Longitudinal_ana.Rmd

---
title: "Prediction of toddler vocabulary from infant speech and non-speech processing"
author: "Alejandrina Cristia"
date: "Main version 2020-07-30"
output: pdf_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
library(Hmisc) #for cor mat
library(brms) #used for bayesian ana
library(bayestestR) #used for bayesian ana
library(car) #used for outlier test
library(gvlma) #used for model test
library(MBESS) #used for tab5
library(apaTables) #used for tab5

#functions
zscore<-function(x) (x - mean(x,na.rm=T))/ sd(x,na.rm=T)

fit_uni_print <- function(mymodel, thisvar) {
  print(thisvar)
  print(plot(mymodel))
  pp_check(mymodel, nsamples = 1000)
  print(mymodel)
  saveRDS(summary(mymodel), file = paste(thisvar, "main_model_summary.rds",sep="_"))
  in_bf = bayesfactor_parameters(mymodel, null = 0)
  print(in_bf)
  #print(plot(in_bf))
  saveRDS(in_bf, file = paste(thisvar, "main_model_bf.rds",sep="_"))
}

cohensd<-function(pref_vector) mean(pref_vector-.5, na.rm=T)/sd(pref_vector, na.rm=T)


# IMPORTANT: SET THIS TO TRUE IF YOU WANT TO RECALCULATE ALL THE MODELS
RECALC=FALSE
```

## History

- 2020-07-30: First version
- 2020-07-31: Final version of analyses
- 2020-08-04: Making sure that everything is in the same order as in the manuscript
- 2020-12-16: Integrating changes by YYW, adding table 6, checking for reproducibility


## Read and preprocess data

```{r startup, echo=FALSE}


read.csv("Longitudinal_8_22_16.csv")->mydat # read in the data

#check that everything looks OK
names(mydat)
dim(mydat)
summary(mydat)


#clean up
mydat$Subject.. <- factor(mydat$Subject..)
mydat$ A.not.B.score  <- factor(mydat$ A.not.B.score )
mydat[!is.na(mydat$Subject..), ] -> data #97 observations
mydat[, -29] -> mydat


##there is an outlier in age CDI 24, it has been checked, it is his/her real CDI age 
#after discussion, we decide to remove the data from  this outlier child from the 24m analysis
mydat[mydat$X24mCDIAge>26 & !is.na(mydat$X24mCDIAge), c("X24mCDIAge","X24mCom","X24msay" , "X24mSayALL","X24mSayGenderSpec")] <- NA

# z-scored
mydat$com18z=zscore(mydat$X18mCom)
mydat$say18z=zscore(mydat$X18mSay)
mydat$say24z=zscore(mydat$X24msay)

mydat$anotB=NA
mydat$anotB[mydat$A.not.B.score==1]<-"Error" #mapped onto fail in xl, but this is error in the paper
mydat$anotB[mydat$A.not.B.score==2]<-"Random" #mapped onto error in xl, but this is random in the paper
mydat$anotB[mydat$A.not.B.score==3]<-"Hit"  #mapped onto pass in xl, but this is hit in the paper

#Rename variables so that they match the paper -- always stress, vrm, vowel, anotb
mydat$Stress=mydat$total.tro.pref.quotient
mydat$VRM=mydat$Novelty.VRM
mydat$Vowel=mydat$Vowel.Alt.pref.quotient

# Create stacked version of the data

stdatz=cbind( mydat[,c("Subject..","Gender","Stress","VRM","VRM.age","Vowel","anotB","vowels.Age", "A.not.B.Age")], stack(mydat[,c("com18z","say18z","say24z")]))
#note that the age for vowel and a not b is (mostly) the same, the age for stress & vrm is the same

summary(stdatz)

```

## Beginning of results section

Analyses were implemented in the R environment (R Core Team, 2014), and are available from supplementary materials.  Table 1 presents the summary statistics for each measure.

### Table 1

```{r tab1}


doline<-function(myage,myvec,prettyname,dod=F){
  #myage=mydat$vowels.Age
  #myvec=mydat$Vowel.Alt.pref.quotient
  #prettyname="Vowel"
  #dod=T
  cbind(prettyname,sum(!is.na(myvec)),
        paste0(round(mean(myage,na.rm=T),2)," (",round(sd(myage,na.rm=T),2),")"), #age(sd)
        paste0(round(mean(myvec,na.rm=T),2)," (",round(sd(myvec,na.rm=T),2),")"), #score(sd)
        ifelse(dod,round(cohensd(myvec),3),"")
        )
}


tab1=rbind(
  doline(mydat$VRM.age,mydat$Stress,"Stress",T),
  doline(mydat$VRM.age,mydat$VRM,"VRM",T),
  doline(mydat$vowels.Age,mydat$Vowel,"Vowel",T),
  doline(mydat$A.not.B.Age,as.numeric(mydat$A.not.B.score),"A-not-B",F), #!!! it doesn't make sense to provide numeric
  doline(mydat$X18mCDIAge,mydat$X18mCom,"18m receptive",F),
  doline(mydat$X18mCDIAge,mydat$X18mSay,"18m expressive",F),
  doline(mydat$X24mCDIAge,mydat$X24msay,"24m expressive",F)
  )



```


### Distribution checks

Prior to any analysis, we inspected the distributions of each measure using histograms and QQ plots. The distribution of the 3 continuous infant measures, namely, Stress, Vowel, and VRM, were approximately normal. However, the 3 vocabulary measures were not normally distributed. Therefore, we standardized the three outcome measures by applying z-scoring and then trimmed values more than 3 SD (N = 1) to improve the residual distribution, which yielded an approximately normal distribution of the outcome measures. 
 
```{r checkuni,echo=T}
#outcomes: 
outcomes = c("X18mCom",'X18mComGenderSpec', "X18mSay",'X18mSayGenderSpec',"X24mCom","X24msay", 'X24mSayGenderSpec')
#predictions: 
predictors = c("total.tro.pref.quotient", "Vowel.Alt.pref.quotient", "Novelty.VRM")
# "A.not.B.score" is categorical

table(data$A.not.B.score)

#outcomes
for(thisvar in predictors) hist(data[,thisvar],main=thisvar)

#outcomes - separated
for(thisvar in outcomes) hist(data[,thisvar],main=thisvar)

stdat=cbind( data[,c("Subject..","total.tro.pref.quotient", "Vowel.Alt.pref.quotient",
                     "Novelty.VRM", "A.not.B.score")], stack(data[,outcomes]))

#outcomes - combined - percentiles
hist(stdat$values[stdat$ind %in% c('X18mComGenderSpec')], main='X18mComGenderSpec')
hist(stdat$values[stdat$ind %in% c('X18mSayGenderSpec')], main='X18mSayGenderSpec')
hist(stdat$values[stdat$ind %in% c('X24mSayGenderSpec')], main='X24mSayGenderSpec')

#outcomes - combined - raw
hist(stdat$values[stdat$ind %in% c('X18mCom')], main='X18mCom')
hist(stdat$values[stdat$ind %in% c('X18mSay')], main='X18mSay')
hist(stdat$values[stdat$ind %in% c('X24msay')], main='X24msay')

#outcomes - combined - raw+Z
hist(stdatz$values,main="Combined-raw+Z")


# find outliers for each variable
for(thisvar in c(outcomes,predictors)) {
  #create a z-score for the observations
  print(thisvar)
  z = (data[,thisvar] - mean(data[,thisvar], na.rm=T) )/ sd(data[,thisvar], na.rm=T)
  print(paste("there are",sum(abs(z)> 3, na.rm=T),"observations that are outliers 
          at 3 SD in", thisvar))
} 

table(abs(stdatz$values)>3)
```
 
## Bivariate relationship among predictors     

### Correlation matrix
Table 2 presents the bivariate correlations between infant measures that were continuous (Stress, Vowel, VRM), and language outcome measures (18m receptive, 18m expressive, and 24m expressive vocabulary).

```{r cors}
numvars=as.matrix(mydat[,c("Stress", "VRM","Vowel",
            "com18z","say18z","say24z")])
colnames(numvars)<-c("Stress","VRM","Vowel","18m receptive","18m expressive","24m expressive")
cor.mat=rcorr(numvars)

# r values
cor.mat$r

# p values
cor.mat$P

# Ns
cor.mat$n

# create star 

cor.mat$star=ifelse(cor.mat$P<.001,"**",
                    ifelse(cor.mat$P<.05,"*",
                           ifelse(cor.mat$P<.1,"†","")))

#compose the table

#round
cor.mat$r=format(round(cor.mat$r,2),nsmall=2)

#add dfs
my.cor.mat=matrix(Map("paste", cor.mat$r, (cor.mat$n-2), sep=" ("),nrow=dim(cor.mat$r)[1])
my.cor.mat=matrix(Map("paste", my.cor.mat, ")", sep=""),nrow=dim(cor.mat$r)[1])
#add *
my.cor.mat=matrix(Map("paste", my.cor.mat, cor.mat$star, sep=""),nrow=dim(cor.mat$r)[1])

colnames(my.cor.mat)=colnames(cor.mat$r)
rownames(my.cor.mat)=colnames(cor.mat$r)

#remove the values at or below the diagonal
for(i in 1:dim(my.cor.mat)[1]) for(j in 1:dim(my.cor.mat)[1]) if(i>=j) my.cor.mat[i,j]<-""

write.table(my.cor.mat,file="tab2.txt",row.names=T,quote=T,sep="\t")

```


## Regressions for AnotB
Given that the A-not-B measure was categorical, we performed 6 separate one-way analyses of variance (ANOVAs) to examine whether there were differences on the other tasks with continuous data as a function of A-not-B outcome.

```{r anotb}
dothiscell<-function(thistype,thisvar){
  paste0(round(mean(mydat[mydat$anotB==thistype,thisvar],na.rm=T),2), 
         " (", 
         round(sd(mydat[mydat$anotB==thistype,thisvar],na.rm=T),2),"; ", 
         sum(!is.na(mydat[mydat$anotB==thistype,thisvar])),
         ")")
}
regtab=NULL

for(thisvar in c("Stress","VRM","Vowel",
            "com18z","say18z","say24z")) {
  myaov=summary(aov(mydat[,thisvar]~anotB,data=mydat))

  regtab=rbind(regtab,
               cbind(thisvar, 
                     dothiscell("Hit",thisvar),dothiscell("Random",thisvar),dothiscell("Error",thisvar),
                     paste0("F(", unlist(myaov)["Df2"], ")=", round(unlist(myaov)["F value1"],2),
                            " p=", round(unlist(myaov)["Pr(>F)1"],3))
               ))}

colnames(regtab)<-c(
"Task",
"Hit",
"Error",
"Random",
"F(df), p"
)
regtab[4:6,'Task']<-c("18m receptive","18m expressive","24m expressive")
regtab
write.table(regtab,file="tab3.txt",row.names=F,quote=T,sep="\t")
```


## Setting up models

If RECALC is TRUE then the next chunk will not be done...
```{r readrds, eval=!RECALC}

readRDS("vowel_main_model.rds")->vowel
readRDS("anotb_main_model.rds")->anb
readRDS("stress_main_model.rds")->strs
readRDS("vrm_main_model.rds")->vrm
readRDS("main_model.rds")->main
main_summary=readRDS("main_model_summary.rds")
main_BF=readRDS("main_model_bf.rds")
```

... but this one will (and vice versa):

```{r setprior, eval=RECALC}
niter=4000
nwarmup=500

#values for scaled variables -- this cannot be passed as a variable to stan, but it's noted here for clarity
nu=3
s=1

our_priors <- c(prior("student_t(3,0,1)", class = b),
              prior("student_t(3,0,1)", class = Intercept)
             )
```

## Prediction of vocabulary from each infant measure     

### Univariate Bayesian models

#### Stress

```{r strs, eval=RECALC}

strs = brm(values ~ 
   Stress*VRM.age +
  + ind + (1 | Subject..), data=stdatz,
  prior = our_priors,
             iter=niter, warmup=nwarmup, chains=4,cores=2,
             seed=12,
             save_all_pars = T,
             sample_prior = T
  )

saveRDS(strs, file = paste("stress", "main_model.rds",sep="_"))

```

```{r print-strs}
fit_uni_print(strs,"stress")
```

#### VRM

```{r vrm, eval=RECALC}

vrm = brm(values ~ 
   VRM*VRM.age +
  + ind + (1 | Subject..), data=stdatz,
  prior = our_priors,
             iter=niter, warmup=nwarmup, chains=4,cores=2,
             seed=12,
             save_all_pars = T,
             sample_prior = T
  )

saveRDS(vrm, file = paste("vrm", "main_model.rds",sep="_"))

```

```{r print-vrm}
fit_uni_print(vrm,"vrm")
```


#### Vowel

```{r vow, eval=RECALC}

vowel = brm(values ~ 
   Vowel*vowels.Age +
  + ind + (1 | Subject..), data=stdatz,
  prior = our_priors,
             iter=niter, warmup=nwarmup, chains=4,cores=2,
             seed=12,
             save_all_pars = T,
             sample_prior = T
  )
saveRDS(vowel, file = paste("vowel", "main_model.rds",sep="_"))

```

```{r print-vow}
fit_uni_print(vowel,"vowel")
```


#### A-not-B

```{r anb, eval=RECALC}

anb = brm(values ~ 
   anotB*A.not.B.Age +
  + ind + (1 | Subject..), data=stdatz,
  prior = our_priors,
             iter=niter, warmup=nwarmup, chains=4,cores=2,
             seed=12,
             save_all_pars = T,
             sample_prior = T
  )

saveRDS(anb, file = paste("anotb", "main_model.rds",sep="_"))

```

```{r print-anb}
fit_uni_print(anb,"anotb")
```



#### Add estimates to table 1

```{r add2tab1}

myvec=c(paste0(round(fixef(strs)["Stress","Estimate"],2)," (",round(fixef(strs)["Stress","Est.Error"],2),")"),
        paste0(round(fixef(vrm)["VRM","Estimate"],2)," (",round(fixef(vrm)["VRM","Est.Error"],2),")"),
        paste0(round(fixef(vowel)["Vowel","Estimate"],2)," (",round(fixef(vowel)["Vowel","Est.Error"],2),")"),
        paste0("<",round(max(fixef(anb)[c("anotBHit","anotBRandom"),"Estimate"]),2)," (>",round(min(fixef(anb)[c("anotBHit","anotBRandom"),"Est.Error"]),2),")"),
        "--",
        "--",
        "--"
        )
cbind(tab1,myvec)->tab1
colnames(tab1)<-c("Measure",	"No.",	"Age (SD)",	"Score (SD)",	"Cohen's d", "Estimate (SE)")
write.table(tab1,file="tab1.txt",row.names=F,quote=F,sep="\t")
```

### Table 4

Estimate (standard error), 95 percent credibility interval, and Bayes Factor for each measure as predictor of vocabulary (in a Bayesian mixed model declaring all vocabulary measures together), as well as the same metrics for this predictor's interaction with age in that model. Null>Alt indicates that the Bayes Factor shows more support for the null than the alternative equal to the ratio provided. No predictor or interaction showed more support for the alternative than the null. 

```{r tab4}
# Predictor Interaction with age
#Measure, Estimate (SE), 95% CI, BF

dolinetab4<-function(mymod,varname){
  #print(varname)
  #mymod=strs ; varname="Stress"
  if(varname %in% c("anotBHit","anotBRandom")) readRDS(file = paste("anotb", "main_model_bf.rds",sep="_"))->temp else readRDS(file = paste(tolower(varname), "main_model_bf.rds",sep="_"))->temp
  
  age_interaction_line=grep(varname,rownames(fixef(mymod)))[2]

  cbind(varname, paste0(round(fixef(mymod)[varname,"Estimate"],2)," (",round(fixef(mymod)[varname,"Est.Error"],2),")"), #Measure, Estimate (SE)
       paste0("[",round(fixef(mymod)[varname,"Q2.5"],2),", ",round(fixef(mymod)[varname,"Q97.5"],2),"]"), #95% CI
       round(1/temp[grep(varname,temp$Parameter),"BF"][1],2), #bf #this is ugly but basically there are 2 lines with the varname, the first is the main, the second the interaction with age
       #repeat for interaction with age 
       paste0(round(fixef(mymod)[age_interaction_line,"Estimate"],2)," (",round(fixef(mymod)[age_interaction_line,"Est.Error"],2),")"), #Estimate (SE)
       paste0("[",round(fixef(mymod)[age_interaction_line,"Q2.5"],2),", ",round(fixef(mymod)[age_interaction_line,"Q97.5"],2),"]"), #95% CI
      round(1/temp[grep(varname,temp$Parameter),"BF"][2],2) #bf
  )
}

tab4=rbind(
  dolinetab4(strs,"Stress"),
  dolinetab4(vrm,"VRM"),
  dolinetab4(vowel,"Vowel"),
  dolinetab4(anb,"anotBHit"),
  dolinetab4(anb,"anotBRandom")
)
colnames(tab4)<-c("Task",	"Estimate (SE)",	"95% CI",	"Null>Alt BF",	"Estimate (SE)",	"95% CI",	"Null>Alt BF")
tab4
write.table(tab4,file="tab4.txt",row.names=F,quote=F,sep="\t")   
```


## Evaluating the relative importance of different predictors 
### Frequentist analysis

```{r model-test-rawz,echo=T}
lm(values ~ Stress + Vowel +
     VRM + anotB + ind + Gender + (1/Subject..), data= stdatz) -> lmrz

outlierTest(lmrz)

plot(residuals(lmrz) ~ fitted(lmrz))

qqPlot(lmrz, main="QQ Plot")

gvlma(lmrz)

```

Conclusion: should do something about outlier; non-linear relationship between fitted and residuals?, qqplot looks OK, all assumptions are acceptable --> it's a go!!

Decision point: I'll trim the value of the outlier 

```{r out, echo=T}
stdatz.noout<-stdatz
stdatz.noout[stdatz.noout$values>2 & !is.na(stdatz.noout$values),] #yields 2 observations, the outlier and another one

stdatz.noout[stdatz.noout$values>4 & !is.na(stdatz.noout$values),"values"]<-2.186494 #this line assigns to the outlier the other highest value  - about 2SD above the mean for CDI

lm(values ~ Stress + Vowel +
     VRM + anotB  +Gender+ ind + (1/Subject..), data= stdatz.noout) -> lmrzno
outlierTest(lmrzno) 
gvlma(lmrzno) #all assumptions met

```

#### Table 5

```{r inspect-model-fit, echo=T}

summary(lmrzno)
anova(lmrzno)
apa.reg.table(lmrzno, filename = "tab5.rtf", table.number = 5)
```

#### Figure 3

```{r fig3}
png("fig3.png")
mycol=c("black","darkgray","lightgray")
mypch=c(4,1,20)
names(mycol)=names(mypch)<-levels(factor(stdatz.noout$ind))
plot(values~Vowel,data=stdatz.noout,xlab="Preference quotient in the Vowel task",ylab="Vocabulary (z-scored)",col=mycol[ind],pch=mypch[ind])
abline(lm(values~Vowel,data=stdatz.noout))
dev.off()

png("fig4.png")
mycol=c("black","darkgray","lightgray")
mypch=c(4,1,20)
names(mycol)=names(mypch)<-levels(factor(stdatz.noout$ind))
plot(values~Stress,data=stdatz.noout,xlab="Preference quotient in the Stress task",ylab="Vocabulary (z-scored)",col=mycol[ind],pch=mypch[ind])
abline(lm(values~Stress,data=stdatz.noout))
dev.off()
```


### Multivariate Bayesian model


```{r pred_ini, eval=RECALC}



main = brm(values ~ 
   total.tro.pref.quotient + Vowel.Alt.pref.quotient + Novelty.VRM + A.not.B.score +
     Gender + ind + (1 | Subject..), data = stdatz,
  prior = our_priors,
             iter=niter, warmup=nwarmup, chains=4,cores=2,
             seed=12,
             save_all_pars = T,
             sample_prior = T
  )
saveRDS(main,file="main_model.rds")

main_summary=summary(main)

saveRDS(main_summary,file="main_model_summary.rds")

main_BF = bayesfactor_parameters(main, null = 0)

saveRDS(main_BF,file="main_model_bf.rds")

```

```{r printout-full}

#plot(main)

pp_check(main, nsamples = 1000)

main

main_BF
plot(main_BF)


```

#### Table 6
```{r tab6}

mytab=cbind(main_summary$fixed[,"Estimate"],main_summary$fixed[,"l-95% CI"],main_summary$fixed[,"u-95% CI"],main_BF$BF)
mytab=round(mytab,3)
colnames(mytab)<-c("ß","LCI","HCI","BF10")
write.table(mytab,"tab6.txt",sep="\t")
```