1 Hypothesis

We measured cross-situational word learning children with DLD as well as different types of lexical proficiency. We want to test whether the ability of learning word-referent pairs in a CSWL task correlates with abilities underlying building up a mental lexicon (N=26).

2 Data preparation

2.1 Load data

CSL_cor <- read.delim("Data/CSL_regression_DLD.txt")

2.2 Summary of the data

summary(CSL_cor)
##    Subject           Condition          CSL_offline       Age_months    
##  Length:26          Length:26          Min.   :0.1250   Min.   : 86.00  
##  Class :character   Class :character   1st Qu.:0.3750   1st Qu.: 91.25  
##  Mode  :character   Mode  :character   Median :0.5000   Median : 96.50  
##                                        Mean   :0.4904   Mean   : 97.04  
##                                        3rd Qu.:0.6250   3rd Qu.:102.75  
##                                        Max.   :0.8750   Max.   :111.00  
##                                                                         
##   Vocab_Active    DigitSpan_FW    DigitSpan_BW   DigitSpan_Tot   
##  Min.   : 8.00   Min.   :3.000   Min.   :0.000   Min.   : 4.000  
##  1st Qu.:21.25   1st Qu.:4.000   1st Qu.:2.000   1st Qu.: 7.000  
##  Median :27.50   Median :5.000   Median :3.000   Median : 8.000  
##  Mean   :28.19   Mean   :5.385   Mean   :2.654   Mean   : 8.038  
##  3rd Qu.:36.00   3rd Qu.:6.000   3rd Qu.:3.000   3rd Qu.: 9.000  
##  Max.   :41.00   Max.   :9.000   Max.   :4.000   Max.   :12.000  
##                                                                  
##       NWR        Vocab_Passive        Raven       WordAssociations
##  Min.   :0.000   Min.   : 70.00   Min.   :11.00   Min.   :10.00   
##  1st Qu.:2.000   1st Qu.: 80.25   1st Qu.:17.75   1st Qu.:21.00   
##  Median :3.000   Median : 91.50   Median :23.00   Median :23.00   
##  Mean   :3.385   Mean   : 90.65   Mean   :23.12   Mean   :23.81   
##  3rd Qu.:4.000   3rd Qu.: 97.75   3rd Qu.:27.75   3rd Qu.:27.00   
##  Max.   :9.000   Max.   :119.00   Max.   :38.00   Max.   :42.00   
##                                                                   
##  RepeatingSentences WordCategories_Exp WordCategories_Rec WordCategories_Tot
##  Min.   : 4.00      Min.   : 1.000     Min.   : 2.000     Min.   : 1.000    
##  1st Qu.:13.00      1st Qu.: 5.000     1st Qu.: 5.000     1st Qu.: 5.000    
##  Median :18.00      Median : 7.000     Median : 7.000     Median : 6.000    
##  Mean   :18.68      Mean   : 6.654     Mean   : 7.038     Mean   : 6.654    
##  3rd Qu.:22.00      3rd Qu.: 7.750     3rd Qu.:10.000     3rd Qu.: 8.000    
##  Max.   :42.00      Max.   :13.000     Max.   :12.000     Max.   :13.000    
##  NA's   :1                                                                  
##     Group               CSL_ET            SES         
##  Length:26          Min.   :0.4142   Min.   :-1.9553  
##  Class :character   1st Qu.:0.4785   1st Qu.:-1.1716  
##  Mode  :character   Median :0.5269   Median :-0.2289  
##                     Mean   :0.5450   Mean   :-0.3004  
##                     3rd Qu.:0.5900   3rd Qu.: 0.3707  
##                     Max.   :0.7988   Max.   : 1.5239  
##

2.3 Histogram predictor variables: accuracy CSL task off-line

Visualization of the predictor variables reflecting cross-situational word learning in children with DLD

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p

2.4 Histogram predictor variables: accuracy CSWL eye-tracking

p <-
  ggplot(plot_ET, aes(x=CSL_ET))+
  geom_histogram(fill="gray", alpha=.4, binwidth=0.04)+
  labs(y="Count", x="Proportion looking at the correct referent", title="Histogram eye-tracking accuracy during CSL task")+
  theme_bw()
ggsave("Graphs/Histogram_accuracy_CSL_online.png")
## Saving 7 x 5 in image
p

2.5 Are predictor variables (offline/online CSL) correlated?

lmpredictors <- lm(CSL_offline~CSL_ET, CSL_cor)
summary(lmpredictors)
## 
## Call:
## lm(formula = CSL_offline ~ CSL_ET, data = CSL_cor)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.36094 -0.10223  0.01377  0.12799  0.41989 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)
## (Intercept)   0.2608     0.2452   1.063    0.298
## CSL_ET        0.4213     0.4435   0.950    0.352
## 
## Residual standard error: 0.2123 on 24 degrees of freedom
## Multiple R-squared:  0.03624,    Adjusted R-squared:  -0.003915 
## F-statistic: 0.9025 on 1 and 24 DF,  p-value: 0.3516

3 Variable reduction: Principal component analysis

3.1 Standardize variables

CSL_cor$CSL_offline <- scale(CSL_cor$CSL_offline, center = T, scale = T)
CSL_cor$CSL_ET <- scale(CSL_cor$CSL_ET, center = T, scale = T)
CSL_cor$Vocab_Active <- scale(CSL_cor$Vocab_Active, center = T, scale = T)
CSL_cor$Vocab_Passive <- scale(CSL_cor$Vocab_Passive, center = T, scale = T)
CSL_cor$WordCategories_Tot <- scale(CSL_cor$WordCategories_Tot, center = T, scale = T)
CSL_cor$WordAssociations<- scale(CSL_cor$WordAssociations, center = T, scale = T)
CSL_cor$DigitSpan_FW <- scale(CSL_cor$DigitSpan_FW, center = T, scale = T)
CSL_cor$DigitSpan_BW <- scale(CSL_cor$DigitSpan_BW, center = T, scale = T)
CSL_cor$NWR <- scale(CSL_cor$NWR, center = T, scale = T)
CSL_cor$Raven <- scale(CSL_cor$Raven, center = T, scale = T)
CSL_cor$Age_months <- scale(CSL_cor$Age_months, center = T, scale = T)
CSL_cor$SES <- scale(CSL_cor$SES, center = T, scale = T)

3.2 PCA

#Make dataframe with predictor values
Pred <- subset(CSL_cor, select=c("DigitSpan_FW","DigitSpan_BW", "NWR", "Raven"))
fit <- princomp(Pred, cor=TRUE)
summary(fit) # print variance accounted for
## Importance of components:
##                           Comp.1    Comp.2    Comp.3     Comp.4
## Standard deviation     1.3371239 1.1950668 0.7765735 0.42526312
## Proportion of Variance 0.4469751 0.3570461 0.1507666 0.04521218
## Cumulative Proportion  0.4469751 0.8040212 0.9547878 1.00000000
plot(fit,type="lines") # scree plot

The four components explain 44% and 36%, 15% and 5% of the variance respectively. We run a varimax rotated PCA for 3 components.

3.3 Varimax rotated PCA for 3 components

pca <- principal(Pred, nfactors=3, rotate="varimax")
pca
## Principal Components Analysis
## Call: principal(r = Pred, nfactors = 3, rotate = "varimax")
## Standardized loadings (pattern matrix) based upon correlation matrix
##                RC1   RC2  RC3   h2      u2 com
## DigitSpan_FW  0.93 -0.22 0.03 0.91 0.08761 1.1
## DigitSpan_BW  0.04  0.21 0.98 1.00 0.00084 1.1
## NWR           0.95  0.13 0.02 0.92 0.07977 1.0
## Raven        -0.05  0.97 0.22 0.99 0.01264 1.1
## 
##                        RC1  RC2  RC3
## SS loadings           1.77 1.05 1.00
## Proportion Var        0.44 0.26 0.25
## Cumulative Var        0.44 0.70 0.95
## Proportion Explained  0.46 0.27 0.26
## Cumulative Proportion 0.46 0.74 1.00
## 
## Mean item complexity =  1.1
## Test of the hypothesis that 3 components are sufficient.
## 
## The root mean square of the residuals (RMSR) is  0.04 
##  with the empirical chi square  0.48  with prob <  NA 
## 
## Fit based upon off diagonal values = 0.99

The first component seems to represent phonological short-term memory (digit span forwards and non-word repetition). The other components represent the variables non-verbal intelligence (Raven) and verbal working memory (digit span backwards). We save the components for further analyses.

CSL_cor <- cbind(CSL_cor, pca$scores)
colnames(CSL_cor)[colnames(CSL_cor)=="RC1"] <- "C_PhonProc"
colnames(CSL_cor)[colnames(CSL_cor)=="RC2"] <- "C_NonVerbInt"
colnames(CSL_cor)[colnames(CSL_cor)=="RC3"] <- "C_VerbWM"

4 Regression analyses

4.1 Check correlations between predictors

Pred <- subset(CSL_cor, select=c("CSL_offline","CSL_ET","C_NonVerbInt", "C_PhonProc","C_VerbWM", "Age_months", "SES"))
rcorr(as.matrix(Pred), type="pearson")
##              CSL_offline CSL_ET C_NonVerbInt C_PhonProc C_VerbWM Age_months
## CSL_offline         1.00   0.19         0.38      -0.28    -0.01      -0.06
## CSL_ET              0.19   1.00         0.41      -0.26    -0.05      -0.30
## C_NonVerbInt        0.38   0.41         1.00       0.00     0.00      -0.20
## C_PhonProc         -0.28  -0.26         0.00       1.00     0.00       0.11
## C_VerbWM           -0.01  -0.05         0.00       0.00     1.00       0.12
## Age_months         -0.06  -0.30        -0.20       0.11     0.12       1.00
## SES                -0.15   0.11         0.01       0.05    -0.30       0.15
##                SES
## CSL_offline  -0.15
## CSL_ET        0.11
## C_NonVerbInt  0.01
## C_PhonProc    0.05
## C_VerbWM     -0.30
## Age_months    0.15
## SES           1.00
## 
## n= 26 
## 
## 
## P
##              CSL_offline CSL_ET C_NonVerbInt C_PhonProc C_VerbWM Age_months
## CSL_offline              0.3516 0.0583       0.1724     0.9654   0.7668    
## CSL_ET       0.3516             0.0395       0.2030     0.7973   0.1300    
## C_NonVerbInt 0.0583      0.0395              1.0000     1.0000   0.3323    
## C_PhonProc   0.1724      0.2030 1.0000                  1.0000   0.5813    
## C_VerbWM     0.9654      0.7973 1.0000       1.0000              0.5725    
## Age_months   0.7668      0.1300 0.3323       0.5813     0.5725             
## SES          0.4508      0.6016 0.9561       0.8271     0.1340   0.4642    
##              SES   
## CSL_offline  0.4508
## CSL_ET       0.6016
## C_NonVerbInt 0.9561
## C_PhonProc   0.8271
## C_VerbWM     0.1340
## Age_months   0.4642
## SES

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4.2 LM Passive vocabulary

model.passvocab <- lm(Vocab_Passive~Age_months+SES+C_NonVerbInt+C_PhonProc+C_VerbWM+CSL_offline+CSL_ET, data=CSL_cor)
tab_model(model.passvocab,  show.se = T, show.stat = T, show.df = T,df.method = "satterthwaite", digits.p = 3)
  Vocab_Passive
Predictors Estimates std. Error CI Statistic p df
(Intercept) -0.00 0.21 -0.43 – 0.43 -0.00 1.000 18.00
Age months 0.15 0.23 -0.33 – 0.63 0.65 0.523 18.00
SES 0.16 0.23 -0.33 – 0.64 0.68 0.507 18.00
C NonVerbInt 0.14 0.25 -0.39 – 0.67 0.56 0.584 18.00
C PhonProc 0.25 0.23 -0.23 – 0.74 1.10 0.284 18.00
C VerbWM 0.11 0.22 -0.37 – 0.58 0.47 0.644 18.00
CSL offline 0.22 0.24 -0.28 – 0.73 0.93 0.366 18.00
CSL ET -0.19 0.25 -0.71 – 0.34 -0.75 0.464 18.00
Observations 26
R2 / R2 adjusted 0.209 / -0.098

4.3 LM Active vocabulary

model.actvocab <- lm(Vocab_Active~Age_months+SES+C_NonVerbInt+C_PhonProc+C_VerbWM+CSL_offline+CSL_ET, data=CSL_cor)
tab_model(model.actvocab,  show.se = T, show.stat = T, show.df = T,df.method = "satterthwaite", digits.p = 3)
  Vocab_Active
Predictors Estimates std. Error CI Statistic p df
(Intercept) -0.00 0.19 -0.40 – 0.40 -0.00 1.000 18.00
Age months 0.22 0.21 -0.22 – 0.67 1.05 0.306 18.00
SES 0.37 0.22 -0.09 – 0.82 1.70 0.107 18.00
C NonVerbInt 0.13 0.23 -0.36 – 0.62 0.57 0.573 18.00
C PhonProc 0.27 0.21 -0.18 – 0.71 1.25 0.227 18.00
C VerbWM 0.04 0.21 -0.40 – 0.47 0.18 0.860 18.00
CSL offline 0.09 0.22 -0.39 – 0.56 0.38 0.708 18.00
CSL ET -0.12 0.23 -0.61 – 0.37 -0.52 0.609 18.00
Observations 26
R2 / R2 adjusted 0.317 / 0.052

4.4 LM Word categories

model.wordcat <- lm(WordCategories_Tot~Age_months+SES+C_NonVerbInt+C_PhonProc+C_VerbWM+CSL_offline+CSL_ET, data=CSL_cor)
tab_model(model.wordcat,  show.se = T, show.stat = T, show.df = T,df.method = "satterthwaite", digits.p = 3)
  WordCategories_Tot
Predictors Estimates std. Error CI Statistic p df
(Intercept) 0.00 0.18 -0.37 – 0.37 0.00 1.000 18.00
Age months -0.37 0.20 -0.78 – 0.05 -1.87 0.077 18.00
SES 0.04 0.20 -0.38 – 0.46 0.19 0.848 18.00
C NonVerbInt 0.32 0.22 -0.13 – 0.78 1.49 0.153 18.00
C PhonProc -0.18 0.20 -0.59 – 0.24 -0.90 0.382 18.00
C VerbWM 0.18 0.19 -0.22 – 0.59 0.96 0.350 18.00
CSL offline 0.22 0.21 -0.22 – 0.65 1.04 0.311 18.00
CSL ET -0.10 0.21 -0.55 – 0.35 -0.48 0.639 18.00
Observations 26
R2 / R2 adjusted 0.415 / 0.188

4.5 LM Word associations

model.wordass <- lm(WordAssociations~Age_months+SES+C_NonVerbInt+C_PhonProc+C_VerbWM+CSL_offline+CSL_ET, data=CSL_cor)
tab_model(model.wordass,  show.se = T, show.stat = T, show.df = T,df.method = "satterthwaite", digits.p = 3)
  WordAssociations
Predictors Estimates std. Error CI Statistic p df
(Intercept) 0.00 0.20 -0.42 – 0.42 0.00 1.000 18.00
Age months -0.05 0.23 -0.53 – 0.42 -0.24 0.816 18.00
SES 0.24 0.23 -0.24 – 0.72 1.05 0.306 18.00
C NonVerbInt 0.22 0.25 -0.30 – 0.74 0.88 0.389 18.00
C PhonProc 0.00 0.23 -0.47 – 0.48 0.02 0.983 18.00
C VerbWM -0.23 0.22 -0.69 – 0.23 -1.03 0.315 18.00
CSL offline 0.05 0.24 -0.45 – 0.55 0.22 0.825 18.00
CSL ET -0.38 0.24 -0.90 – 0.13 -1.57 0.134 18.00
Observations 26
R2 / R2 adjusted 0.237 / -0.060