[R-sig-ME] FW: Unrealistic fixed effect coefficients
Seth Bigelow
seth at swbigelow.net
Tue Oct 15 16:02:11 CEST 2013
Dave,
Perhaps you should go back to a simple model and build up from there,
examining residuals at each step as outlined in, e.g., Pinheiro & Bates
Chapter 1, or Simon Wood's GAM book (Chap. 6, Mixed models and GAMMS's is
great).
My first cut at a simple model for your situation would be to ignore
chambers, specify random effects with species nested within functional
types, and use a likelihood ratio test to compare models with interaction
vs. no interaction of main effects, as in
M1 <- Lmer(response ~ CO2 + FT + (1|FT/spp))
M2 <- Lmer(response ~ CO2*FT + (1|FT/spp))
anova(M1,M2)
...analogous to the 'machines' example in section 1.3 of Pinheiro & Bates.
Then, if this makes sense and the residual errors make sense, move
(incrementally) to a model that incorporates the chamber effect, using,
e.g., Jake's suggestions.
-Seth
-----Original Message-----
From: r-sig-mixed-models-bounces at r-project.org
[mailto:r-sig-mixed-models-bounces at r-project.org] On Behalf Of Dave Marvin
Sent: Tuesday, October 15, 2013 9:06 AM
To: r-sig-mixed-models at r-project.org
Subject: Re: [R-sig-ME] Unrealistic fixed effect coefficients
Thank you for the clarification Jake.
Your assumptions were correct in that a single Species can only be one
Functional Type (in this experiment at least), and a single Chamber will
only have one CO2 level. The model output with this random effects structure
is below, and gives much more realistic estimates of the fixed effects.
However, this brings up a second issue (which maybe belongs in a new post?).
The standard errors of the estimated fixed effects are huge -- 3 to 9 times
as large as in the raw data. Is this to be interpreted as just having very
poor explanatory variables? Why, then, would my standard errors not be at
least in the same ballpark when just looking at the raw data group SEs?
> Linear mixed model fit by REML
> Formula: HtChg ~ CO2 * FT + (FT | Chamber) + (CO2 | Spp)
> Data: striAseasonal
> AIC BIC logLik deviance REMLdev
> 2744 2784 -1361 2750 2722
> Random effects:
> Groups Name Variance Std.Dev. Corr
> Chamber (Intercept) 236.215 15.3693
> FTT 81.171 9.0095 -1.000
> Spp (Intercept) 2995.561 54.7317
> CO2E 5.195 2.2793 -0.261
> Residual 828.383 28.7816
> Number of obs: 281, groups: Chamber, 36; Spp, 8
>
> Fixed effects:
> Estimate Std. Error t value
> (Intercept) 68.911 27.819 2.477
> CO2E 7.429 7.138 1.041
> FTT -43.882 39.065 -1.123
> CO2E:FTT -7.214 7.675 -0.940
>
> Correlation of Fixed Effects:
> (Intr) CO2E FTT
> CO2E -0.167
> FTT -0.707 0.100
> CO2E:FTT 0.130 -0.732 -0.149
On Oct 14, 2013, at 8:40 PM, Jake Westfall wrote:
> Hi Dave,
>
> Your random effects specification doesn't make sense. You say that you
have 8 random Species, each of which are observed in a number of random
Chambers. So Species and Chamber are crossed. So a preliminary model would
look like this:
>
> response ~ CO2 * FT + (1|Chamber) + (1|Spp)
>
> Now, Species are nested under Functional Type, meaning each Species is of
one and only one FT (right??), so we cannot estimate a random FT slope
across Species. But each species *is* observed under both levels of CO2. So
we can modify the Spp random effects thusly:
>
> response ~ CO2 * FT + (1|Chamber) + (CO2|Spp)
>
> I assume that growth Chambers are nested under CO2 level (so that a single
Chamber can't have both CO2 levels). So we can't estimate a random CO2 slope
across Chambers. But each Chamber *does* contain Species of both Functional
Types, right? So our final model, if I have understood the experimental
design correctly, should look like this:
>
> response ~ CO2 * FT + (FT|Chamber) + (CO2|Spp)
>
> Hope this helps,
> Jake
>> From: marvs at umich.edu
>> Date: Mon, 14 Oct 2013 19:55:45 -0400
>> To: r-sig-mixed-models at r-project.org
>> Subject: [R-sig-ME] Unrealistic fixed effect coefficients
>>
>> I am analyzing the growth response of two plant types (vines vs. trees)
to different CO2 levels, for a mix of species of each plant type in plant
growth chambers. I am fitting a mixed model with lmer using the following
fixed and random effects structures:
>>
>> response ~ CO2 * FT + (1 + Spp | Chamber)
>>
>> CO2 and FT are categorical predictors, each with two levels
(elevated/ambient CO2, vine/tree plant Functional Types). Each growth
chamber had the same mix of 8 species (Spp), so I would like to include both
species and chamber as random effects. With this random effects structure,
and please correct me if I am wrong, I believe I am modeling the variation
of each species among the growth chambers independent of the CO2 treatment
each chamber received. I would like to use this approach since each growth
chamber differs slightly in its microsite environment, and want to account
for species variation due to microsite (chamber) differences as a random
effect.
>>
>> However, the result of the model for most of my response variables (e.g.,
plant height below) give completely unrealistic fixed effect coefficients
(i.e., the plant height is never going to be negative, and the intercept
isn't even close to either of the group means from the raw data). Response
variables are untransformed and unstandardized.
>>
>> Am I specifying my random effects incorrectly? Or is there another
problem I am not seeing/addressing? Thank you.
>>
>>> Linear mixed model fit by REML
>>> Formula: HtChg ~ CO2 * FT + (1 + Spp | Chamber)
>>> Data: striAseasonal
>>> AIC BIC logLik deviance REMLdev
>>> 2640 2789 -1279 2571 2558
>>> Random effects:
>>> Groups Name Variance Std.Dev. Corr
>>> Chamber (Intercept) 613.032 24.7595
>>> SppCLIJAV 6680.902 81.7368 0.747
>>> SppCONN 1046.801 32.3543 -0.987 -0.773
>>> SppCORALL 1479.760 38.4676 0.565 0.619 -0.630
>>> SppPHRCO 461.740 21.4881 -0.995 -0.772 0.989 -0.597
>>> SppSTIHY 19240.737 138.7110 0.799 0.762 -0.878 0.777
-0.809
>>> SppTABRO 690.773 26.2826 -0.095 -0.348 0.027 0.144
0.043 0.027
>>> SppTERAM 211.084 14.5287 -0.752 -0.291 0.679 -0.126
0.699 -0.348 0.136
>>> Residual 91.938 9.5884
>>> Number of obs: 281, groups: Chamber, 36
>>>
>>> Fixed effects:
>>> Estimate Std. Error t value
>>> (Intercept) 13.459 1.629 8.260
>>> CO2E 3.216 2.276 1.413
>>> FTT -15.751 2.498 -6.305
>>> CO2E:FTT -2.251 3.538 -0.636
>>>
>>> Correlation of Fixed Effects:
>>> (Intr) CO2E FTT
>>> CO2E -0.716
>>> FTT -0.518 0.371
>>> CO2E:FTT 0.366 -0.512 -0.706
>>
>>
>>
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