova(model1)
> From this I wanted to work out whether 'treatment'
> was significantly affecting BiP levels by calculating
> the critical value of F for this design. I have 2
> groups of animals and 3 animals per group. My calculation
> for the degrees of freedom for treatment is 4-1=3.
>
> I'm not sure about the degrees of freedom for the denominator
> though. Since I'm comparing a model with
> treatment to one without (i.e. the grand mean) would the
> df for my denominator be 6-1=5?
>
> So I'd then have:
>
> qf(0.95,3,5)
>
> for my critical F value?
>
> Best
>
> iain
I started to answer this, but then realized I'd really recommend that
you re-post this to r-sig-mixed-models at r-project.org. I have a couple
of points for you to think about that might help:
* since you only have two treatments, I think you can analyze this
as a _paired_ model, that is, reduce the data to (treatment-control,
i.e. overload - non_overload) for each animal. Then you'll have 6 data
points, 3 in each group, and you can just do a regular 1-way ANOVA on
them.
* I *think* you've only got 1 df for treatment
* You might also be able to handle this problem via aov() with
an Error stratum
Ben Bolker
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