Read section 2.4.2 of Pinheiro and Bates again. It describes the
differences between the 4 methods of inference you tried (marginal
t-test, sequential F-tests, LRTs and CIs) and makes some
recommendations. There are some tricky issues involved in drawing
inferences from mixed models, and unfortunately the issues are
compounded by the sparseness of your data in the predictor space.
hth,
Kingsford Jones
On Mon, Mar 9, 2009 at 4:44 PM, Menelaos Stavrinides <menstav at
gmail.com> wrote:> I am running an lme model with the main effects of four fixed variables (3
> continuous and one categorical ? see below) and one random variable. The
> data describe the densities of a mite species ? awsm ? in relation to four
> variables: adh31 (temperature related), apsm (another plant feeding mite)
> awpm (a predatory mite), ?and orien (sampling location within plant ? north
> or south).
>
>
>
> I have read in Pinheiro and Bates that anova(model) can be used to asses
the
> significance of fixed factors. In my case, anova(model) gives different
> results than summary(model) and I am not sure which p values I should use
as
> a guide for model simplification.
>
>
>
> I have tried using either as a guide, but I get to a point where
> summary(model) or anova(model) suggest that a factor is not significant (p
> value>0.05) but when I remove it and compare the model with and without
the
> F value is significant ? the same is true for all three factors that appear
> as non significant in my final model. It makes me a bit suspicious that the
> F-value for the deletion test is always 0.0099 independently of the factor
> that I remove. Any suggestions greatly appreciated.
>
>
>
> The actual data follow at the end of the R code.
>
>
>
> Thanks,
>
> Mel
>
>
>
>
>
>> library(nlme)
>
>> model<-lme(awsm~adh31+awpm+apsm+orien,random=~1|viney)
>
>> summary(model)
>
> Linear mixed-effects model fit by REML
>
> ?Data: NULL
>
> ? ? ? AIC ? ? ?BIC ? ?logLik
>
> ?49.84102 51.22159 -17.92051
>
>
>
> Random effects:
>
> ?Formula: ~1 | viney
>
> ? ? ? ?(Intercept) ?Residual
>
> StdDev: ? ? 1.59297 0.2689783
>
>
>
> Fixed effects: awsm ~ adh31 + awpm + apsm + orien
>
> ? ? ? ? ? ? ? ? Value Std.Error DF ? ?t-value p-value
>
> (Intercept) ?0.7192961 0.8020099 ?7 ?0.8968669 ?0.3996
>
> adh31 ? ? ? ?0.3105583 0.3175280 ?2 ?0.9780504 ?0.4312
>
> awpm ? ? ? ? 0.4373813 0.2282457 ?2 ?1.9162743 ?0.1954
>
> apsm ? ? ? ? 0.1487537 0.2099112 ?2 ?0.7086502 ?0.5520
>
> oriensouth ?-0.5599473 0.2254709 ?2 -2.4834566 ?0.1310
>
> ?Correlation:
>
> ? ? ? ? ? (Intr) adh31 ?awpm ? apsm
>
> adh31 ? ? ?-0.636
>
> awpm ? ? ? -0.440 ?0.451
>
> apsm ? ? ? ?0.317 -0.756 -0.310
>
> oriensouth ?0.433 -0.608 -0.274 ?0.201
>
>
>
> Standardized Within-Group Residuals:
>
> ? ? ? ?Min ? ? ? ? ?Q1 ? ? ? ? Med ? ? ? ? ?Q3 ? ? ? ? Max
>
> -0.81103399 -0.31639155 -0.03371192 ?0.29211809 ?0.80633666
>
>
>
> Number of Observations: 14
>
> Number of Groups: 8
>
>> intervals(model)
>
> Approximate 95% confidence intervals
>
>
>
> ?Fixed effects:
>
> ? ? ? ? ? ? ? ? lower ? ? ? est. ? ? upper
>
> (Intercept) -1.1771559 ?0.7192961 2.6157481
>
> adh31 ? ? ? -1.0556542 ?0.3105583 1.6767709
>
> awpm ? ? ? ?-0.5446806 ?0.4373813 1.4194432
>
> apsm ? ? ? ?-0.7544215 ?0.1487537 1.0519289
>
> oriensouth ?-1.5300704 -0.5599473 0.4101758
>
> attr(,"label")
>
> [1] "Fixed effects:"
>
>
>
> ?Random Effects:
>
> ?Level: viney
>
> ? ? ? ? ? ? ? ? ? ?lower ? ?est. ? ?upper
>
> sd((Intercept)) 0.9312527 1.59297 2.724882
>
>
>
> ?Within-group standard error:
>
> ? ?lower ? ? ?est. ? ? upper
>
> 0.1096949 0.2689783 0.6595509
>
>> anova(model)
>
> ? ? ? ? ? ?numDF denDF ?F-value p-value
>
> (Intercept) ? ? 1 ? ? 7 9.702400 ?0.0170
>
> adh31 ? ? ? ? ? 1 ? ? 2 0.015683 ?0.9118
>
> awpm ? ? ? ? ? ?1 ? ? 2 2.824076 ?0.2349
>
> apsm ? ? ? ? ? ?1 ? ? 2 1.520431 ?0.3428
>
> orien ? ? ? ? ? 1 ? ? 2 6.167557 ?0.1310
>
>>
>
>>
>
>>
model2<-lme(awsm~adh31+awpm+apsm+orien,random=~1|viney,method="ML")
>
>>
model3<-lme(awsm~adh31+awpm+orien,random=~1|viney,method="ML")
>
>> anova(model2,model3)
>
> ? ? ? Model df ? ? ?AIC ? ? ?BIC ? ?logLik ? Test ?L.Ratio p-value
>
> model2 ? ? 1 ?7 42.44324 46.91664 -14.22162
>
> model3 ? ? 2 ?6 41.47847 45.31281 -14.73924 1 vs 2 1.035230 ?0.3089
>
>>
>
>> model3.1<-lme(awsm~adh31+awpm+orien,random=~1|viney)
>
>> summary(model3.1)
>
> Linear mixed-effects model fit by REML
>
> ?Data: NULL
>
> ? ? ? AIC ? ? ?BIC ? ?logLik
>
> ?47.01767 48.83318 -17.50883
>
>
>
> Random effects:
>
> ?Formula: ~1 | viney
>
> ? ? ? ?(Intercept) ?Residual
>
> StdDev: ? ?1.592549 0.2471161
>
>
>
> Fixed effects: awsm ~ adh31 + awpm + orien
>
> ? ? ? ? ? ? ? ? Value Std.Error DF ? ?t-value p-value
>
> (Intercept) ?0.5357316 0.7333251 ?7 ?0.7305512 ?0.4888
>
> adh31 ? ? ? ?0.4829425 0.1911191 ?3 ?2.5269194 ?0.0857
>
> awpm ? ? ? ? 0.4850814 0.1996481 ?3 ?2.4296822 ?0.0934
>
> oriensouth ?-0.5961750 0.2031294 ?3 -2.9349512 ?0.0608
>
> ?Correlation:
>
> ? ? ? ? ? (Intr) adh31 ?awpm
>
> adh31 ? ? ?-0.609
>
> awpm ? ? ? -0.360 ?0.345
>
> oriensouth ?0.379 -0.712 -0.225
>
>
>
> Standardized Within-Group Residuals:
>
> ? ? ? ?Min ? ? ? ? ?Q1 ? ? ? ? Med ? ? ? ? ?Q3 ? ? ? ? Max
>
> -1.10623050 -0.20081291 -0.09441451 ?0.19507694 ?1.08369449
>
>
>
> Number of Observations: 14
>
> Number of Groups: 8
>
>>
>
>> model4<-lme(awsm~adh31+orien,random=~1|viney,method="ML")
>
>> anova(model3,model4)
>
> ? ? ? Model df ? ? ?AIC ? ? ?BIC ? ?logLik ? Test ?L.Ratio p-value
>
> model3 ? ? 1 ?6 41.47847 45.31281 -14.73924
>
> model4 ? ? 2 ?5 46.13353 49.32881 -18.06676 1 vs 2 6.655056 ?0.0099
>
>>
>
>>
>
>> model5<-lme(awsm~awpm+orien,random=~1|viney,method="ML")
>
>> anova(model3,model5)
>
> ? ? ? Model df ? ? ?AIC ? ? ?BIC ? ?logLik ? Test ?L.Ratio p-value
>
> model3 ? ? 1 ?6 41.47847 45.31281 -14.73924
>
> model5 ? ? 2 ?5 46.13124 49.32653 -18.06562 1 vs 2 6.652772 ?0.0099
>
>>
>
>> model6<-lme(awsm~awpm+orien,random=~1|viney,method="ML")
>
>> anova(model3,model6)
>
> ? ? ? Model df ? ? ?AIC ? ? ?BIC ? ?logLik ? Test ?L.Ratio p-value
>
> model3 ? ? 1 ?6 41.47847 45.31281 -14.73924
>
> model6 ? ? 2 ?5 46.13124 49.32653 -18.06562 1 vs 2 6.652772 ?0.0099
>
>>
>
>
>
>
>
> # actual data used for analyses
>
>
>
>
>
>
>
>> awsm<-log(wsmmax/days+1)
>
>> apsm<-log(psm/days+1)
>
>> awpm<-log(wpm/days+1)
>
>> adh31<-log(dh31/days+1)
>
>>
>
>> awsm
>
> ?[1] 0.52224518 3.29454964 0.01695951 1.36088200 2.01692487 4.57307785
>
> ?[7] 0.41499043 2.66783465 1.02173903 2.66030752 0.83589370 1.22387225
>
> [13] 4.93707366 2.25271004
>
>> apsm
>
> ?[1] 1.9938465 1.8572201 0.2595992 1.3926976 0.0000000 0.5222452 2.1845666
>
> ?[8] 3.0942586 3.8885649 2.6691373 0.0000000 0.0000000 1.9460277 4.2546503
>
>> awpm
>
> ?[1] 0.9333715 1.9485709 0.0000000 0.1381489 1.5627542 0.0000000 0.4149904
>
> ?[8] 0.0000000 0.7482365 0.5215986 0.5113811 1.4076002 1.0598621 0.1732711
>
>> adh31
>
> ?[1] 0.8329868 1.4813520 2.5733515 2.8888284 1.4217520 2.1184476 2.5843313
>
> ?[8] 2.9896871 3.0351911 2.4386017 2.4736569 2.2904899 2.7930367 3.3185963
>
>> orien
>
> ?[1] int ? int ? int ? int ? int ? int ? int ? int ? south south south
south
>
> [13] south south
>
> Levels: int south
>
>> viney
>
> ?[1] lpsm06 lwsm06 mpsm06 mwsm06 lpsm07 lwsm07 mpsm07 mwsm07 lpsm06 lwsm06
>
> [11] mwsm06 lpsm07 lwsm07 mwsm07
>
> Levels: lpsm06 lpsm07 lwsm06 lwsm07 mpsm06 mpsm07 mwsm06 mwsm07
>
>
>
>
> --
> Menelaos Stavrinides
> Ph.D. Candidate
> Environmental Science, Policy and Management
> 137 Mulford Hall MC #3114
> University of California
> Berkeley, CA 94720-3114 USA
> Tel: 510 717 5249
>
> ? ? ? ?[[alternative HTML version deleted]]
>
>
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