[R-sig-ME] treatment and sum contrasts in ME models

[Cristiano Alessandro]

Hi all,

I am fitting a linear mixed effect models with two factors (mPair with 6
levels, and spd_des with 3 levels) and their interaction in R. I obtain
inconsistent results depending on the contrasts that I choose, and I would
like to understand why and how to deal with it.

If I use treatment contrasts, I obtain the following (I only copy the
relevant info of the results)

> options(contrasts = c("contr.treatment","contr.poly"))
> linM1 <- lme(cc_marg ~ mPair*spd_des , random = ~mPair|ratID, data=dat_trf, na.action=na.omit, method = "ML", control=lCtr )
> summary(linM1)

Fixed effects: cc_marg ~ mPair * spd_des
                         Value  Std.Error DF   t-value p-value
(Intercept)          1.4628761 0.09618167 94 15.209511  0.0000
mPairRFVI           -0.8180718 0.10454920 94 -7.824754  0.0000
mPairVLRF           -0.7990828 0.13193991 94 -6.056415  0.0000
mPairVLVI           -0.6077804 0.13734253 94 -4.425289  0.0000
mPairVMRF           -0.7444267 0.13294167 94 -5.599649  0.0000
mPairVMVI           -0.4799995 0.12194383 94 -3.936234  0.0002
spd_des15           -0.0830016 0.07990370 94 -1.038771  0.3016
spd_des20           -0.0856339 0.08321984 94 -1.029008  0.3061
mPairRFVI:spd_des15 -0.1576193 0.13500809 94 -1.167481  0.2460
mPairVLRF:spd_des15  0.0866510 0.11385875 94  0.761039  0.4485
mPairVLVI:spd_des15  0.0083311 0.13500809 94  0.061708  0.9509
mPairVMRF:spd_des15  0.0184844 0.11385875 94  0.162345  0.8714
mPairVMVI:spd_des15 -0.0672286 0.13500809 94 -0.497960  0.6197
mPairRFVI:spd_des20 -0.1705514 0.14201095 94 -1.200973  0.2328
mPairVLRF:spd_des20  0.0899629 0.11949193 94  0.752879  0.4534
mPairVLVI:spd_des20 -0.0626845 0.14359174 94 -0.436547  0.6634
mPairVMRF:spd_des20 -0.0106400 0.11969131 94 -0.088895  0.9294
mPairVMVI:spd_des20 -0.0608750 0.14286017 94 -0.426116  0.6710

I interpret this as follows: Since the interaction terms are all
non-significant, then the factor spd_des (also non-significant) does not
influence the data at any level of the factor mPair.

On the other hand, using sum contrasts I obtain the following results.

> options(contrasts = c("contr.sum","contr.poly"))
> linM2 <- lme(cc_marg ~ mPair*spd_des , random = ~mPair|ratID, data=dat_trf, na.action=na.omit, method = "ML", control=lCtr )
> summary(linM2)

Fixed effects: cc_marg ~ mPair * spd_des
                     Value  Std.Error DF   t-value p-value
(Intercept)      0.8137433 0.04791890 94 16.981678  0.0000
mPair1           0.5929117 0.06609665 94  8.970373  0.0000
mPair2          -0.3341386 0.04969616 94 -6.723629  0.0000
mPair3          -0.1472874 0.07260892 94 -2.028503  0.0453
mPair4          -0.0328631 0.08993236 94 -0.365421  0.7156
mPair5          -0.1488959 0.06991733 94 -2.129600  0.0358
spd_des1         0.0743293 0.02315254 94  3.210416  0.0018
spd_des2        -0.0272358 0.02325774 94 -1.171043  0.2445
mPair1:spd_des1 -0.0181081 0.04414399 94 -0.410206  0.6826
mPair2:spd_des1  0.0912334 0.05726538 94  1.593168  0.1145
mPair3:spd_des1 -0.0769866 0.04518813 94 -1.703691  0.0917
mPair4:spd_des1  0.0000066 0.05743544 94  0.000114  0.9999
mPair5:spd_des1 -0.0207337 0.04518548 94 -0.458859  0.6474
mPair1:spd_des2  0.0004559 0.04558473 94  0.010002  0.9920
mPair2:spd_des2 -0.0478225 0.05730295 94 -0.834555  0.4061
mPair3:spd_des2  0.0282279 0.04525282 94  0.623781  0.5343
mPair4:spd_des2  0.0269011 0.05747689 94  0.468034  0.6408
mPair5:spd_des2  0.0163141 0.04525367 94  0.360503  0.7193

> anova.lme(linM2,type="marginal")
              numDF denDF   F-value p-value
(Intercept)       1    94 288.37740  <.0001
mPair             5    94  35.30799  <.0001
spd_des           2    94   5.17279  0.0074
mPair:spd_des    10    94   0.52159  0.8710

The results are now telling me that the first level of the factor spd_des
is significant; i.e. the mean of the data at that level of spd_des is
significantly different from the grand mean (Intercept), and since the
interactions are all non-significant, this is true at all levels of mPair.

So, with treatment contrasts spd_des does not influence the data at any
level of mPair, and with sum contrast spd_des influence the data at all
level of mPair. How do I deal with this? What result should I trust?
Thanks in advance for your help

Best
Cristiano

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