# [R-sig-ME] DF in lme

i white i.m.s.white at ed.ac.uk
Wed Mar 16 11:10:19 CET 2011

```Ben,

What happens if you include plate as another random effect?

random = ~1|Plate/Dish/Disk

Ben Ward wrote:
> Hi, I'm using lme and lmer in my dissertation and it's the first time
> I've used these methods. Taking into account replies from my previous
> query I decided to go through with a model simplification, and then try
> to validate the models in various ways and come up with the best one to
> include in my work, be it a linear mixed effects model or general linear
> effects model, with log() data or not etc - interestingly it does not
> seems like doing transofrmations and such makes much difference so far,
> looking at changes in diagnostic plots and AIC.
>
> Anywho, I simplified to the model using lme (I've pasted it at the
> bottom). And looking at the anova output the numDF looks right. However
> I'm concerned about the 342 df in the denDF in anova() and in the
> summary() output, as it seems to high to me, because at the observation
> level is too high and pseudoreplicated; 4 readings per disk, 3 disks,
> per plate, 3 plates per lineage, 5 lineages per group, 2 groups so:
> 4*3*3*5*2=360. If I take this to disk level 3*3*5*2=90, and at dish
> level it's 3*5*2=30 degrees of freedom for error. And either dish or
> disk (arguments for both) is the level at which one independant point of
> datum is obtained, most probably Dish. So I'm wondering if either I'de
> done something wrong, or I'm not understanding how df are presented and
> used in mixed models. It's not really explained in my texts, and my
> lecturer told me I'm working at the edge of his personal/professional
> experience.
> I've used lmer and the function in languageR to extract p-values without
> it even mentioning df. Now if the lmer method with pvals.fnc() makes it
> so as I don't have to worry about these df then in a way it makes my
> issue a bit redundant. But it is playing on my mind a bit so felt I
>
> My second question is about when I do the equivalent model using lmer:
> "lmer(Diameter~Group*Lineage+(1|Dish)+(1|Disk), data=Dataset)" - which
> I'm sure does the same because all my plots of residuals against fitted
> and such are the same, if I define it with the poisson family, which
> uses log, then I get a much lower AIC of about 45, compared to over 1000
> without family defined, which I think defaults to gaussian/normal. And
> my diagnostic plots still give me all the same patters, but just looking
> a bit different because of the family distribution specified. I then did
> a model logging the response variable by using log(Diameter), again, I
> get the same diagnostic plot patterns, but on a different scale, and I
> get an AIC of - 795.6. Now normally I'd go for the model with the lowest
> AIC, however, I've never observed this beahviour before, and can't help
> but think thhat the shift from a posotive 1000+ AIC to a negative one is
> due to the fact the data has been logged, rather than that the model
> fitted to log data in this way is genuinley better.
>
> Finally, I saw in a text, an example of using lmer but "Recoding Factor
> Levels" like:
> lineage<-Group:Lineage
> dish<-Group:Lineage:Dish
> disk<-Group:Lineage:Dish:Disk
> model<-lmer(Diameter~Group+(1|lineage)+(1|dish)+(1|disk)
>
> However I don't see why this should need to be done, considering, the
> study was hieracheal, just like all other examples in that chapter, and
> it does not give a reason why, but says it does the same job as a nested
> anova, which I though mixed models did anyway.
>
> Hopefully sombody can shed light on my concerns. In terms of my work and
> university, I could include what I've done here and be as transparrant
> as possible and discuss these issues, because log() of the data or
> defining a distribution in the model is leading to the same plots and
> conclusions. But I'd like to make sure I come to term with what's
> actually happening here.
>
> A million thanks,
> Ben W.
>
>
> lme14 <- lme(Diameter~Group*Lineage,random=~1|Dish/Disk, data=Dataset,
> method="REML")
>
>  >anova(lme14):
>
>  numDF denDF   F-value p-value
> (Intercept)       1   342 16538.253 <.0001
> Group             1   342   260.793 <.0001
> Lineage           4   342     8.226 <.0001
> Group:Lineage     4   342     9.473 <.0001
>
>  > summary(lme14)
> Linear mixed-effects model fit by REML
>  Data: Dataset
>        AIC      BIC    logLik
>   1148.317 1198.470 -561.1587
>
> Random effects:
>  Formula: ~1 | Dish
>         (Intercept)
> StdDev:   0.1887527
>
>  Formula: ~1 | Disk %in% Dish
>          (Intercept) Residual
> StdDev: 6.303059e-05 1.137701
>
> Fixed effects: Diameter ~ Group * Lineage
>                                         Value Std.Error  DF  t-value
> p-value
> (Intercept)                         15.049722 0.2187016 342 68.81396
> 0.0000
> Group[T.NEDettol]                    0.980556 0.2681586 342  3.65662
> 0.0003
> Lineage[T.First]                    -0.116389 0.2681586 342 -0.43403
> 0.6645
> Lineage[T.Fourth]                   -0.038056 0.2681586 342 -0.14191
> 0.8872
> Lineage[T.Second]                   -0.177500 0.2681586 342 -0.66192
> 0.5085
> Lineage[T.Third]                     0.221111 0.2681586 342  0.82455
> 0.4102
> Group[T.NEDettol]:Lineage[T.First]   2.275000 0.3792336 342  5.99894
> 0.0000
> Group[T.NEDettol]:Lineage[T.Fourth]  0.955556 0.3792336 342  2.51970
> 0.0122
> Group[T.NEDettol]:Lineage[T.Second]  0.828333 0.3792336 342  2.18423
> 0.0296
> Group[T.NEDettol]:Lineage[T.Third]   0.721667 0.3792336 342  1.90296
> 0.0579
>  Correlation:
>                                     (Intr) Gr[T.NED] Lng[T.Frs] Lng[T.Frt]
> Group[T.NEDettol]                   -0.613
> Lineage[T.First]                    -0.613  0.500
> Lineage[T.Fourth]                   -0.613  0.500     0.500
> Lineage[T.Second]                   -0.613  0.500     0.500      0.500
> Lineage[T.Third]                    -0.613  0.500     0.500      0.500
> Group[T.NEDettol]:Lineage[T.First]   0.434 -0.707    -0.707     -0.354
> Group[T.NEDettol]:Lineage[T.Fourth]  0.434 -0.707    -0.354     -0.707
> Group[T.NEDettol]:Lineage[T.Second]  0.434 -0.707    -0.354     -0.354
> Group[T.NEDettol]:Lineage[T.Third]   0.434 -0.707    -0.354     -0.354
>                                     L[T.S] L[T.T] Grp[T.NEDttl]:Lng[T.Frs]
> Group[T.NEDettol]
> Lineage[T.First]
> Lineage[T.Fourth]
> Lineage[T.Second]
> Lineage[T.Third]                     0.500
> Group[T.NEDettol]:Lineage[T.First]  -0.354 -0.354
> Group[T.NEDettol]:Lineage[T.Fourth] -0.354 -0.354  0.500
> Group[T.NEDettol]:Lineage[T.Second] -0.707 -0.354  0.500
> Group[T.NEDettol]:Lineage[T.Third]  -0.354 -0.707  0.500
>                                     Grp[T.NEDttl]:Lng[T.Frt] G[T.NED]:L[T.S
> Group[T.NEDettol]
> Lineage[T.First]
> Lineage[T.Fourth]
> Lineage[T.Second]
> Lineage[T.Third]
> Group[T.NEDettol]:Lineage[T.First]
> Group[T.NEDettol]:Lineage[T.Fourth]
> Group[T.NEDettol]:Lineage[T.Second]  0.500
> Group[T.NEDettol]:Lineage[T.Third]   0.500                    0.500
>
> Standardized Within-Group Residuals:
>         Min          Q1         Med          Q3         Max
> -2.47467771 -0.75133489  0.06697157  0.67851126  3.27449064
>
> Number of Observations: 360
> Number of Groups:
>           Dish Disk %in% Dish
>              3              9
>
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>

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