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

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