# LMM models with two difference reference categories yield two different results

I have run LMM models with different reference categories and this yield different results:

> summary(lmer3)
Linear mixed model fit by maximum likelihood ['merModLmerTest']
Formula: v000001 ~ (1 | item) + (1 + color | speaker) + Language * color *      sex
Data: data1.frame

AIC       BIC    logLik  deviance
16279.975 16377.355 -8119.988 16239.975

Random effects:
Groups   Name        Variance  Std.Dev.  Corr
speaker  (Intercept) 8.904e+05 9.436e+02
colorblue   1.821e+05 4.267e+02 -0.35
colorred    3.428e+05 5.855e+02 -0.44  1.00
item     (Intercept) 9.502e-06 3.083e-03
Residual             1.067e+06 1.033e+03
Number of obs: 962, groups: speaker, 53; item, 10

Fixed effects:
Estimate Std. Error       df t value Pr(>|t|)
(Intercept)                       10664.67     318.69    38.45  33.464   <2e-16
Languagel2_like                     391.48     421.40    42.13   0.917   0.3642
colorblue                          -179.31     211.02    44.50  -0.850   0.4000
colorred                            116.96     241.44    36.27   0.484   0.6310
sexmale                            -168.01     450.11    38.26  -0.373   0.7110
Languagel2_like:colorblue           758.22     301.01    54.20   2.519   0.0147
Languagel2_like:colorred            463.37     344.01    45.73   1.344   0.1857
Languagel2_like:sexmale            -811.49     607.85    43.49  -1.326   0.1917
colorblue:sexmale                   342.76     294.97    42.57   1.162   0.2517
colorred:sexmale                     13.25     337.44    34.81   0.039   0.9689
Languagel2_like:colorblue:sexmale  -721.37     438.78    54.19  -1.644   0.1059
Languagel2_like:colorred:sexmale   -605.76     497.75    45.29  -1.216   0.2304

(Intercept)                       ***
Languagel2_like
colorblue
colorred
sexmale
Languagel2_like:colorblue         *
Languagel2_like:colorred
Languagel2_like:sexmale
colorblue:sexmale
colorred:sexmale
Languagel2_like:colorblue:sexmale
Languagel2_like:colorred:sexmale
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


And this is the second model:

> summary(lmer43)
Linear mixed model fit by maximum likelihood ['merModLmerTest']
Formula: v000001 ~ (1 | item) + (1 + color3 | speaker) + Language * color3 *      sex
Data: data1.frame

AIC       BIC    logLik  deviance
16279.975 16377.355 -8119.988 16239.975

Random effects:
Groups   Name        Variance  Std.Dev.  Corr
speaker  (Intercept) 7.945e+05 8.913e+02
color3white 1.821e+05 4.268e+02 -0.11
color3red   2.761e+04 1.661e+02 -0.24 -0.94
item     (Intercept) 4.961e-06 2.227e-03
Residual             1.067e+06 1.033e+03
Number of obs: 962, groups: speaker, 53; item, 10

Fixed effects:
Estimate Std. Error       df t value
(Intercept)                        10485.36     305.33    39.57  34.341
Languagel2_like                     1149.70     399.61    43.91   2.871
color3white                          179.31     211.03    44.50   0.850
color3red                            296.27     167.08   125.59   1.773
sexmale                              174.75     430.05    38.94   0.406
Languagel2_like:color3white         -758.22     301.01    54.10  -2.519
Languagel2_like:color3red           -294.85     244.46   159.09  -1.206
Languagel2_like:sexmale            -1532.85     577.70    44.74  -2.648
color3white:sexmale                 -342.76     294.98    42.57  -1.162
color3red:sexmale                   -329.51     228.57   113.99  -1.442
Languagel2_like:color3white:sexmale  721.36     438.78    54.10   1.644
Languagel2_like:color3red:sexmale    115.61     351.65   162.98   0.329
Pr(>|t|)
(Intercept)                         < 2e-16 ***
Languagel2_like                     0.00627 **
color3white                         0.40004
color3red                           0.07862 .
sexmale                             0.68671
Languagel2_like:color3white         0.01477 *
Languagel2_like:color3red           0.22953
Languagel2_like:sexmale             0.01114 *
color3white:sexmale                 0.25171
color3red:sexmale                   0.15215
Languagel2_like:color3white:sexmale 0.10602
Languagel2_like:color3red:sexmale   0.74275
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


Is it possible to report results from two models? (I know that very little of people would do this but these two models give different pictures). What should I do? Which one should I believe?

• These are the same model, restated. Can you please state what the two different pictures are that you're inferring from the two different views of the same model? (If I understand you correctly, your question has to do with reparameterizing models in general, and is not at all specific to LMMs.) – Ben Bolker Mar 20 '14 at 21:11
• For example, suppose the colours (blue, white, red) have associated mean estimates of 0, 1, 2 with a standard error of about 0.75. If blue is the baseline you'll get (intercept=0, 'white'=1, 'red'=2); the blue-vs-red contrast will be significant at p<0.05. If white is the baseline you'll get (intercept=1,'blue'=-1, 'red'=1), and neither of the individual contrasts will be significant. In the presence of interactions the argument gets a little more complicated but it's basically the same idea. – Ben Bolker Mar 20 '14 at 21:14
• Hi Ben Bolker, yes my question is about reparameterizing models as you said. Comparing these two models, the first one tells me there is no difference in the first parameter whereas the second one shows differece in this parameter. So for me, I should also report both models. What do you think? – user3288202 Mar 21 '14 at 6:05
• I think you don't understand the default parameterization of linear models in R. You might want to read about/use treatment contrasts: in particular, the mixed "helper" package for lme4 does so by default. – Ben Bolker Mar 21 '14 at 12:17
• I really don't have time to give a more thorough answer right now, I hope someone else will, or that you can find a useful discussion of contrasts and interactions online. I will just repeat that the meaning of the LanguageL2 parameter DIFFERS between the first and second models; you can't just say "one model says LanguageL2 is not important, the other says it is" (you should also not be interpreting p-values as denoting "importance"). – Ben Bolker Mar 21 '14 at 17:14