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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