[R] Differences in output of lme() when introducing interactions

[angelo.arcadi at virgilio.it]

Dear List Members, 



I am searching for correlations between a dependent variable and a 
factor or a combination of factors in a repeated measure design. So I 
use lme() function in R. However, I am getting very different results 
depending on whether I add on the lme formula various factors compared 
to when only one is present. If a factor is found to be significant, 
shouldn't remain significant also when more factors are introduced in 
the model?


I give an example of the outputs I get using the two models. In the first model I use one single factor:

library(nlme)
summary(lme(Mode ~ Weight, data = Gravel_ds, random = ~1 | Subject))
Linear mixed-effects model fit by REML
 Data: Gravel_ds 
      AIC      BIC   logLik
  2119.28 2130.154 -1055.64

Random effects:
 Formula: ~1 | Subject
        (Intercept) Residual
StdDev:    1952.495 2496.424

Fixed effects: Mode ~ Weight 
                Value Std.Error DF   t-value p-value
(Intercept) 10308.966 2319.0711 95  4.445299   0.000
Weight        -99.036   32.3094 17 -3.065233   0.007
 Correlation: 
       (Intr)
Weight -0.976

Standardized Within-Group Residuals:
        Min          Q1         Med          Q3         Max 
-1.74326719 -0.41379593 -0.06508451  0.39578734  2.27406649 

Number of Observations: 114
Number of Groups: 19 


As you can see the p-value for factor Weight is significant. 
This is the second model, in which I add various factors for searching their correlations:

library(nlme)
summary(lme(Mode ~ Weight*Height*Shoe_Size*BMI, data = Gravel_ds, random = ~1 | Subject))
Linear mixed-effects model fit by REML
 Data: Gravel_ds 
       AIC      BIC    logLik
  1975.165 2021.694 -969.5825

Random effects:
 Formula: ~1 | Subject
        (Intercept) Residual
StdDev:    1.127993 2494.826

Fixed effects: Mode ~ Weight * Height * Shoe_Size * BMI 
                                Value Std.Error DF    t-value p-value
(Intercept)                   5115955  10546313 95  0.4850941  0.6287
Weight                      -13651237   6939242  3 -1.9672518  0.1438
Height                         -18678     53202  3 -0.3510740  0.7487
Shoe_Size                       93427    213737  3  0.4371115  0.6916
BMI                         -13011088   7148969  3 -1.8199949  0.1663
Weight:Height                   28128     14191  3  1.9820883  0.1418
Weight:Shoe_Size               351453    186304  3  1.8864467  0.1557
Height:Shoe_Size                 -783      1073  3 -0.7298797  0.5183
Weight:BMI                      19475     11425  3  1.7045450  0.1868
Height:BMI                     226512    118364  3  1.9136867  0.1516
Shoe_Size:BMI                  329377    190294  3  1.7308827  0.1819
Weight:Height:Shoe_Size          -706       371  3 -1.9014817  0.1534
Weight:Height:BMI                -109        63  3 -1.7258742  0.1828
Weight:Shoe_Size:BMI             -273       201  3 -1.3596421  0.2671
Height:Shoe_Size:BMI            -5858      3200  3 -1.8306771  0.1646
Weight:Height:Shoe_Size:BMI         2         1  3  1.3891782  0.2589
 Correlation: 
                            (Intr) Weight Height Sho_Sz BMI    Wght:H Wg:S_S Hg:S_S Wg:BMI Hg:BMI S_S:BM Wg:H:S_S W:H:BM W:S_S: H:S_S:
Weight                      -0.895                                                                                                    
Height                      -0.996  0.869                                                                                             
Shoe_Size                   -0.930  0.694  0.933                                                                                      
BMI                         -0.911  0.998  0.887  0.720                                                                               
Weight:Height                0.894 -1.000 -0.867 -0.692 -0.997                                                                        
Weight:Shoe_Size             0.898 -0.997 -0.873 -0.700 -0.999  0.995                                                                 
Height:Shoe_Size             0.890 -0.612 -0.904 -0.991 -0.641  0.609  0.619                                                          
Weight:BMI                   0.911 -0.976 -0.887 -0.715 -0.972  0.980  0.965  0.637                                                   
Height:BMI                   0.900 -1.000 -0.875 -0.703 -0.999  0.999  0.999  0.622  0.973                                            
Shoe_Size:BMI                0.912 -0.992 -0.889 -0.726 -0.997  0.988  0.998  0.649  0.958  0.995                                     
Weight:Height:Shoe_Size     -0.901  0.999  0.876  0.704  1.000 -0.997 -1.000 -0.623 -0.971 -1.000 -0.997                              
Weight:Height:BMI           -0.908  0.978  0.886  0.704  0.974 -0.982 -0.968 -0.627 -0.999 -0.975 -0.961  0.973                       
Weight:Shoe_Size:BMI        -0.949  0.941  0.928  0.818  0.940 -0.946 -0.927 -0.751 -0.980 -0.938 -0.924  0.935    0.974              
Height:Shoe_Size:BMI        -0.901  0.995  0.878  0.707  0.998 -0.992 -1.000 -0.627 -0.960 -0.997 -0.999  0.999    0.964  0.923       
Weight:Height:Shoe_Size:BMI  0.952 -0.948 -0.933 -0.812 -0.947  0.953  0.935  0.747  0.985  0.946  0.932 -0.943   -0.980 -0.999 -0.931

Standardized Within-Group Residuals:
        Min          Q1         Med          Q3         Max 
-2.03523736 -0.47889716 -0.02149143  0.41118126  2.20012158 

Number of Observations: 114
Number of Groups: 19 


This time the p-value associated to Weight is not significant anymore. Why? Which analysis should I trust?


In addition, while in the first output the field "value" (which 
should give me the slope) is -99.036 in the second output it is 
-13651237. Why they are so different? The one in the first output is the
 one that seems definitively more reasonable to me.
I would very grateful if someone could give me an answer


Thanks in advance


Angelo












       
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