complexity_analysis_DTA.R

setwd("./Datasets")

library(readxl)
library(ggplot2)
library(matrixStats)
library(effects)
library(lmtest)
library(reshape2)
library(dplyr)
library(CADFtest)

#### morphology ####

# read data
morph_data <- read_xlsx("zipped_morphology_DTA.xlsx", col_names = TRUE)
zipped <- read_xlsx("DTA_Zipped_Sizes.xlsx", col_names = TRUE)

# merge data
morph_total <- merge(zipped, morph_data, by="...1")

# make all numbers negative
morph_total[,6:105] <- morph_total[,6:105]*(-1)
# divide by full zipped size to get complexity ratio
morph_total[,6:105] <- morph_total[,6:105]/morph_total[,4]
# get means for each row = get mean complexity ratio
morph_means <- rowMeans(morph_total[,6:105])
# add mean complexity ratios to data frame
morph_total$morph_means <- morph_means
# get standard deviations
morph_std = rowSds(as.matrix(morph_total[,6:105]))


# linear model
morph_model <- lm(morph_means ~ year, data=morph_total)
summary(morph_model)
plot(allEffects(morph_model))

# make plots

mp <- ggplot(morph_total, 
             aes(x = year, y = morph_means))+
  ggtitle("Morphological complexity ratio over time") +
  xlab("Year")+
  ylab("Mean morphological complexity ratio")+
  geom_point()
mp

ml <- ggplot(morph_total, 
             aes(x = year, y = morph_means))+
  ggtitle("Morphological complexity ratio over time") +
  xlab("Year")+
  ylab("Mean morphological complexity ratio")+
  geom_point()+
  geom_smooth()
ml

#### syntax ####

# read data
synt_data <- read_xlsx("zipped_syntax_DTA.xlsx", col_names = TRUE)

# merge data
synt_total <- merge(zipped, synt_data, by="...1")

# divide by full zipped size to get complexity ratio
synt_total[,6:105] <- synt_total[,6:105]/synt_total[,4]
# get means for each row = get mean complexity ratio
synt_means <- rowMeans(synt_total[,6:105])
# add mean complexity ratios to data frame
synt_total$synt_means <- synt_means
# get standard deviations
synt_std = rowSds(as.matrix(synt_total[,6:105]))


# linear model
synt_model <- lm(synt_means ~ year, data=synt_total)
summary(synt_model)
plot(allEffects(synt_model))

# make plots

sp <- ggplot(synt_total, 
             aes(x = year, y = synt_means))+
  ggtitle("Syntactic complexity ratio over time") +
  xlab("Year")+
  ylab("Mean syntactic complexity ratio")+
  geom_point()
sp

sl <- ggplot(synt_total, 
             aes(x = year, y = synt_means))+
  ggtitle("Syntactic complexity ratio over time") +
  xlab("Year")+
  ylab("Mean syntactic complexity ratio")+
  geom_point()+
  geom_smooth()
sl

#### morphology vs syntax ####

morph_and_synt <- data.frame("morph" = morph_total$morph_means, 
                             "synt" = synt_total$synt_means,
                             "year" = synt_total$year,
                             "filename" = synt_total$filename)

morph_and_synt <- morph_and_synt[morph_and_synt$year >= 1863 & morph_and_synt$year <= 1927, ]


morph_and_synt_model <- lm(morph_means ~ synt_means, data=morph_and_synt)
summary(morph_and_synt_model)

scp <- ggplot(morph_and_synt,
              aes(x = synt, y = morph))+
  ggtitle("") +
  xlab("Mean word order rigidity ratio")+
  ylab("Mean morphological complexity ratio")+
  geom_point()
scp

#### Time series analysis ####

# make time series for morphology means
morph_ts <- ts(morph_and_synt$morph, start = 1863, frequency = 1)

CADFtest(morph_ts) # significant
plot(morph_ts)

morph_diff_ts <- diff(morph_ts) # detrending

# make time series for syntax means
synt_ts <- ts(morph_and_synt$synt, start = 1863, frequency = 1)

CADFtest(synt_ts) # significant
plot(synt_ts)

synt_diff_ts <- diff(synt_ts) # detrending

# granger causality test
grangertest(synt_diff_ts ~ morph_diff_ts, order = 2)
grangertest(morph_diff_ts ~ synt_diff_ts, order = 2)

grangertest(synt_ts ~ morph_ts, order = 1)
grangertest(morph_ts ~ synt_ts, order = 1)

# visualization

tsDF <- data.frame(Year = seq(from = 1863, to = 1927, by = 1),
                   "Syntax" = synt_ts,
                   "Morphology" = morph_ts)

library(latticeExtra)

m <- xyplot(Morphology ~ Year, tsDF, type = "l", lwd = 2, ylab = "Morphological complexity")
s <- xyplot(Syntax ~ Year, tsDF, type = "l", lwd = 2, ylab = "Word order rigidity")
doubleYScale(m, s, add.ylab2 = TRUE, use.style=TRUE)

# Z-scored plot

# Z-score the time series
z_scored_morph <- scale(morph_ts)
z_scored_synt <- scale(synt_ts)

# Determine the range of y-values
y_range <- range(z_scored_morph, z_scored_synt)

# Create a plot without drawing the x-axis
plot(z_scored_morph, type = "l", lty = 1, ylim = y_range, 
     ylab = "Z-Scored Values", 
     xlab = "Time", 
     xaxt = "n")  # Suppress drawing of the x-axis

# Add the second z-scored time series to the plot with a different line type
lines(z_scored_synt, lty = 2)

# Add a legend
legend("topright", legend = c("Morphological complexity", "Word order rigidity"), lty = c(1, 2), cex = 0.5)

# Add years to the plot
years <- seq(1863, 1927, by = 5)  # Starting from 1863, incrementing by 5 until 1927
last_year <- 1927
years <- c(years, last_year)  # Include 1927

# Calculate the positions of the ticks based on the length of the time series
tick_positions <- seq(1, length(z_scored_morph), length.out = length(years))

axis(1, at = tick_positions, labels = years)