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InfoRate.Rmd
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---
title: "Different languages, similar encoding efficiency"
subtitle: "Full statistical analysis and plots"
author: "Christophe Coupé, Yoon Mi Oh, Dan Dediu and François Pellegrino"
date: '`r date()`'
output:
html_document:
fig_caption: yes
highlight: textmate
theme: readable
toc: yes
toc_depth: 6
toc_float: yes
word_document: default
editor_options:
chunk_output_type: console
---
```{r setup, echo=F, message=F, warning=FALSE}
knitr::opts_chunk$set(echo = TRUE)
library(ggplot2);
library(ggrepel);
library(reshape2);
library(plyr);
library(lmerTest);
library(gamlss);
library(gamlss.mx);
library(sjstats);
library(sjPlot);
library(moments);
library(parallel);
library(pander);
knitr::opts_chunk$set(echo = TRUE, warning=FALSE, message=FALSE, # default code chunk options
fig.width=9, fig.height=6, fig.align = "center", comment=NA, # default figure dimensions
fig.path = "figures/", # save images to ./figures/
dpi=72, dev="jpeg", # please set dpi=300 and comment out dev="jpeg" for high resolution images but very big resulting HTML document
cache=TRUE, autodep=TRUE); # cache computations
dir.create("./figures", showWarnings=FALSE); # figures are saved here
do.expensive.computations = FALSE; # force the expensive computations
no.cores <- ifelse(.Platform$OS.type == "windows", 1, max(detectCores()-1, 1, na.rm=TRUE)); # use all cores in the system except 1 (including hyperthreading), except on Windows, were this defaults to 1 core
options(width = 250);
options(contrasts=c("contr.treatment","contr.poly"));
set.seed(3683); # For reproducibility of the results
```
<style>
caption, .caption {
color: #555555;
font-weight: bold;
font-size: 105%;
text-align: left}
a[hreflang]:before{}
</style>
```{r local_functions, echo=FALSE}
# Local functions ####
get_re_distrib <- function(v, myTitle = "") {
myDF <- data.frame(myCoef=v)
y <- quantile(myDF$myCoef, c(0.25, 0.75))
x <- qnorm(c(0.25, 0.75))
slope <- diff(y)/diff(x)
int <- y[1L] - slope * x[1L]
p_re <- ggplot(data = myDF, aes(sample=myCoef)) + stat_qq() + ggtitle(myTitle)
p_re <- p_re + geom_abline(slope = slope, intercept = int) + theme(text = element_text(size=11, family="serif"))
p_re
}
zeropad <- function(x, nz=1, exc.int=TRUE) {
if (is.integer(x) & exc.int) {
x
} else {
sprintf(paste0("%.", nz, "f"), x)
}
}
analyses <- function(myModel) {
# Preparing graphs
tmpDF <- data.frame(x=predict(myModel), y=residuals(myModel))
p_res <- ggplot(data=tmpDF, aes(x=x, y=y)) + geom_point(size=0.5) + xlab("Fitted values") + ylab("Quantile residuals")
p_res <- p_res + geom_smooth(method="loess")
p_res <- p_res + theme_minimal()
p_qq <- get_re_distrib(tmpDF$y, "")
momentsNames <- c("mean", "variance", "coef. of skewness", "coef. of kurtosis")
momentsValues <- zeropad(c(mean(tmpDF$y), var(tmpDF$y), skewness(tmpDF$y), kurtosis(tmpDF$y)), 3)
(tmpMoments <- data.frame(momentsNames, momentsValues))
(coef <- coef(getSmo(myModel, "mu", which = 1)))
families_re_p <- get_re_distrib(coef, 'First random effect, mu')
list(p_res, p_qq, tmpMoments, families_re_p)
}
lm.eqn <- function(m) {
l <- list(a = format(coef(m)[1], digits = 2),
b = format(abs(coef(m)[2]), digits = 2),
r2 = format(summary(m)$r.squared, digits = 3));
if (coef(m)[2] >= 0) {
eq <- substitute(italic(y) == a + b %.% italic(x)*","~~italic(r)^2~"="~r2,l)
} else {
eq <- substitute(italic(y) == a - b %.% italic(x)*","~~italic(r)^2~"="~r2,l)
}
as.character(as.expression(eq));
}
display.graph.equation <- function(x, y, param1, param2, title) {
df <- data.frame(x=x, y=y)
p <- ggplot(data = df, aes(x = x, y = y)) +
geom_smooth(method = "lm", se=FALSE, color="black", formula = y ~ x) + geom_point() + ggtitle(title) + xlab(param1) + ylab(param2) +
annotate("text", x=min(df$x), y=min(df$y), hjust = 0.2, vjust = 0.8, label = lm.eqn(lm(y ~ x, df)), colour="black", size = 5, parse=TRUE)
return (p)
}
display.correlation <- function(m, param1, param2, position, predictor.name, model.Name) {
x <- coef(getSmo(m, param1, which = position))
y <- coef(getSmo(m, param2, which = position))
print(summary(x));
print(summary(y));
print(cor.test(x,y,method="pearson"));
print(cor.test(x,y,method="spearman"));
myTitle <- paste0(model.Name, ": ", param1, " and " , param2, " for ", predictor.name)
print(myTitle)
p <- display.graph.equation(x, y, param1, param2, myTitle)
return(p)
}
# http://www.cookbook-r.com/Graphs/Multiple_graphs_on_one_page_(ggplot2)/
#
# Multiple plot function
#
# ggplot objects can be passed in ..., or to plotlist (as a list of ggplot objects)
# - cols: Number of columns in layout
# - layout: A matrix specifying the layout. If present, 'cols' is ignored.
#
# If the layout is something like matrix(c(1,2,3,3), nrow=2, byrow=TRUE),
# then plot 1 will go in the upper left, 2 will go in the upper right, and
# 3 will go all the way across the bottom.
#
multiplot <- function(..., plotlist=NULL, file, cols=1, layout=NULL) {
library(grid)
# Make a list from the ... arguments and plotlist
plots <- c(list(...), plotlist)
numPlots = length(plots)
# If layout is NULL, then use 'cols' to determine layout
if (is.null(layout)) {
# Make the panel
# ncol: Number of columns of plots
# nrow: Number of rows needed, calculated from # of cols
layout <- matrix(seq(1, cols * ceiling(numPlots/cols)),
ncol = cols, nrow = ceiling(numPlots/cols))
}
if (numPlots==1) {
print(plots[[1]])
} else {
# Set up the page
grid.newpage()
pushViewport(viewport(layout = grid.layout(nrow(layout), ncol(layout))))
# Make each plot, in the correct location
for (i in 1:numPlots) {
# Get the i,j matrix positions of the regions that contain this subplot
matchidx <- as.data.frame(which(layout == i, arr.ind = TRUE))
print(plots[[i]], vp = viewport(layout.pos.row = matchidx$row,
layout.pos.col = matchidx$col))
}
}
}
```
```{r loading_data, echo=FALSE, message=FALSE, warning=FALSE}
# Loading and preparing the data:
info.rate.data <- read.table("./InfoRateData.csv", header=TRUE, sep="\t", quote="", stringsAsFactors=FALSE);
# Compute Speech Rate (SR), Shannon Information Rate (ShIR), and Conditional Information Rate (IR):
info.rate.data$SR <- (info.rate.data$NS / info.rate.data$Duration);
info.rate.data$ShIR <- (info.rate.data$SR * info.rate.data$ShE);
info.rate.data$IR <- (info.rate.data$SR * info.rate.data$ID);
# Add NS(VIE) / NS(L) for each language L and text T:
info.rate.data <- merge(info.rate.data, unique(info.rate.data[info.rate.data$Language=="VIE", c("Text", "NS")]), by="Text", suffixes=c("",".y"), all.x=TRUE);
names(info.rate.data)[ncol(info.rate.data)] <- "NSVR";
info.rate.data$NSVR <- info.rate.data$NSVR / info.rate.data$NS;
# Add language family data:
info.rate.data$Family <- Vectorize(function(a) # assign language family to langauge codes
{
switch(as.character(a),
"CAT" = "Indo-European",
"CMN" = "Sino-Tibetan",
"DEU" = "Indo-European",
"ENG" = "Indo-European",
"EUS" = "Basque",
"FIN" = "Uralic",
"FRA" = "Indo-European",
"HUN" = "Uralic",
"ITA" = "Indo-European",
"JPN" = "Japanese",
"KOR" = "Korean",
"SPA" = "Indo-European",
"SRP" = "Indo-European",
"THA" = "Tai-Kadai",
"TUR" = "Turkic",
"VIE" = "Austroasiatic",
"YUE" = "Sino-Tibetan",
NA)
}, "a")(as.character(info.rate.data$Language));
# Convert to factors:
info.rate.data$Text <- as.factor(info.rate.data$Text);
info.rate.data$Speaker <- as.factor(info.rate.data$Speaker);
info.rate.data$Language <- as.factor(info.rate.data$Language);
info.rate.data$Sex <- as.factor(info.rate.data$Sex);
info.rate.data$Family <- as.factor(info.rate.data$Family);
# Make sure we use contrasts to the overall mean for factors:
contrasts(info.rate.data$Text) <- contr.sum(length(levels(info.rate.data$Text)));
contrasts(info.rate.data$Speaker) <- contr.sum(length(levels(info.rate.data$Speaker)));
contrasts(info.rate.data$Language) <- contr.sum(length(levels(info.rate.data$Language)));
contrasts(info.rate.data$Sex) <- contr.sum(length(levels(info.rate.data$Sex)));
contrasts(info.rate.data$Family) <- contr.sum(length(levels(info.rate.data$Family)));
# Sort by Language, Speaker and Text:
info.rate.data <- info.rate.data[order(info.rate.data$Language, info.rate.data$Speaker, info.rate.data$Text),];
```
## Introduction
This `Rmarkdown` script (and the corresponding TAB-separated CSV input data files `InfoRateData.csv` and `AutomaticSylDetect.csv`, and the resulting `HTML` document) contains the full analysis and plotting code accompanying the paper *Different languages, similar encoding efficiency: comparable information rates across the human communicative niche*.
## The data
```{r echo=FALSE, message=FALSE, warning=FALSE}
# Transform it into the long format:
info.rate.data.long <- melt(info.rate.data, id.vars=c("Language", "Text", "Speaker", "Sex", "Family"));
# Extract speakers, languages and texts:
speakers <- sort(unique(info.rate.data$Speaker));
languages <- sort(unique(info.rate.data$Language));
lgfams <- sort(unique(info.rate.data$Family));
texts <- sort(unique(info.rate.data$Text));
```
For more information on the data, please see [Oh (2015)](#references).
There are in total `r length(unique(info.rate.data$Language))` languages (see the table below).
### The Oral Corpus
The oral corpus is based on a subset of the *Multext* (Multilingual Text Tools and Corpora) parallel corpus [(Campione & Véronis, 1998)](#campioneveronis1998) in *British English*, *German*, and *Italian*.
The material consists of 15 short texts of 3-5 semantically connected sentences carefully translated by a native speaker in each language.
For the other 14 languages, two of the authors supervised the translation and recording of new datasets.
All participants were native speakers of the target language, with a focus on a specific variety of the language when possible – e.g. *Mandarin* spoken in Beijing, *Serbian* in Belgrade and *Korean* in Seoul.
No strict control on age or on the speakers’ social diversity was performed, but speakers were mainly students or members of academic institutions.
Speakers were asked to read three or four times (first silently and then loudly two or three times) each text.
The texts were presented one by one on the screen in random order, in a self-paced reading paradigm.
This way, speakers familiarized themselves with the text and reduced their reading errors.
The last loud recording was analyzed in this study.
With these, the oral corpus contains `r nrow(info.rate.data)` texts read by `r length(speakers)` speakers coming from `r length(languages)` languages and `r length(texts)` texts.
For each language and text we have the following number of syllables (*NS*):
```{r echo=FALSE, message=FALSE, warning=FALSE}
knitr::kable(unique(info.rate.data[,c("Language","Text","NS")]),
row.names=FALSE, caption="Number of syllables (*NS*) per language and text.");
```
### Text Corpus
Text datasets were acquired from various sources as illustrated in the table below.
After an initial data curation, each dataset was phonetically transcribed and automatically syllabified by a rule-based program written by one of the authors, except in the following cases:
i) when syllabification was already provided with the dataset (*English*, *French*, *German*, and *Vietnamese* for the multisyllabic words);
ii) when the corpus was syllabified by an automatic grapheme-to-phoneme converter (*Catalan*, *Spanish*, and *Thai*).
Additionally, no syllabification was required for Sino-Tibetan languages (*Cantonese* and *Mandarin Chinese*) since one ideogram corresponds to one syllable.
| Language | Family | ISO 639-3 | Corpus |
|------------------|----------------|-----------|-------------------------------------------------------------|
| Basque | Basque | EUS | E-Hitz [(Perea et al., 2006)](#references) |
| British English | Indo-European | ENG | WebCelex (MPI for Psycholinguistics) |
| Cantonese | Sino-Tibetan | YUE | A linguistic corpus of mid-20th century Hong Kong Cantonese |
| Catalan | Indo-European | CAT | Frequency dictionary [(Zséder et al., 2012)](#references) |
| Finnish | Uralic | FIN | Finnish Parole Corpus |
| French | Indo-European | FRA | Lexique 3.80 [(New et al., 2001)](#references) |
| German | Indo-European | DEU | WebCelex (MPI for Psycholinguistics) |
| Hungarian | Uralic | HUN | Hungarian National Corpus [(Váradi, 2002)](#references) |
| Italian | Indo-European | ITA | The PAISÀ Corpus [(Lyding et al., 2014)](#references) |
| Japanese | Japanese | JPN | Japanese Internet Corpus [(Sharoff, 2006)](#references) |
| Korean | Korean | KOR | Leipzig Corpora Collection (LCC) |
| Mandarin Chinese | Sino-Tibetan | CMN | Chinese Internet Corpus [(Sharoff, 2006)](#references) |
| Serbian | Indo-European | SRP | Frequency dictionary [(Zséder et al., 2012)](#references) |
| Spanish | Indo-European | SPA | Frequency dictionary [(Zséder et al., 2012)](#references) |
| Thai | Tai-Kadai | THA | Thai National Corpus (TNC) |
| Turkish | Turkic | TUR | Leipzig Corpora Collection (LCC) |
| Vietnamese | Austroasiatic | VIE | VNSpeechCorpus [(Le et al., 2004)](#references) |
### Dataset structure
The data is structured as follows:
- *Language* is the unique language ISO 639-3 ID with `r length(unique(info.rate.data$Language))` possible values: `r paste0('"',sort(unique(info.rate.data$Language)),'"',collapse=", ")`;
- *Language family* is the language family with `r length(unique(info.rate.data$Family))` possible values: `r paste0('"',sort(unique(info.rate.data$Family)),'"',collapse=", ")`;
- *Text* is the text identifier (similar across languages and speakers) with `r length(unique(info.rate.data$Text))` possible values: `r paste0('"',sort(unique(info.rate.data$Text)),'"',collapse=", ")`;
- *Speaker* is the unique speaker's ID (there are `r length(unique(info.rate.data$Speaker))` in the dataset);
- *Sex* is the speaker's sex;
- *Age* is the speaker's age (available only for a subset of `r tmp <- unique(info.rate.data[,c("Speaker","Age")]); sum(!is.na(tmp$Age))` speakers);
- *Duration* is the duration of the texts in seconds as spoken by a given speaker (pauses longer than 150ms being excluded);
- *NS* is the number of of syllables of the texts (the same for a given text in a given language);
- *SR* is the speech rate (syllables/second) for a given text spoken by a given speaker;
- *ShE* (resp. *ID*) is the first-order (resp. second-order) language-level entropy estimate;
- *ShIR* and *IR* are text * speaker properties obtained by multiplying *SR* by *ShE* and *ID* respectively.
### Technical notes on regressions
We use throughout *sum contrasts* for the factor IVs, which are orthogonal contrasts which compare every level of the IV to the overall mean (for example, for a two-levels factor such as *Sex* we do not compare *Males* with *Females* but each with their overall mean, which is included in the intercept).
However, in `R` the `contr.sum()` function used to define these contrasts produces level names that are very uninformative, so we explicit these below (please note that in the model outputs the *last* level is usually not shown):
```{r echo=FALSE, message=FALSE, warning=FALSE, results='asis'}
for( tmp in c("Sex", "Text", "Language", "Family") ) cat(paste0(" - ***",tmp,"***: ",paste0("`",tmp,1:length(levels(info.rate.data[,tmp])),"` = *",levels(info.rate.data[,tmp]),"*", collapse=", "), " (the last level, `",tmp, length(levels(info.rate.data[,tmp])),",` is usually not displayed);\n"));
```
### Exploratory plots and summaries
#### Speaker characteristics
```{r Speaker characteristics, echo=FALSE, message=FALSE, warning=FALSE, fig.width=10, fig.height=10, fig.cap="NS: exploratory plots."}
tmp <- info.rate.data;
tmp$Language <- factor(tmp$Language, levels=c("VIE","EUS","CAT","DEU","ENG","FRA","ITA","SPA","SRP","JPN","KOR","CMN","YUE","THA","TUR","FIN","HUN"));
tmp$Family <- factor(tmp$Family); tmp$Family <- revalue(tmp$Family, c("Austroasiatic"="AA", "Basque"="B", "Indo-European"="IE", "Japanese"="J", "Korean"="K", "Sino-Tibetan"="ST", "Tai-Kadai"="TK", "Turkic"="T", "Uralic"="U"));
knitr::kable(unique(tmp[,c("Speaker", "Sex", "Language", "Age")]) %>%
dplyr::group_by(Language) %>%
dplyr::summarise("no.speakers"=length(Speaker),
#"females"=sum(Sex=="F",na.rm=TRUE),
"females.perc"=100*sum(Sex=="F",na.rm=TRUE)/length(Speaker),
"with.age"=sum(!is.na(Age)),
"mean.age"=mean(Age,na.rm=TRUE),
#"median.age"=median(Age,na.rm=TRUE),
"sd.age"=sd(Age,na.rm=TRUE),
"ages"=paste0("(",paste0(sort(Age),collapse=", "),")")) %>%
dplyr::arrange(as.character(Language)),
col.names=c("Lng",
"# spkrs",
#"# females",
"% fem",
"# age",
"mean(age)",
#"median(age)",
"sd(age)",
"actual ages"),
row.names=FALSE,
digits=c(NA,
0,
#0,
1,
0,
1,
#1,
1,
NA), caption="Distribution of speaker number and characteristics (sex and age) by language. *Lng*=language, *# spkrs*=number of speakers, *% fem*=percentage of female speakers, *# age*=number of speakers with age info, and for those, *mean(age)*=mean age, *sd(age)*=standard deviation of age, and *actual ages*=the sorted ages.");
```
#### NS
```{r NS by Language and Text, echo=FALSE, message=FALSE, warning=FALSE, fig.width=10, fig.height=10, fig.cap="NS: exploratory plots."}
multiplot(plotlist=list(ggplot(tmp, aes(x=NS)) + geom_histogram(col="yellow") + xlab("NS"),
{
# From http://mgimond.github.io/ES218/Week06a.html:
y <- quantile(tmp$NS, c(0.25, 0.75)) # Find the 1st and 3rd quartiles
x <- qnorm( c(0.25, 0.75)) # Find the matching normal values on the x-axis
slope <- diff(y) / diff(x) # Compute the line slope
int <- y[1] - slope * x[1] # Compute the line intercept
ggplot(tmp, aes(sample=NS))+stat_qq(distribution=qnorm, color="royalblue", alpha=0.5) + geom_abline(intercept=int, slope=slope, color="firebrick2")
},
ggplot(tmp, aes(x=Language, y=NS, colour=Family)) + geom_boxplot() + ylab("NS") + theme(axis.text.x = element_text(angle = 45, hjust = 1)),
ggplot(tmp, aes(x=Text, y=NS, colour=substr(Text,1,1))) + geom_boxplot() + ylab("NS") + scale_color_discrete(name = "Text") + theme(axis.text.x = element_text(angle = 45, hjust = 1))),
cols=2);
```
```{r , echo=FALSE, message=FALSE, warning=FALSE}
cat(paste0("mean=",round(mean(tmp$NS,na.rm=TRUE),3),", ",
"median=",round(median(tmp$NS,na.rm=TRUE),3),", ",
"sd=",round(sd(tmp$NS,na.rm=TRUE),3),", ",
"CV=",round(sd(tmp$NS,na.rm=TRUE) / mean(tmp$NS,na.rm=TRUE),3),", ",
"min=",round(min(tmp$NS,na.rm=TRUE),3),", ",
"max=",round(max(tmp$NS,na.rm=TRUE),3),", ",
"kurtosis=",round(kurtosis(tmp$NS,na.rm=TRUE),3),", ",
"skewness=",round(skewness(tmp$NS,na.rm=TRUE),3),".\n"));
```
#### SR
```{r SR by Language and Text, echo=FALSE, message=FALSE, warning=FALSE, fig.width=10, fig.height=10, fig.cap="SR: exploratory plots."}
multiplot(plotlist=list(ggplot(tmp, aes(x=SR)) + geom_histogram(col="yellow") + xlab("SR"),
{
# From http://mgimond.github.io/ES218/Week06a.html:
y <- quantile(tmp$SR, c(0.25, 0.75)) # Find the 1st and 3rd quartiles
x <- qnorm( c(0.25, 0.75)) # Find the matching normal values on the x-axis
slope <- diff(y) / diff(x) # Compute the line slope
int <- y[1] - slope * x[1] # Compute the line intercept
ggplot(tmp, aes(sample=SR))+stat_qq(distribution=qnorm, color="royalblue", alpha=0.5) + geom_abline(intercept=int, slope=slope, color="firebrick2")
},
ggplot(tmp, aes(x=Language, y=SR, colour=Family)) + geom_boxplot() + ylab("SR") + theme(axis.text.x = element_text(angle = 45, hjust = 1)),
ggplot(tmp, aes(x=Text, y=SR, colour=substr(Text,1,1))) + geom_boxplot() + ylab("SR") + scale_color_discrete(name = "Text") + theme(axis.text.x = element_text(angle = 45, hjust = 1))),
cols=2);
```
```{r SR by Speaker, echo=FALSE, message=FALSE, warning=FALSE, fig.width=10, fig.height=5, fig.cap="SR per speaker."}
# ggplot(info.rate.data, aes(x=Speaker, y=SR, color=Language, fill=Sex)) +
# geom_boxplot() +
# scale_fill_manual(values=c("F"="white", "M"="gray50")) +
# ylab("SR") + xlab("Speakers") + theme(axis.text.x=element_blank());
ggplot(info.rate.data %>%
mutate(Speaker=reorder(Speaker, SR, median)) %>%
mutate(Speaker=reorder(Speaker, as.character(Sex), min)) %>%
mutate(Speaker=reorder(Speaker, as.character(Language), min)),
aes(x=Speaker, y=SR, color=Language, fill=Sex)) +
geom_boxplot() + #geom_vline(aes(xintercept=Language)) +
scale_fill_manual(values=c("F"="white", "M"="gray70")) +
#facet_wrap(. ~ Language, scales="free_x") +
ylab("SR") + xlab("Speakers") + theme(axis.text.x=element_blank());
```
```{r SR by Sex and Age across Languages, echo=FALSE, message=FALSE, warning=FALSE, fig.width=10, fig.height=5, fig.cap="SR by Sex and Age across Languages."}
ggplot(info.rate.data,
aes(x=Age, y=SR, color=Language, shape=Sex, fill=Sex)) +
geom_point() +
geom_smooth(aes(group=Sex), method="lm", formula=y ~ poly(x,2));
```
```{r SR by Sex, Age and Language, echo=FALSE, message=FALSE, warning=FALSE, fig.width=10, fig.height=8, fig.cap="SR by Sex, Age and Language."}
ggplot(info.rate.data,
aes(x=Age, y=SR, color=Sex, shape=Sex)) +
geom_point() +
geom_smooth(method="lm", formula=y ~ poly(x,2)) +
facet_wrap(. ~ Language, scales="free_x");
```
```{r SR distributions by language, echo=FALSE, message=FALSE, warning=FALSE, fig.width=7, fig.height=6, fig.cap="SR by language."}
ggplot(info.rate.data, aes(SR, fill = Language, colour = Language)) +
geom_density(alpha = 0.1) + geom_density(aes(SR), data=info.rate.data, fill=NA, color="black") + xlab("SR")
```
```{r , echo=FALSE, message=FALSE, warning=FALSE}
cat(paste0("mean=",round(mean(tmp$SR,na.rm=TRUE),3),", ",
"median=",round(median(tmp$SR,na.rm=TRUE),3),", ",
"sd=",round(sd(tmp$SR,na.rm=TRUE),3),", ",
"CV=",round(sd(tmp$SR,na.rm=TRUE) / mean(tmp$SR,na.rm=TRUE),3),", ",
"min=",round(min(tmp$SR,na.rm=TRUE),3),", ",
"max=",round(max(tmp$SR,na.rm=TRUE),3),", ",
"kurtosis=",round(kurtosis(tmp$SR,na.rm=TRUE),3),", ",
"skewness=",round(skewness(tmp$SR,na.rm=TRUE),3),".\n"));
```
#### ShE and ID
```{r ShE and ID, echo=FALSE, message=FALSE, warning=FALSE, fig.width=10, fig.height=10, fig.cap="ShE and ID: exploratory plots."}
multiplot(plotlist=list(ggplot(tmp, aes(x=ShE)) + geom_histogram(col="yellow") + xlab("ShE"),
{
# From http://mgimond.github.io/ES218/Week06a.html:
y <- quantile(tmp$ShE, c(0.25, 0.75)) # Find the 1st and 3rd quartiles
x <- qnorm( c(0.25, 0.75)) # Find the matching normal values on the x-axis
slope <- diff(y) / diff(x) # Compute the line slope
int <- y[1] - slope * x[1] # Compute the line intercept
ggplot(tmp, aes(sample=ShE))+stat_qq(distribution=qnorm, color="royalblue", alpha=0.5) + geom_abline(intercept=int, slope=slope, color="firebrick2")
},
ggplot(tmp, aes(x=ID)) + geom_histogram(col="yellow") + xlab("ID"),
{
# From http://mgimond.github.io/ES218/Week06a.html:
y <- quantile(tmp$ID, c(0.25, 0.75)) # Find the 1st and 3rd quartiles
x <- qnorm( c(0.25, 0.75)) # Find the matching normal values on the x-axis
slope <- diff(y) / diff(x) # Compute the line slope
int <- y[1] - slope * x[1] # Compute the line intercept
ggplot(tmp, aes(sample=ID))+stat_qq(distribution=qnorm, color="royalblue", alpha=0.5) + geom_abline(intercept=int, slope=slope, color="firebrick2")
}),
cols=2);
```
```{r ShE vs ID, echo=FALSE, message=FALSE, warning=FALSE, fig.width=8, fig.height=6, fig.cap="ShE vs ID."}
tmp1 <- unique(info.rate.data[,c("Language","ShE","ID","Family")]);
ggplot(tmp1, aes(x=ShE, y=ID, color=Family)) +
geom_text(aes(label=Language)) + geom_smooth(method="lm", color="black") + xlab("ShE") + ylab("ID");
cor.test(tmp1$ShE, tmp1$ID, method="pearson");
cor.test(tmp1$ShE, tmp1$ID, method="spearman");
t.test(tmp1$ShE, tmp1$ID, paired=TRUE);
```
*ShE:*
```{r , echo=FALSE, message=FALSE, warning=FALSE}
cat(paste0("mean=",round(mean(tmp$ShE,na.rm=TRUE),3),", ",
"median=",round(median(tmp$ShE,na.rm=TRUE),3),", ",
"sd=",round(sd(tmp$ShE,na.rm=TRUE),3),", ",
"CV=",round(sd(tmp$ShE,na.rm=TRUE) / mean(tmp$ShE,na.rm=TRUE),3),", ",
"min=",round(min(tmp$ShE,na.rm=TRUE),3),", ",
"max=",round(max(tmp$ShE,na.rm=TRUE),3),", ",
"kurtosis=",round(kurtosis(tmp$ShE,na.rm=TRUE),3),", ",
"skewness=",round(skewness(tmp$ShE,na.rm=TRUE),3),".\n"));
```
*ID:*
```{r , echo=FALSE, message=FALSE, warning=FALSE}
cat(paste0("mean=",round(mean(tmp$ID,na.rm=TRUE),3),", ",
"median=",round(median(tmp$ID,na.rm=TRUE),3),", ",
"sd=",round(sd(tmp$ID,na.rm=TRUE),3),", ",
"CV=",round(sd(tmp$ID,na.rm=TRUE) / mean(tmp$ID,na.rm=TRUE),3),", ",
"min=",round(min(tmp$ID,na.rm=TRUE),3),", ",
"max=",round(max(tmp$ID,na.rm=TRUE),3),", ",
"kurtosis=",round(kurtosis(tmp$ID,na.rm=TRUE),3),", ",
"skewness=",round(skewness(tmp$ID,na.rm=TRUE),3),".\n"));
```
#### ShIR and IR
```{r ShIR by Language and Text, echo=FALSE, message=FALSE, warning=FALSE, fig.width=10, fig.height=10, fig.cap="ShIR: exploratory plots."}
multiplot(plotlist=list(ggplot(tmp, aes(x=ShIR)) + geom_histogram(col="yellow") + xlab("ShIR"),
{
# From http://mgimond.github.io/ES218/Week06a.html:
y <- quantile(tmp$ShIR, c(0.25, 0.75)) # Find the 1st and 3rd quartiles
x <- qnorm( c(0.25, 0.75)) # Find the matching normal values on the x-axis
slope <- diff(y) / diff(x) # Compute the line slope
int <- y[1] - slope * x[1] # Compute the line intercept
ggplot(tmp, aes(sample=ShIR))+stat_qq(distribution=qnorm, color="royalblue", alpha=0.5) + geom_abline(intercept=int, slope=slope, color="firebrick2")
},
ggplot(tmp, aes(x=Language, y=ShIR, colour=Family)) + geom_boxplot() + ylab("ShIR") + theme(axis.text.x = element_text(angle = 45, hjust = 1)),
ggplot(tmp, aes(x=Text, y=ShIR, colour=substr(Text,1,1))) + geom_boxplot() + ylab("ShIRe") + scale_color_discrete(name = "Text") + theme(axis.text.x = element_text(angle = 45, hjust = 1))),
cols=2);
```
```{r ShIR by Speaker, echo=FALSE, message=FALSE, warning=FALSE, fig.width=10, fig.height=5, fig.cap="ShIR per speaker."}
#ggplot(info.rate.data, aes(x=Speaker, y=ShIR, color=Language)) + geom_boxplot() + ylab("ShIR") + xlab("Speakers") + theme(axis.text.x=element_blank());
ggplot(info.rate.data %>%
mutate(Speaker=reorder(Speaker, ShIR, median)) %>%
mutate(Speaker=reorder(Speaker, as.character(Sex), min)) %>%
mutate(Speaker=reorder(Speaker, as.character(Language), min)),
aes(x=Speaker, y=ShIR, color=Language, fill=Sex)) +
geom_boxplot() + #geom_vline(aes(xintercept=Language)) +
scale_fill_manual(values=c("F"="white", "M"="gray70")) +
#facet_wrap(. ~ Language, scales="free_x") +
ylab("ShIR") + xlab("Speakers") + theme(axis.text.x=element_blank());
```
```{r ShIR by Sex and Age across Languages, echo=FALSE, message=FALSE, warning=FALSE, fig.width=10, fig.height=5, fig.cap="ShIR by Sex and Age across Languages."}
ggplot(info.rate.data,
aes(x=Age, y=ShIR, color=Language, shape=Sex, fill=Sex)) +
geom_point() +
geom_smooth(aes(group=Sex), method="lm", formula=y ~ poly(x,2));
```
```{r ShIR by Sex, Age and Language, echo=FALSE, message=FALSE, warning=FALSE, fig.width=10, fig.height=8, fig.cap="ShIR by Sex, Age and Language."}
ggplot(info.rate.data,
aes(x=Age, y=ShIR, color=Sex, shape=Sex)) +
geom_point() +
geom_smooth(method="lm", formula=y ~ poly(x,2)) +
facet_wrap(. ~ Language, scales="free_x");
```
```{r ShIR distributions by language, echo=FALSE, message=FALSE, warning=FALSE, fig.width=7, fig.height=6, fig.cap="ShIR by language."}
ggplot(info.rate.data, aes(ShIR, fill = Language, colour = Language)) +
geom_density(alpha = 0.1) + geom_density(aes(ShIR), data=info.rate.data, fill=NA, color="black") + xlab("ShIR")
```
```{r IR by Language and Text, echo=FALSE, message=FALSE, warning=FALSE, fig.width=10, fig.height=10, fig.cap="IR: exploratory plots."}
multiplot(plotlist=list(ggplot(tmp, aes(x=IR)) + geom_histogram(col="yellow") + xlab("IR"),
{
# From http://mgimond.github.io/ES218/Week06a.html:
y <- quantile(tmp$IR, c(0.25, 0.75)) # Find the 1st and 3rd quartiles
x <- qnorm( c(0.25, 0.75)) # Find the matching normal values on the x-axis
slope <- diff(y) / diff(x) # Compute the line slope
int <- y[1] - slope * x[1] # Compute the line intercept
ggplot(tmp, aes(sample=IR))+stat_qq(distribution=qnorm, color="royalblue", alpha=0.5) + geom_abline(intercept=int, slope=slope, color="firebrick2")
},
ggplot(tmp, aes(x=Language, y=IR, colour=Family)) + geom_boxplot() + ylab("IR") + theme(axis.text.x = element_text(angle = 45, hjust = 1)),
ggplot(tmp, aes(x=Text, y=IR, colour=substr(Text,1,1))) + geom_boxplot() + ylab("IRe") + scale_color_discrete(name = "Text") + theme(axis.text.x = element_text(angle = 45, hjust = 1))),
cols=2);
```
```{r IR by Speaker, echo=FALSE, message=FALSE, warning=FALSE, fig.width=10, fig.height=5, fig.cap="IR per speaker."}
#ggplot(info.rate.data, aes(x=Speaker, y=IR, color=Language)) + geom_boxplot() + ylab("IR") + xlab("Speakers") + theme(axis.text.x=element_blank());
ggplot(info.rate.data %>%
mutate(Speaker=reorder(Speaker, IR, median)) %>%
mutate(Speaker=reorder(Speaker, as.character(Sex), min)) %>%
mutate(Speaker=reorder(Speaker, as.character(Language), min)),
aes(x=Speaker, y=IR, color=Language, fill=Sex)) +
geom_boxplot() + #geom_vline(aes(xintercept=Language)) +
scale_fill_manual(values=c("F"="white", "M"="gray70")) +
#facet_wrap(. ~ Language, scales="free_x") +
ylab("IR") + xlab("Speakers") + theme(axis.text.x=element_blank());
```
```{r IR by Sex and Age across Languages, echo=FALSE, message=FALSE, warning=FALSE, fig.width=10, fig.height=5, fig.cap="IR by Sex and Age across Languages."}
ggplot(info.rate.data,
aes(x=Age, y=IR, color=Language, shape=Sex, fill=Sex)) +
geom_point() +
geom_smooth(aes(group=Sex), method="lm", formula=y ~ poly(x,2));
```
```{r IR by Sex, Age and Language, echo=FALSE, message=FALSE, warning=FALSE, fig.width=10, fig.height=8, fig.cap="IR by Sex, Age and Language."}
ggplot(info.rate.data,
aes(x=Age, y=IR, color=Sex, shape=Sex)) +
geom_point() +
geom_smooth(method="lm", formula=y ~ poly(x,2)) +
facet_wrap(. ~ Language, scales="free_x");
```
```{r IR distributions by language, echo=FALSE, message=FALSE, warning=FALSE, fig.width=7, fig.height=6, fig.cap="IR by language."}
ggplot(info.rate.data, aes(IR, fill = Language, colour = Language)) +
geom_density(alpha = 0.1) + geom_density(aes(IR), data=info.rate.data, fill=NA, color="black") + xlab("IR")
```
*ShIR:*
```{r , echo=FALSE, message=FALSE, warning=FALSE}
cat(paste0("mean=",round(mean(tmp$ShIR,na.rm=TRUE),3),", ",
"median=",round(median(tmp$ShIR,na.rm=TRUE),3),", ",
"sd=",round(sd(tmp$ShIR,na.rm=TRUE),3),", ",
"CV=",round(sd(tmp$ShIR,na.rm=TRUE) / mean(tmp$ShIR,na.rm=TRUE),3),", ",
"min=",round(min(tmp$ShIR,na.rm=TRUE),3),", ",
"max=",round(max(tmp$ShIR,na.rm=TRUE),3),", ",
"kurtosis=",round(kurtosis(tmp$ShIR,na.rm=TRUE),3),", ",
"skewness=",round(skewness(tmp$ShIR,na.rm=TRUE),3),".\n"));
```
*IR:*
```{r , echo=FALSE, message=FALSE, warning=FALSE}
cat(paste0("mean=",round(mean(tmp$IR,na.rm=TRUE),3),", ",
"median=",round(median(tmp$IR,na.rm=TRUE),3),", ",
"sd=",round(sd(tmp$IR,na.rm=TRUE),3),", ",
"CV=",round(sd(tmp$IR,na.rm=TRUE) / mean(tmp$IR,na.rm=TRUE),3),", ",
"min=",round(min(tmp$IR,na.rm=TRUE),3),", ",
"max=",round(max(tmp$IR,na.rm=TRUE),3),", ",
"kurtosis=",round(kurtosis(tmp$IR,na.rm=TRUE),3),", ",
"skewness=",round(skewness(tmp$IR,na.rm=TRUE),3),".\n"));
```
#### SR and ID
```{r SR vs ID, echo=FALSE, message=FALSE, warning=FALSE, fig.width=8, fig.height=6, fig.cap="SR vs ID"}
ggplot(info.rate.data, aes(y=SR, x=ID, color=Family)) + ylim(range(info.rate.data$SR)+c(0.0,0.5)) +
geom_point(alpha=0.5, size=1) +
geom_smooth(aes(y=SR, x=ID), method="lm", color="yellow") +
geom_smooth(aes(y=SR, x=ID), method="loess", color="black") +
geom_text(aes(x=ID, label=Language), data=unique(info.rate.data[,c("ID","Language","Family")]), y=max(info.rate.data$SR), angle=90, hjust=-0.30, size=3, show.legend = FALSE) +
ylab("SR") + xlab("ID");
cor.test(info.rate.data$SR, info.rate.data$ID, method="pearson");
cor.test(info.rate.data$SR, info.rate.data$ID, method="spearman");
```
## Linear Mixed Models (LMMs)
### Linear ICCs
```{r echo=FALSE, message=FALSE, warning=FALSE}
tmp1 <- icc(lmer(NS ~ 1 + (1 | Text) + (1 | Family/Language) + (1 | Speaker), data=info.rate.data))
knitr::kable(data.frame("f"=c("Text", "Family", "Language", "Speaker"), "ICC"=c(tmp1["Text"], tmp1["Family"], tmp1["Language:Family"], tmp1["Speaker"])),
digits=2, row.names=FALSE, col.names=c("Level-1 factor (f)", "ICC"), caption="ICC for model `NS ~ 1 + (1 | Text) + (1 | Family/Language)+ (1 | Speaker)`.");
tmp1 <- icc(lmer(SR ~ 1 + (1 | Text) + (1 | Family/Language) + (1 | Speaker), data=info.rate.data))
knitr::kable(data.frame("f"=c("Text", "Family", "Language", "Speaker"), "ICC"=c(tmp1["Text"], tmp1["Family"], tmp1["Language:Family"], tmp1["Speaker"])),
digits=2, row.names=FALSE, col.names=c("Level-1 factor (f)", "ICC"), caption="ICC for model `SR ~ 1 + (1 | Text) + (1 | Family/Language)+ (1 | Speaker)`.");
tmp1 <- icc(lmer(ShIR ~ 1 + (1 | Text) + (1 | Family/Language) + (1 | Speaker), data=info.rate.data))
knitr::kable(data.frame("f"=c("Text", "Family", "Language", "Speaker"), "ICC"=c(tmp1["Text"], tmp1["Family"], tmp1["Language:Family"], tmp1["Speaker"])),
digits=2, row.names=FALSE, col.names=c("Level-1 factor (f)", "ICC"), caption="ICC for model `ShIR ~ 1 + (1 | Text) + (1 | Family/Language)+ (1 | Speaker)`.");
tmp1 <- icc(lmer(IR ~ 1 + (1 | Text) + (1 | Family/Language) + (1 | Speaker), data=info.rate.data))
knitr::kable(data.frame("f"=c("Text", "Family", "Language", "Speaker"), "ICC"=c(tmp1["Text"], tmp1["Family"], tmp1["Language:Family"], tmp1["Speaker"])),
digits=2, row.names=FALSE, col.names=c("Level-1 factor (f)", "ICC"), caption="ICC for model `IR ~ 1 + (1 | Text) + (1 | Family/Language)+ (1 | Speaker)`.");
```
### SR
#### Comparing models
```{r SR_lmm, echo=F}
lmr0 <- lmer(SR ~ 1 + (1 | Text) + (1 | Family/Language) + (1 | Speaker), data=info.rate.data);
lmr1 <- lmer(SR ~ 1 + (1 | Family/Language) + (1 | Speaker), data=info.rate.data);
lmr2 <- lmer(SR ~ 1 + (1 | Text) + (1 | Speaker), data=info.rate.data);
lmr3 <- lmer(SR ~ 1 + (1 | Text) + (1 | Family/Language), data=info.rate.data);
lmr4 <- lmer(SR ~ 1 + Sex + (1 | Text) + (1 | Family/Language) + (1 | Speaker), data=info.rate.data);
lmr5 <- lmer(SR ~ 1 + Sex + (1 | Family/Language) + (1 | Speaker), data=info.rate.data);
lmr6 <- lmer(SR ~ 1 + Sex + (1 | Text) + (1 | Speaker), data=info.rate.data);
lmr7 <- lmer(SR ~ 1 + Sex + (1 | Text) + (1 | Family/Language), data=info.rate.data);
tmp <- do.call(rbind, lapply(list(lmr0, lmr1, lmr2, lmr3, lmr4, lmr5, lmr6, lmr7),
function(lmr) data.frame("model"=as.character(summary(lmr, ddf="lme4")$call$formula)[3], "AIC"=round(AIC(lmr),2), "BIC"=round(BIC(lmr),2))));
tmp$AIC[ which.min(tmp$AIC) ] <- paste0("**",tmp$AIC[ which.min(tmp$AIC) ],"**");
tmp$BIC[ which.min(tmp$BIC) ] <- paste0("**",tmp$BIC[ which.min(tmp$BIC) ],"**");
knitr::kable(tmp, row.names=FALSE, caption="AIC and BIC for various hierarchical models of `SR` (in **bold** are the minimum values).");
```
#### Residuals and random effects
We consider here the full model `SR ~ 1 + Sex + (1|Text) + (1|Family/Language) + (1|Speaker)`.
```{r SR_assumptions, echo=F}
lmr <- lmer(SR ~ 1 + Sex + (1|Text) + (1|Family/Language) + (1|Speaker), data=info.rate.data)
# summary(lmr)
plot(lmr)
get_re_distrib(residuals(lmr), "Residuals")
get_re_distrib(ranef(lmr)$Text[,1], "Levels of Text as random effect")
get_re_distrib(ranef(lmr)$Language[,1], "Levels of Language as random effect")
get_re_distrib(ranef(lmr)$Family[,1], "Levels of Family as random effect")
get_re_distrib(ranef(lmr)$Speaker[,1], "Levels of Speaker as random effect")
# sjp.lmer(lmr0,
# facet.grid = FALSE,
# sort.est = "sort.all",
# y.offset = .4)
#plot_model(lmr,
# facet.grid = FALSE,
# sort.est = "sort.all",
# y.offset = .4)
```
### IR
#### Comparing models
```{r IR_lmm, echo=F}
lmr0 <- lmer(IR ~ 1 + (1 | Text) + (1 | Family/Language) + (1 | Speaker), data=info.rate.data);
lmr1 <- lmer(IR ~ 1 + (1 | Family/Language) + (1 | Speaker), data=info.rate.data);
lmr2 <- lmer(IR ~ 1 + (1 | Text) + (1 | Speaker), data=info.rate.data);
lmr3 <- lmer(IR ~ 1 + (1 | Text) + (1 | Family/Language), data=info.rate.data);
lmr4 <- lmer(IR ~ 1 + Sex + (1 | Text) + (1 | Family/Language) + (1 | Speaker), data=info.rate.data);
lmr5 <- lmer(IR ~ 1 + Sex + (1 | Family/Language) + (1 | Speaker), data=info.rate.data);
lmr6 <- lmer(IR ~ 1 + Sex + (1 | Text) + (1 | Speaker), data=info.rate.data);
lmr7 <- lmer(IR ~ 1 + Sex + (1 | Text) + (1 | Family/Language), data=info.rate.data);
tmp <- do.call(rbind, lapply(list(lmr0, lmr1, lmr2, lmr3, lmr4, lmr5, lmr6, lmr7),
function(lmr) data.frame("model"=as.character(summary(lmr, ddf="lme4")$call$formula)[3], "AIC"=round(AIC(lmr),2), "BIC"=round(BIC(lmr),2))));
tmp$AIC[ which.min(tmp$AIC) ] <- paste0("**",tmp$AIC[ which.min(tmp$AIC) ],"**");
tmp$BIC[ which.min(tmp$BIC) ] <- paste0("**",tmp$BIC[ which.min(tmp$BIC) ],"**");
knitr::kable(tmp, row.names=FALSE, caption="AIC and BIC for various hierarchical models of `IR` (in **bold** are the minimum values).");
```
#### Residuals and random effects
We consider here the full model `IR ~ 1 + Sex + (1|Text) + (1|Family/Language) + (1|Speaker)`.
```{r IR_assumptions, echo=F}
lmr <- lmer(IR ~ 1 + Sex + (1|Text) + (1|Family/Language) + (1|Speaker), data=info.rate.data)
#summary(lmr)
plot(lmr)
get_re_distrib(residuals(lmr), "Residuals")
get_re_distrib(ranef(lmr)$Text[,1], "Levels of Text as random effect")
get_re_distrib(ranef(lmr)$Language[,1], "Levels of Language as random effect")
get_re_distrib(ranef(lmr)$Family[,1], "Levels of Family as random effect")
get_re_distrib(ranef(lmr)$Speaker[,1], "Levels of Speaker as random effect")
# sjp.lmer(lmr0,
# facet.grid = FALSE,
# sort.est = "sort.all",
# y.offset = .4)
#plot_model(lmr,
# facet.grid = FALSE,
# sort.est = "sort.all",
# y.offset = .4)
```
## Generalized Additive Models for Location, Scale and Shape (GAMLSS)
We will use a Gaussian distribution (with fixed or modelled variance).
### SR
#### Fixed or modelled *σ* (variance)
##### Fixed *σ*
```{r SR_check_NO_no_sigma, echo=FALSE}
d <- info.rate.data[,c("SR","Sex","Text","Language","Family","Speaker")]; # use only the columns we actually need (avoid errors about NAs in other columns)
model.NO.no.modelled.sigma.SR <- gamlss(SR ~ 1 + Sex + random(Text) + random(Language) + random(Family) + random(Speaker),
data=d,
family=NO(mu.link="identity"),
control = gamlss.control(n.cyc = 800, trace = FALSE), i.control=glim.control(bf.cyc = 800))
plot(model.NO.no.modelled.sigma.SR)
wp(model.NO.no.modelled.sigma.SR, ylim.all=2)
cat("\nDeviance=",deviance(model.NO.no.modelled.sigma.SR, what = "G"),"\n");
cat("\nAIC=",AIC(model.NO.no.modelled.sigma.SR),"\n");
```
##### Modelled *σ*
```{r SR_check_NO, echo=FALSE}
d <- info.rate.data[,c("SR","Sex","Text","Language","Family","Speaker")]; # use only the columns we actually need (avoid errors about NAs in other columns)
model.NO.SR <- gamlss(SR ~ 1 + Sex + random(Text) + random(Language) + random(Family) + random(Speaker),
sigma.fo = ~ 1 + Sex + random(Text) + random(Language) + random(Family) + random(Speaker),
data=d,
family=NO(mu.link="identity"),
control = gamlss.control(n.cyc = 800, trace = FALSE), i.control=glim.control(bf.cyc = 800))
plot(model.NO.SR)
wp(model.NO.SR, ylim.all=0.4)
cat("\nDeviance=",deviance(model.NO.SR, what = "G"),"\n");
cat("\nAIC=",AIC(model.NO.SR),"\n");
```
The distribution of the residuals is less heteroscedastic than before and the fit to the data better.
The full summary of the model is:
```{r SR_summary, echo=FALSE}
summary(model.NO.SR)
```
#### Random effects
##### *μ*
**Text**
```{r SR_re_mu_text, echo=FALSE}
getSmo(model.NO.SR, "mu", which = 1)
```
**Language**
```{r SR_re_mu_lg, echo=FALSE}
getSmo(model.NO.SR, "mu", which = 2)
```
**Family**
```{r SR_re_mu_fam, echo=FALSE}
getSmo(model.NO.SR, "mu", which = 3)
```
**Speaker**
```{r SR_re_mu_spk, echo=FALSE}
getSmo(model.NO.SR, "mu", which = 4)
```
##### *σ*
**Text**
```{r SR_re_sigma_text, echo=FALSE}
getSmo(model.NO.SR, "sigma", which = 1)
```
**Language**
```{r SR_re_sigma_lg, echo=FALSE}
getSmo(model.NO.SR, "sigma", which = 2)
```
**Family**
```{r SR_re_sigma_fam, echo=FALSE}
getSmo(model.NO.SR, "sigma", which = 3)
```
**Speaker**
```{r SR_re_sigma_spk, echo=FALSE}
getSmo(model.NO.SR, "sigma", which = 4)
```
### IR
#### Fixed or modelled *σ* (variance)
##### Fixed *σ*
```{r IR_check_NO_no_sigma, echo=FALSE}
d <- info.rate.data[,c("IR","Sex","Text","Language","Family","Speaker")]; # use only the columns we actually need (avoid errors about NAs in other columns)
model.NO.no.modelled.sigma.IR <- gamlss(IR ~ 1 + Sex + random(Text) + random(Language) + random(Family) + random(Speaker),
data=d,
family=NO(mu.link="identity"),
control = gamlss.control(n.cyc = 800, trace = FALSE), i.control=glim.control(bf.cyc = 800))
plot(model.NO.no.modelled.sigma.IR)
wp(model.NO.no.modelled.sigma.IR, ylim.all=0.4)
cat("\nDeviance=",deviance(model.NO.no.modelled.sigma.IR, what = "G"),"\n");
cat("\nAIC=",AIC(model.NO.no.modelled.sigma.IR),"\n");
```
##### Modelled *σ*
```{r IR_check_NO, echo=FALSE}
d <- info.rate.data[,c("IR","Sex","Text","Language","Family","Speaker")]; # use only the columns we actually need (avoid errors about NAs in other columns)
model.NO.IR <- gamlss(IR ~ 1 + Sex + random(Text) + random(Language) + random(Family) + random(Speaker),
sigma.fo = ~ 1 + Sex + random(Text) + random(Language) + random(Family) + random(Speaker),
data=d,
family=NO(mu.link="identity"),
control = gamlss.control(n.cyc = 800, trace = FALSE), i.control=glim.control(bf.cyc = 800))
plot(model.NO.IR)
wp(model.NO.IR, ylim.all=0.4)
cat("\nDeviance=",deviance(model.NO.IR, what = "G"),"\n");
cat("\nAIC=",AIC(model.NO.IR),"\n");
```
Again, this is a better fit to the data.
The full summary of the model is:
```{r IR_summary, echo=FALSE}
summary(model.NO.IR)
```
#### Random effects
##### *μ*
**Text**
```{r IR_re_mu_text, echo=FALSE}
getSmo(model.NO.IR, "mu", which = 1)
```
**Language**
```{r IR_re_mu_lg, echo=FALSE}
getSmo(model.NO.IR, "mu", which = 2)
```
**Family**
```{r IR_re_mu_fam, echo=FALSE}
getSmo(model.NO.IR, "mu", which = 3)
```
**Speaker**
```{r IR_re_mu_spk, echo=FALSE}
getSmo(model.NO.IR, "mu", which = 4)
```
##### *σ*
**Text**
```{r IR_re_sigma_text, echo=FALSE}
getSmo(model.NO.IR, "sigma", which = 1)
```
**Language**
```{r IR_re_sigma_lg, echo=FALSE}
getSmo(model.NO.IR, "sigma", which = 2)
```
**Family**
```{r IR_re_sigma_fam, echo=FALSE}
getSmo(model.NO.IR, "sigma", which = 3)
```
**Speaker**
```{r IR_re_sigma_spk, echo=FALSE}
getSmo(model.NO.IR, "sigma", which = 4)
```
## Modelling the relationship between SR and ID
Let's model *SR* with *ID* as an additional predictor (fixed effect) interacting with *Sex*.
*N.B.* In this case, we must drop *Language* as a random effect, since each language has, by definition, only one value of *ID.*
```{r SR_ID_gamlss, echo=FALSE}
d <- info.rate.data[,c("SR","ID","Sex","Text","Family","Speaker")]; # use only the columns we actually need (avoid errors about NAs in other columns)
model.NO.SR.ID <- gamlss(SR ~ 1 + ID * Sex + random(Text) + random(Speaker) + random(Family),
sigma.fo = ~ 1 + ID + Sex + random(Text) + random(Speaker) + random(Family),
data=d,
family=NO(mu.link="identity"),
control = gamlss.control(n.cyc = 800, trace = FALSE), i.control=glim.control(bf.cyc = 800))
summary(model.NO.SR.ID)
plot(model.NO.SR.ID)
wp(model.NO.SR.ID, ylim.all=0.5)
cat("\nDeviance=",deviance(model.NO.SR.ID, what = "G"),"\n");
cat("\nAIC=",AIC(model.NO.SR.ID),"\n");
```
Adding *ID* as a predictor improves the fits (as judged by AIC).
There is a negative estimate for ID, but significance is difficult to assess with GAMLSS model involving smoothing functions.
However, also using a simple `lmer` model we have a significant effect of *ID*:
```{r SR_ID_lmer, echo=FALSE}
lmer.SR.ID <- lmer(SR ~ 1 + ID * Sex + (1 | Text) + (1 | Speaker) + (1 | Family), data=info.rate.data)
summary(lmer.SR.ID)
anova(lmer.SR.ID)
```
### Random effects
#### *μ*