[R] lmer( ) parameter estimates changing depending on dummy-coded reference level

Alan Mishler amishler at umd.edu
Wed Aug 7 18:01:44 CEST 2013


Hi everyone,

I'm writing with a question about lmer( ) in the lme4 package. I've
searched around for
answers and done quite a bit of experimentation with toy data sets to
figure out my issue, and I haven't been able to resolve it.

I'm running linear mixed effects models on a large, sparse dataset in
which I'm regressing reaction time (a continuous variable) on several
categorical factors: Block (Block1/Block2/Block3), Group
(monolingual/bilingual), and Type (target/nontarget).

As a way of examining simple effects, I am dummy-coding specific
factors, setting each level of a given factor as the reference level
in turn. For example, I generate three models with each of the three
levels of Block coded as the reference level, without changing the
codings of the other factors:

## Model with Block 1 as reference level
contrasts(nback.low$Group) <- c(1, 0) # monoling ref
contrasts(nback.low$Type) <- c(1, -1)
contrasts(nback.low$Block) <- matrix(c(0, 1, 0, 0, 0, 1), ncol=2) #B1
ref, B2: 1, B3: 2
glmerNL.RS.SI_RTgxb1 <- glmer(WinRTs~(Group*Block*Type) +
(1+Block+Type|Subject) + (1+Group+Block|Item),data=nback.low)

## Model with Block 2 as reference level
contrasts(nback.low$Group) <- c(1, 0) # monoling ref
contrasts(nback.low$Type) <- c(1, -1)
contrasts(nback.low$Block) <- matrix(c(1, 0, 0, 0, 0, 1), ncol=2) #B2
ref, B1: 1, B3: 2
glmerNL.RS.SI_RTgxb2 <- glmer(WinRTs~(Group*Block*Type) +
(1+Block+Type|Subject) + (1+Group+Block|Item),data=nback.low)

## Model with Block 3 as reference level
contrasts(nback.low$Group) <- c(1, -1) # monoling 'ref'
contrasts(nback.low$Type) <- c(1, 0) # target ref
contrasts(nback.low$Block) <- matrix(c(1, 0, 0, 0, 1, 0), ncol=2) #B3
ref, B1: 1, B2: 2
glmerNL.RS.SI_RTbxt3 <- glmer(WinRTs~(Group*Block*Type) +
(1+Block+Type|Subject) + (1+Group+Block|Item),data=nback.low)
summary(glmerNL.RS.SI_RTbxt3)

The issue I'm having is that contrasts that I believe should be
identical are not. Below are summaries of the three
models. You can see that the estimate of the fixed effect of Block1
(the contrast between Block 1 and Block 2) is -117.98 in the first
model and 118.478 in the second model. To my understanding, they
should be identical except for the sign. Similar discrepancies can be
seen in the other Block contrasts.

There are two subjects who have no data at Block 1, so I removed them
and re-ran the models, but the same issue occurred. Separately, I
removed the random effects for Item, without removing those two
subjects, and when I did that the discrepancies disappeared. I have a
feeling this means that my models are too complex for my data, but I'm
not sure what I should look at to (dis)confirm this hunch or how
exactly to proceed if that is the case. (As an example of the
sparseness of the data, items are repeated across subjects, but each
subject has only one data point per item, or zero data points per item
for trials where they didn't respond correctly. However, I didn't get
any warnings about model convergence, or any warnings at
all.)

Any clues  as to why I'm getting this results would be
very much appreciated.

Thanks in advance,

Alan Mishler
Research Assistant
University of Maryland
--
## Model 1 output: Block 1 as reference level ##
> glmerNL.RS.SI_RTgxb1
Linear mixed model fit by REML
Formula: WinRTs ~ (Group * Block * Type) + (1 + Block + Type |
Subject) +      (1 + Group + Block | Item)
   Data: nback.low
    AIC    BIC logLik deviance REMLdev
 181965 182210 -90949   181990  181899

Random effects:
 Groups   Name        Variance  Std.Dev. Corr
 Item     (Intercept)   6134.64  78.324
          Group1        2336.31  48.335  -1.000
          Block1        1759.56  41.947   1.000 -1.000
          Block2         846.06  29.087   0.771 -0.771  0.771
 Subject  (Intercept) 132462.22 363.954
          Block1        6011.83  77.536  -0.034
          Block2       10883.42 104.324  -0.127  0.915
          Type1        13653.97 116.850  -0.194  0.260  0.109
 Residual              97048.54 311.526
Number of obs: 12640, groups: Item, 288; Subject, 52

Fixed effects:
                    Estimate Std. Error t value
(Intercept)          1016.73      73.39  13.855
Group1                 12.39     101.67   0.122
Block1               -117.98      18.97  -6.220
Block2               -175.96      23.60  -7.455
Type1                -136.36      24.96  -5.463
Group1:Block1          46.43      26.05   1.782
Group1:Block2          76.70      32.53   2.358
Group1:Type1           20.55      34.15   0.602
Block1:Type1           62.16      10.47   5.934
Block2:Type1           96.66      10.46   9.243
Group1:Block1:Type1   -18.39      14.05  -1.309
Group1:Block2:Type1   -39.94      14.13  -2.826

Correlation of Fixed Effects:
            (Intr) Group1 Block1 Block2 Type1  Gr1:B1 Gr1:B2 Gr1:T1
Bl1:T1 Bl2:T1 G1:B1:
Group1      -0.721
Block1      -0.065  0.049
Block2      -0.146  0.106  0.815
Type1       -0.186  0.134  0.219  0.106
Grop1:Blck1  0.053 -0.074 -0.715 -0.587 -0.160
Grop1:Blck2  0.108 -0.150 -0.586 -0.721 -0.077  0.818
Group1:Typ1  0.136 -0.189 -0.160 -0.078 -0.721  0.226  0.110
Block1:Typ1  0.012 -0.009 -0.086 -0.038 -0.163  0.063  0.028  0.131
Block2:Typ1  0.013 -0.009 -0.051 -0.070 -0.189  0.037  0.051  0.144
0.533
Grp1:Bl1:T1 -0.009  0.013  0.064  0.028  0.153 -0.090 -0.043 -0.216
-0.702 -0.371
Grp1:Bl2:T1 -0.010  0.014  0.038  0.052  0.156 -0.055 -0.072 -0.218
-0.371 -0.717  0.527

## Model 2 output: Block 2 as reference level ##
> glmerNL.RS.SI_RTgxb2 [Block 2 as reference level]
Linear mixed model fit by REML
Formula: WinRTs ~ (Group * Block * Type) + (1 + Block + Type |
Subject) +      (1 + Group + Block | Item)
   Data: nback.low
    AIC    BIC logLik deviance REMLdev
 181931 182177 -90933   181957  181865

Random effects:
 Groups   Name        Variance  Std.Dev. Corr
 Item     (Intercept)  14663.50 121.093
          Group1        2400.09  48.991  -1.000
          Block1        6561.73  81.004  -0.582  0.582
          Block2         590.58  24.302  -0.677  0.677 -0.205
 Subject  (Intercept) 136638.85 369.647
          Block1        5868.05  76.603  -0.172
          Block2        2128.70  46.138  -0.146 -0.388
          Type1        13788.61 117.425  -0.140 -0.259 -0.188
 Residual              95743.04 309.424
Number of obs: 12640, groups: Item, 288; Subject, 52

Fixed effects:
                    Estimate Std. Error t value
(Intercept)          898.925     74.610  12.048
Group1                58.779    103.098   0.570
Block1               118.478     19.267   6.149
Block2               -58.059     13.680  -4.244
Type1                -74.323     25.553  -2.909
Group1:Block1        -46.515     25.799  -1.803
Group1:Block2         30.232     18.734   1.614
Group1:Type1           2.166     34.141   0.063
Block1:Type1         -64.291     11.246  -5.717
Block2:Type1          33.892     10.045   3.374
Group1:Block1:Type1   19.392     13.995   1.386
Group1:Block2:Type1  -21.160     13.634  -1.552

Correlation of Fixed Effects:
            (Intr) Group1 Block1 Block2 Type1  Gr1:B1 Gr1:B2 Gr1:T1
Bl1:T1 Bl2:T1 G1:B1:
Group1      -0.720
Block1      -0.183  0.126
Block2      -0.152  0.108 -0.033
Type1       -0.132  0.096 -0.174 -0.095
Grop1:Blck1  0.126 -0.176 -0.699  0.019  0.130
Grop1:Blck2  0.106 -0.147  0.021 -0.722  0.070 -0.030
Group1:Typ1  0.099 -0.137  0.130  0.071 -0.714 -0.188 -0.102
Block1:Typ1  0.009 -0.007 -0.079 -0.049 -0.239  0.059  0.036  0.148
Block2:Typ1  0.010 -0.008 -0.036 -0.107 -0.219  0.027  0.079  0.152
0.416
Grp1:Bl1:T1 -0.008  0.010  0.063  0.040  0.137 -0.092 -0.050 -0.194
-0.655 -0.345
Grp1:Bl2:T1 -0.008  0.010  0.026  0.079  0.141 -0.036 -0.101 -0.200
-0.315 -0.722  0.482

## Model 3 output: Block 3 as reference level ##
> glmerNL.RS.SI_RTgxb3 [Block 3 as reference level]
Linear mixed model fit by REML
Formula: WinRTs ~ (Group * Block * Type) + (1 + Block + Type |
Subject) +      (1 + Group + Block | Item)
   Data: nback.low
    AIC    BIC logLik deviance REMLdev
 181932 182177 -90933   181958  181866

Random effects:
 Groups   Name        Variance  Std.Dev. Corr
 Item     (Intercept)  11296.69 106.286
          Group1        2419.00  49.183  -1.000
          Block1        7418.92  86.133  -0.522  0.522
          Block2         494.56  22.239   0.596 -0.596  0.373
 Subject  (Intercept) 133759.20 365.731
          Block1       10713.51 103.506  -0.153
          Block2        2123.58  46.082   0.021  0.733
          Type1        13764.21 117.321  -0.165 -0.107  0.189
 Residual              95762.39 309.455
Number of obs: 12640, groups: Item, 288; Subject, 52

Fixed effects:
                    Estimate Std. Error t value
(Intercept)           840.86      73.76  11.399
Group1                 89.07     102.02   0.873
Block1                176.58      23.92   7.381
Block2                 58.07      13.66   4.251
Type1                 -40.40      25.30  -1.597
Group1:Block1         -76.71      32.29  -2.376
Group1:Block2         -30.30      18.72  -1.618
Group1:Type1          -18.88      34.08  -0.554
Block1:Type1          -98.00      11.46  -8.555
Block2:Type1          -33.93      10.03  -3.382
Group1:Block1:Type1    40.12      14.06   2.853
Group1:Block2:Type1    21.06      13.63   1.545

Correlation of Fixed Effects:
            (Intr) Group1 Block1 Block2 Type1  Gr1:B1 Gr1:B2 Gr1:T1
Bl1:T1 Bl2:T1 G1:B1:
Group1      -0.720
Block1      -0.170  0.119
Block2      -0.031  0.024  0.595
Type1       -0.156  0.113 -0.073  0.138
Grop1:Blck1  0.119 -0.164 -0.706 -0.434  0.054
Grop1:Blck2  0.026 -0.034 -0.429 -0.723 -0.101  0.603
Group1:Typ1  0.116 -0.161  0.054 -0.102 -0.717 -0.079  0.142
Block1:Typ1  0.009 -0.006 -0.063 -0.045 -0.231  0.047  0.034  0.148
Block2:Typ1  0.009 -0.007 -0.032 -0.107 -0.177  0.024  0.079  0.138
0.461
Grp1:Bl1:T1 -0.007  0.009  0.052  0.037  0.141 -0.073 -0.048 -0.195
-0.651 -0.357
Grp1:Bl2:T1 -0.007  0.009  0.025  0.079  0.144 -0.030 -0.101 -0.200
-0.324 -0.723  0.490



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