Distributional learning of novel visual object categories in children with and without developmental language disorder: Data analysis group comparison.
Iris Broedelet
29 September 2020
1 Hypotheses
Participants (25 children with DLD, 25 TD children) are subjected to either Condition 1 or Condition 2 (between-subjects) of the learning phase, during which they see tokens from the continuum (stimuli 1-11). Participants in Condition 1 are hypothesized to categorize stimuli S and D2 together, while participants in Condition 2 are hypothesized to categorize stimuli S and D1 together. In the test phase (8 test items), participants were asked which stimulus looked more like stimulus S: stimulus D1 or stimulus D2. A significant main effect of Condition would indicate a learning effect: Condition 1 participants are expected to have a larger preference for stimulus D2 than Condition 2 participants. We expect that this effect of Condition will be weaker in children with DLD compared to the TD children (significant interaction between Condition and Group).
2 Load data
CAT_Test <- read.delim("CAT_Test.txt")
head(CAT_Test)## Subject Condition Trial Item ACC StimRef StimLeft StimRight Target RT
## 1 501 Condition 1 2 1 0 S D2 D1 D2 2287
## 2 501 Condition 1 3 7 0 S D2 D1 D2 3803
## 3 501 Condition 1 4 5 0 S D2 D1 D2 2696
## 4 501 Condition 1 6 6 0 S D1 D2 D2 3585
## 5 501 Condition 1 7 2 0 S D1 D2 D2 2224
## 6 501 Condition 1 9 8 0 S D1 D2 D2 3677
## AnswerStim PositionD2 AnswerStimD1 AnswerStimD2 MeanAccPP Gender Group
## 1 D1 Left 1 0 0 F TD
## 2 D1 Left 1 0 0 F TD
## 3 D1 Left 1 0 0 F TD
## 4 D1 Right 1 0 0 F TD
## 5 D1 Right 1 0 0 F TD
## 6 D1 Right 1 0 0 F TD
## Age_months Age_ym
## 1 100 8;4
## 2 100 8;4
## 3 100 8;4
## 4 100 8;4
## 5 100 8;4
## 6 100 8;42.1 Age check
#Age (months) per group
tapply(CAT_Test$Age_months, list(CAT_Test$Group), mean, na.rm=TRUE)## DLD TD
## 96.56 97.64tapply(CAT_Test$Age_months, list(CAT_Test$Group), sd, na.rm=TRUE)## DLD TD
## 6.491308 4.999538t.test(CAT_Test$Age_months~CAT_Test$Group)##
## Welch Two Sample t-test
##
## data: CAT_Test$Age_months by CAT_Test$Group
## t = -1.8641, df = 373.64, p-value = 0.06309
## alternative hypothesis: true difference in means between group DLD and group TD is not equal to 0
## 95 percent confidence interval:
## -2.21922219 0.05922219
## sample estimates:
## mean in group DLD mean in group TD
## 96.56 97.64There is no significant age difference between groups.
3 Plot
Plot the stimulus choice (D1/D2) per Condition and Group
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4 Data analysis
4.1 Set contrasts and center Age
#Condition
CAT_Test$Condition <- as.factor(CAT_Test$Condition)
contrast <- cbind(c(+0.5, -0.5)) # Condition 1, Condition 2
colnames (contrast) <- c("-Condition2+Condition1")
contrasts (CAT_Test$Condition) <- contrast
contrasts(CAT_Test$Condition)## -Condition2+Condition1
## Condition 1 0.5
## Condition 2 -0.5#Group
CAT_Test$Group <- as.factor(CAT_Test$Group)
contrast <- cbind(c(-0.5, +0.5)) # DLD, TD
colnames (contrast) <- c("-DLD+TD")
contrasts (CAT_Test$Group) <- contrast
contrasts(CAT_Test$Group)## -DLD+TD
## DLD -0.5
## TD 0.5#PositionD2: whether token D2 was positioned left or right in the test questions
CAT_Test$PositionD2 <- as.factor(CAT_Test$PositionD2)
contrast <- cbind(c(+0.5, -0.5)) # Left, Right
colnames (contrast) <- c("+Left-Right")
contrasts (CAT_Test$PositionD2) <- contrast
contrasts(CAT_Test$PositionD2)## +Left-Right
## Left 0.5
## Right -0.5#Age
CAT_Test$Age_months <- scale(CAT_Test["Age_months"],center=T,scale=F)4.2 Generalized mixed effects model
Testing whether odds of choosing for stimulus D2 depend on Condition and Group. Expectation: participants in Condition 1 are more likely to choose stimulus D2 than in Condition 2. A significant positive main effect of Condition on the odds of choosing stimulus D2 would show a learning effect. A significant interaction between Condition and Group would show that this learning effect is different for the two groups. PositionD2 is added as a within-participant variable, reflecting the position of token D2 (left or right) that varied between test items.
fullmodel <- glmer(AnswerStimD2~Condition*Group*Age_months + Condition*PositionD2+(PositionD2|Subject), data=CAT_Test, family = binomial, control=glmerControl(optimizer="bobyqa", optCtrl=list(maxfun=2e5)))
summary(fullmodel)## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: binomial ( logit )
## Formula:
## AnswerStimD2 ~ Condition * Group * Age_months + Condition * PositionD2 +
## (PositionD2 | Subject)
## Data: CAT_Test
## Control: glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 2e+05))
##
## AIC BIC logLik deviance df.resid
## 445.8 497.7 -209.9 419.8 387
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.9002 -0.5204 -0.2933 0.5531 3.0038
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## Subject (Intercept) 1.8189 1.3487
## PositionD2+Left-Right 0.4132 0.6428 -0.79
## Number of obs: 400, groups: Subject, 50
##
## Fixed effects:
## Estimate Std. Error
## (Intercept) -1.205520 0.262462
## Condition-Condition2+Condition1 1.396512 0.506359
## Group-DLD+TD 0.576854 0.489379
## Age_months -0.033864 0.042227
## PositionD2+Left-Right 0.602817 0.360215
## Condition-Condition2+Condition1:Group-DLD+TD 0.006743 0.971575
## Condition-Condition2+Condition1:Age_months -0.065209 0.094284
## Group-DLD+TD:Age_months 0.007933 0.088645
## Condition-Condition2+Condition1:PositionD2+Left-Right -0.122360 0.627916
## Condition-Condition2+Condition1:Group-DLD+TD:Age_months -0.349615 0.209861
## z value Pr(>|z|)
## (Intercept) -4.593 4.37e-06 ***
## Condition-Condition2+Condition1 2.758 0.00582 **
## Group-DLD+TD 1.179 0.23850
## Age_months -0.802 0.42259
## PositionD2+Left-Right 1.673 0.09423 .
## Condition-Condition2+Condition1:Group-DLD+TD 0.007 0.99446
## Condition-Condition2+Condition1:Age_months -0.692 0.48917
## Group-DLD+TD:Age_months 0.089 0.92869
## Condition-Condition2+Condition1:PositionD2+Left-Right -0.195 0.84550
## Condition-Condition2+Condition1:Group-DLD+TD:Age_months -1.666 0.09573 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) Cn-C2+C1 Gr-DLD+TD Ag_mnt PD2+L- Cn-C2+C1:G-DLD+TD
## Cndtn-C2+C1 -0.180
## Grop-DLD+TD -0.051 -0.005
## Age_months -0.035 0.039 -0.124
## PstnD2+Lf-R -0.313 0.075 0.141 0.010
## Cn-C2+C1:G-DLD+TD -0.014 -0.017 -0.169 0.197 -0.114
## Cn-C2+C1:A_ -0.003 -0.014 0.284 0.088 0.250 -0.212
## G-DLD+TD:A_ -0.145 0.204 0.033 0.223 0.164 -0.027
## C-C2+C1:PD2 0.078 -0.284 -0.087 -0.019 -0.347 0.083
## C-C2+C1:G-DLD+TD: 0.120 -0.082 0.165 -0.031 0.338 -0.160
## C-C2+C1:A G-DLD+TD: C-C2+C1:P
## Cndtn-C2+C1
## Grop-DLD+TD
## Age_months
## PstnD2+Lf-R
## Cn-C2+C1:G-DLD+TD
## Cn-C2+C1:A_
## G-DLD+TD:A_ 0.084
## C-C2+C1:PD2 -0.183 -0.117
## C-C2+C1:G-DLD+TD: 0.426 0.241 -0.252isSingular(fullmodel)## [1] FALSE4.3 Compute CIs
4.3.1 CI for Condition effect
### Compute confidence intervals for the Condition effect
ci <- confint (model1, parm = "Condition-Condition2+Condition1")
lower.bound.logodds.model1 <- ci ["Condition-Condition2+Condition1", 1]
upper.bound.logodds.model1 <- ci ["Condition-Condition2+Condition1", 2]
lower.bound.odds.model1 <- exp(lower.bound.logodds.model1)
upper.bound.odds.model1 <- exp(upper.bound.logodds.model1)
#Estimate and CI Condition effect:
exp(1.396512) # 4.04108
lower.bound.odds.model1 #1.497903
upper.bound.odds.model1 #10.902144.3.2 CI for Condition * Group interaction
### Compute confidence intervals for the Condition * Group effect
ci <- confint (model1, parm = "Condition-Condition2+Condition1:Group-DLD+TD")
lower.bound.logodds.model1 <- ci ["Condition-Condition2+Condition1:Group-DLD+TD", 1]
upper.bound.logodds.model1 <- ci ["Condition-Condition2+Condition1:Group-DLD+TD", 2]
lower.bound.odds.model1 <- exp(lower.bound.logodds.model1)
upper.bound.odds.model1 <- exp(upper.bound.logodds.model1)
#Estimate and CI Condition * Group effect:
exp(0.006743) # 1.006766
lower.bound.odds.model1 #0.1499417
upper.bound.odds.model1 #6.7598124.4 Report
Our results show that Condition significantly influences the choice for stimulus D2. Children in Condition 1 were 4.04 (95% CI 1.497 … 10.9) times more likely to choose stimulus D2 than children in Condition 2: z = 2.758, p = 0.006. This effect shows that, as we predicted, children in Condition 1 were more likely to categorize stimulus S and D2 together than children in Condition 2, indicating that Dutch school-aged children can learn novel visual object categories based on distributional properties.
Our second prediction does not hold: although the effect of Condition is 1.007 (95 CI: 0.15 … 6.76) times stronger in the TD group compared to the DLD group, the interaction between Condition and Group is not significant (z = 0.007, p = 0.994). We thus cannot conclude anything about a difference in distributional learning in children with DLD compared to TD children.
4.5 Model with only DLD group
If we run a distinct model with just the children with DLD, the effect of Condition does not reach significance.
modelDLD <- glmer(AnswerStimD2~Condition*Age_months*PositionD2+(1|Subject), data=subset(CAT_Test, Group=="DLD"), family = binomial, control=glmerControl(optimizer="bobyqa", optCtrl=list(maxfun=2e5)))
summary(modelDLD)## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: binomial ( logit )
## Formula: AnswerStimD2 ~ Condition * Age_months * PositionD2 + (1 | Subject)
## Data: subset(CAT_Test, Group == "DLD")
## Control: glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 2e+05))
##
## AIC BIC logLik deviance df.resid
## 217.3 247.0 -99.6 199.3 191
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.7491 -0.4726 -0.3421 0.5244 2.9231
##
## Random effects:
## Groups Name Variance Std.Dev.
## Subject (Intercept) 2.034 1.426
## Number of obs: 200, groups: Subject, 25
##
## Fixed effects:
## Estimate
## (Intercept) -1.45772
## Condition-Condition2+Condition1 1.32286
## Age_months -0.02640
## PositionD2+Left-Right 0.16609
## Condition-Condition2+Condition1:Age_months 0.13274
## Condition-Condition2+Condition1:PositionD2+Left-Right 0.60988
## Age_months:PositionD2+Left-Right -0.06786
## Condition-Condition2+Condition1:Age_months:PositionD2+Left-Right -0.05087
## Std. Error
## (Intercept) 0.38414
## Condition-Condition2+Condition1 0.73987
## Age_months 0.05711
## PositionD2+Left-Right 0.41181
## Condition-Condition2+Condition1:Age_months 0.11521
## Condition-Condition2+Condition1:PositionD2+Left-Right 0.82346
## Age_months:PositionD2+Left-Right 0.06338
## Condition-Condition2+Condition1:Age_months:PositionD2+Left-Right 0.12675
## z value
## (Intercept) -3.795
## Condition-Condition2+Condition1 1.788
## Age_months -0.462
## PositionD2+Left-Right 0.403
## Condition-Condition2+Condition1:Age_months 1.152
## Condition-Condition2+Condition1:PositionD2+Left-Right 0.741
## Age_months:PositionD2+Left-Right -1.071
## Condition-Condition2+Condition1:Age_months:PositionD2+Left-Right -0.401
## Pr(>|z|)
## (Intercept) 0.000148 ***
## Condition-Condition2+Condition1 0.073783 .
## Age_months 0.643910
## PositionD2+Left-Right 0.686709
## Condition-Condition2+Condition1:Age_months 0.249264
## Condition-Condition2+Condition1:PositionD2+Left-Right 0.458919
## Age_months:PositionD2+Left-Right 0.284302
## Condition-Condition2+Condition1:Age_months:PositionD2+Left-Right 0.688154
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) Cn-C2+C1 Ag_mnt PD2+L- Cn-C2+C1:A_ C-C2+C1:P A_:PD2
## Cndtn-C2+C1 -0.114
## Age_months 0.082 -0.186
## PstnD2+Lf-R -0.005 -0.038 0.051
## Cn-C2+C1:A_ -0.217 0.101 0.209 -0.006
## C-C2+C1:PD2 -0.065 0.025 -0.015 -0.177 0.060
## Ag_:PD2+L-R 0.078 -0.026 0.001 0.123 -0.064 -0.302
## C-C2+C1:A_: 0.018 0.037 -0.051 -0.302 -0.012 0.123 0.171isSingular(modelDLD)## [1] FALSE4.6 CIs for Condition effect model DLD
### Compute confidence intervals for the Condition effect
ci <- confint (modelDLD, parm = "Condition-Condition2+Condition1")
lower.bound.logodds.modelDLD <- ci ["Condition-Condition2+Condition1", 1]
upper.bound.logodds.modelDLD <- ci ["Condition-Condition2+Condition1", 2]
lower.bound.odds.modelDLD <- exp(lower.bound.logodds.modelDLD)
upper.bound.odds.modelDLD <- exp(upper.bound.logodds.modelDLD)
#Estimate and CI Condition effect:
exp(1.32286) # 3.754143
lower.bound.odds.modelDLD #0.8636995
upper.bound.odds.modelDLD #19.428264.7 Report DLD
Children with DLD in Condition 1 were 3.8 (95% CI 0.8 … 19.4) times more likely to choose stimulus D2 than children with DLD in Condition 2, but this effect is not significant: z = 1.788, p = 0.074.