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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