[R-sig-ME] Different lmer results using contrasts() vs numeric coding

[Becky Gilbert]

Thanks very much Dan - that makes sense.

Follow up question: why is there no change to the factor-variable model
after removing 'type' as a fixed factor, while including its interaction
with the 'priming' factor?  For context, this reduced model was run in an
effort to get the main effect of the 'type' factor after accounting for the
effect of 'priming' and the 'type' x 'priming' interaction (i.e. the
ANOVA-like results with type-III SS).  Again, apologies if I'm missing
something obvious here.

Thanks,
Becky
_____________________________________________________
Dr Becky Gilbert
Research Associate
Psychology and Language Sciences
26 Bedford Way
Office: Room 208
University College London
London WC1H 0AP


On 26 January 2016 at 21:48, Dan McCloy <drmccloy at uw.edu> wrote:

> Using numeric variables is not the same as hand-coding the contrasts. If
> you pass in a numeric variable the modeling function will assume it is a
> numerically continuous predictor, and you will get one coefficient
> regardless of how many "levels" you represented numerically. Try something
> like
>
> contrasts(data$type_handcoded) <- as.matrix(cbind(data$type1, data$type2))
>
> to specify the contrast matrix by hand.
> Dear R Mixed Models List,
>
>
>
> I'm working on a LMM for psycholinguistic data with a 3x2 fixed effects
> structure and crossed subject and item random effects. I ran into a
> confusing result when I compared the use of contrasts() for fixed factor
> variables vs 'hand-coding' these contrasts into numeric variables (with the
> same values assigned using contrasts()).
>
>
>
> The summaries for the two models that include all fixed factor terms are
> identical. Here is the syntax used for each:
>
>
>
> modelHandCoded <- lmer(invRT ~ 1 + type1 + type2 + priming1 +
> type1:priming1 + type2:priming1 + (1|pp) + (1|word), data = data)
>
>
>
> # numeric variables to define contrasts
>
> table(data$type1)
>
> -2    1
>
> 1503 3014
>
> table(data$type2)
>
>  -1    0    1
>
> 1520 1503 1494
>
> table(data$priming1)
>
>   -1    1
>
> 2253 2264
>
>
>
> modelContrasts <- lmer(invRT ~ 1 + type + priming + type:priming + (1|pp) +
> (1|word), data = data)
>
>
>
> # factor variables with contrasts
>
> contrasts(data$type)             # [,1] = 'type1' above, [,2] = 'type2'
> above
>
>        [,1] [,2]
>
> SC   -2    0
>
> IC     1    1
>
> IIH    1   -1
>
> contrasts(data$priming)       # [,1] = 'priming1' above
>
>                [,1]
>
> unprimed   -1
>
> primed       1
>
>
>
> However, when I remove the effect of the 3-level fixed factor 'type' (while
> still including its interaction with the 2-level factor 'priming'), the two
> models no longer produce the same results. Here is the syntax for the two
> models without 'type':
>
>
>
> modelHandCoded.NoType <- lmer(invRT ~ 1 + priming1 + type1:priming1 +
> type2:priming1 + (1|pp) + (1|word), data = data)
>
>
>
> modelContrasts.NoType <- lmer(invRT ~ 1 + priming + type:priming + (1|pp) +
> (1|word), data = data)
>
>
>
> The summary for the hand-coded model includes 3 fixed effects that I
> expected (priming1, type1:priming1, type1:priming2):
>
>
>
> summary(modelHandCoded.NoType)
>
> ...
>
> Fixed effects:
>
>                Estimate Std. Error         df t value Pr(>|t|)
>
> (Intercept)   1.428e+00  3.244e-02  2.900e+01  44.031   <2e-16 ***
>
> priming1      8.878e-03  3.572e-03  4.384e+03   2.485    0.013 *
>
> type1:priming1  8.416e-04  2.527e-03  4.385e+03   0.333    0.739
>
> type2:priming1 -1.790e-04  4.373e-03  4.383e+03  -0.041    0.967
>
>
>
> However the summary for the contrasts() model includes additional
> interaction terms for each level of priming1:
>
>
>
> summary(modelContrasts.NoType)
>
> ...
>
> Fixed effects:
>
>                  Estimate Std. Error         df t value Pr(>|t|)
>
> (Intercept)     1.428e+00  3.243e-02  2.900e+01  44.046   <2e-16 ***
>
> priming1        8.872e-03  3.572e-03  4.386e+03   2.484   0.0130 *
>
> priming0:type1  6.289e-03  4.811e-03  3.130e+02   1.307   0.1921
>
> priming1:type1  7.957e-03  4.802e-03  3.110e+02   1.657   0.0985 .
>
> priming0:type2 -9.782e-03  8.323e-03  3.120e+02  -1.175   0.2408
>
> priming1:type2 -1.009e-02  8.316e-03  3.110e+02  -1.213   0.2261
>
>
>
> When I compare each reduced model to the full model, I find that there's a
> difference between the full model and the reduced hand coded model, but not
> between the full model and the reduced model using contrasts(). The
> Df/AIC/BIC/LL for the latter two models are identical, so it appears that
> removing the 'type' term had no effect. (This is true for comparisons with
> both the hand-coded and contrasts() versions of the full model.) Here are
> the results of the anova() for each comparison:
>
>
>
> Model with full fixed-effects structure vs. hand-coded model with 'type'
> removed
>
>        Df    AIC    BIC logLik deviance  Chisq Chi Df Pr(>Chisq)
>
> ..1       7 168.14 213.05 -77.07   154.14
>
> object  9 167.20 224.94 -74.60   149.20 4.9406      2    0.08456 .
>
>
>
> Model with full fixed-effects structure vs. contrast-coded model with
> 'type' removed
>
>        Df   AIC    BIC logLik deviance Chisq Chi Df Pr(>Chisq)
>
> object  9 167.2 224.94  -74.6    149.2
>
> ..1       9 167.2 224.94  -74.6    149.2     0      0  < 2.2e-16 ***
>
>
>
> Can anyone explain why the two reduced models differ depending on whether
> the fixed factor variables are hand-coded numeric vs. factors with
> contrasts() assigned? Also, why is there no effect of removing a fixed
> factor term when contrasts() are used?  Apologies if I'm missing something
> obvious!
>
>
>
> Thanks,
>
> Becky
>
> _____________________________________________________
>
> Dr Becky Gilbert
>
> Research Associate
>
> Psychology and Language Sciences
>
> University College London
>
> London WC1H 0AP
>
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>
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