- Random intercept is needed whenever there are multiple observations per unit
- Any within-unit factor gets a random slope, unless there is only one observation per level per unit
- Between-unit factors do not get a random slope
- For each interaction, include a slope for the highest order combination of within-subject factors subsumed by the interaction
- For time-series data, include random slopes for time predictors if you have more than one time series per unit
- How do we explain referential misspecification?
- Retrieval of past descriptions from memory is an obligatory
consequence of attending to a referent with a referential goal in
mind
- Instance Theory of Automaticity (Logan, 1988)
- Retrieved descriptions checked against context for adequacy, and re-shaped if necessary
- Addressee: New or Old (Between)
- Novelty (of referent): New or Old
- Feedback: Yes or No
- 16 dyads (1 spkr, 1 addr)
- 16 triads (1 spkr, 2 addr)
library(lme4)
crefs <- readRDS("crefs.rds")
head(crefs, 3)
crefs_mit <- subset(crefs, ModInTrain)
with(crefs_mit, aggregate(Modifier ~ Novelty+Addressee+Feedback, FUN=mean))SessionID ItemID RespID Novelty Addressee Feedback ModInTrain Modifier SOT 1 56 2 6314 New New No TRUE 0 1462 2 56 3 6319 New New No TRUE 0 1126 3 56 7 6315 Old New No TRUE 1 1695 Novelty Addressee Feedback Modifier 1 New New No 0.10526316 2 Old New No 0.61224490 3 New Old No 0.08771930 4 Old Old No 0.75510204 5 New New Yes 0.06779661 6 Old New Yes 0.62500000 7 New Old Yes 0.06896552 8 Old Old Yes 0.76000000
| Subjects | Items | |
|---|---|---|
| Addressee | Between | Within |
| Novelty | Within | Within |
| Feedback | Within | Between |
xtabs(~Addressee+SessionID, crefs)
xtabs(~Addressee+ItemID, crefs)crefs_mit2 <- transform(crefs_mit, N=ifelse(Novelty=="New",1,0),
A=ifelse(Addressee=="New",1,0),
F=ifelse(Feedback=="Yes",1,0))
crefs_mit2c <- transform(crefs_mit2,
Nc=N-mean(N),
Ac=A-mean(A),
Fc=F-mean(F))
head(crefs_mit2c)
Our model: \(log\left(\frac{p_{ij}}{1-p{ij}}\right) &= β_0 + β_1 A + β_2 N + β_3 F + β_4 AN + β_5 AF + β_6 NF + β_7 ANF\)
| Subjects | Items | |
|---|---|---|
| Addressee | Between | Within |
| Novelty | Within | Within |
| Feedback | Within | Between |
m1 <- glmer(Modifier ~ Ac*Nc*Fc + (1 + Nc*Fc | SessionID) + (1 + Ac*Nc | ItemID),
data=crefs_mit2c, family=binomial(link="logit"),
control=glmerControl(optimizer="bobyqa"))
# takes a long time but doesn't converge
m1 <- glmer(Modifier ~ Ac*Nc*Fc +
(1 + Nc*Fc | SessionID) + (1 + Ac*Nc | ItemID),
crefs_mit2c, family=binomial(link="logit"),
control=glmerControl(optimizer="bobyqa")): Warning messages: : 1: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : : Model failed to converge with max|grad| = 0.01537 (tol = 0.001, component 20) : 2: In checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, : : Model is nearly unidentifiable: very large eigenvalue : - Rescale variables?;Model is nearly unidentifiable: large eigenvalue ratio : - Rescale variables?
# no-random-correlations model
m2 <- glmer(Modifier ~ Ac*Nc*Fc +
(1 + Nc*Fc || SessionID) + (1 + Ac*Nc || ItemID),
crefs_mit2c, family=binomial(link="logit"),
control=glmerControl(optimizer="bobyqa")) # convergesRandom effects:
Groups Name Variance Std.Dev.
SessionID (Intercept) 6.566e-01 8.103e-01
SessionID.1 Nc 1.132e+00 1.064e+00
SessionID.2 Fc 0.000e+00 0.000e+00
SessionID.3 Nc:Fc 4.297e-15 6.555e-08
ItemID (Intercept) 1.026e+00 1.013e+00
ItemID.1 Ac 1.580e-01 3.975e-01
ItemID.2 Nc 1.216e+00 1.103e+00
ItemID.3 Ac:Nc 0.000e+00 0.000e+00
Number of obs: 427, groups: SessionID, 32; ItemID, 16
Fixed effects:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -1.13298 0.35710 -3.173 0.00151 **
Ac -0.29116 0.46433 -0.627 0.53063
Nc -4.32096 0.61720 -7.001 2.54e-12 ***
Fc -0.38034 0.62448 -0.609 0.54249
Ac:Nc 1.05604 0.78602 1.344 0.17910
Ac:Fc -0.07195 0.71227 -0.101 0.91954
Nc:Fc -0.32425 0.89398 -0.363 0.71683
Ac:Nc:Fc -0.53686 1.33216 -0.403 0.68695
- get rid of REPs estimated to be zero because we’re using model comparison, and those could slow down the estimation procedure
m3 <- glmer(Modifier ~ Ac*Nc*Fc +
(1 | SessionID) +
(0 + Nc | SessionID) +
(1 | ItemID) +
(0 + Ac | ItemID) +
(0 + Nc | ItemID),
crefs_mit2c, family=binomial(link="logit"),
control=glmerControl(optimizer="bobyqa")) # convergesm3_noA <- update(m3, . ~ . - Ac)
m3_noN <- update(m3, . ~ . - Nc)
m3_noF <- update(m3, . ~ . - Fc)
m3_noAN <- update(m3, . ~ . - Ac:Nc)
m3_noAF <- update(m3, . ~ . - Ac:Fc)
m3_noNF <- update(m3, . ~ . - Nc:Fc)
m3_noANF <- update(m3, . ~ . - Ac:Nc:Fc)
anova(m3, m3_noA)
anova(m3, m3_noN)
anova(m3, m3_noF)
anova(m3, m3_noAN)
anova(m3, m3_noAF)
anova(m3, m3_noNF)
anova(m3, m3_noANF)| Chisq | Df | p | |
|---|---|---|---|
| A | .382 | 1 | .537 |
| N | 32.693 | 1 | <.001 |
| F | .372 | 1 | .542 |
| AN | 1.843 | 1 | .175 |
| AF | .010 | 1 | .920 |
| NF | .131 | 1 | .717 |
| ANF | .162 | 1 | .687 |
- Little evidence that the speaker took partner’s perspective into account
- Use of modifier driven by listener’s own experience
- Supports idea that modifier use is (at least partly) based on memory retrieval
- When performing (reviewing) analyses, it is of utmost importance to ensure random effects are appropriately specified
- Random-intercept-only models are rarely appropriate
- Use design-driven rather than data-driven random effects
- Development of
lme4is rapid, and there are many “tricks of the trade”; tune into blogs, mailing lists, and social media to keep up - Don’t give up! It will make sense… at some point…