[R] Differences in output of lme() when introducing interactions
Michael Dewey
lists at dewey.myzen.co.uk
Mon Jul 20 17:56:39 CEST 2015
In-line
On 20/07/2015 15:10, angelo.arcadi at virgilio.it wrote:
> 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?
>
The short answer is 'No'.
The long answer is contained in any good book on statistics which you
really need to have by your side as the long answer is too long to
include in an email.
>
> 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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--
Michael
http://www.dewey.myzen.co.uk/home.html
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