Chapter 10 Bonus Content Reserve Space
All right, well I figure I’d get started with some ‘bonus’ content, which for the moment will be a collection of bits of analysis I’ve done (often connected with research) that may be interesting or relevant, but I am yet to allocate it to specific chapters earlier in this textbook.
10.1 Principle Components Analysis (PCA)
PCA is a pretty powerful and interesting analysis, where essentially it is a type of data reduction. The key idea here is to take data and to reduce it and by doing this, we reveal complex and hidden structures within the original, larger dataset. This analysis can also help highlight important information within datasets while simultaneously reducing it’s size via component reduction. (Please note, this is slightly paraphrased from my paper, which can be read here: https://www.sciencedirect.com/science/article/pii/S0747563222000280) this subsequently is also where half of the analysis will come from as an example of various R packages one can use for PCA (and more generally, factor analyses).
The example in the paper above is a very specific use of a PCA. Here, we were looking at various psychometric scales used to measure people’s smartphone use. By psychometric scales, I mean being given a questionnaire and participants respond to rating scales (often from ‘strongly agree to strongly disagree). There are literally 100s of these scales that claim to measure various types of technology use, and many of which claim to measure unique types of usage, such as ’smartphone addiction’, ‘absent-minded smartphone use’, ‘phobia of being without a smartphone’, or ‘problematic smartphone use’. Each of these in their respective papers (see citations in the paper itself) pertain to be unique constructs. If this is so, when running a PCA over these data, we should find the same number of components as scales, as they should be unique enough, right?
Well, we found here, these scales are all measuring the same thing as they reduce down to only ONE component, whereby none of these scales are unique (nor do they actually measure technology use as we’ve found in other work – I’ll write more about this and add in more of this work ad examples of data analysis using real world data).
Anyway, lets have a look at how we run a PCA (I will expand the above to talk more about this, but I wanted to give a little background).
library('readr')
library('ltm') #for dependencies and the MASS package## Loading required package: msm## Loading required package: polycor##
## Attaching package: 'polycor'## The following object is masked from 'package:psych':
##
## polyserial##
## Attaching package: 'ltm'## The following object is masked from 'package:psych':
##
## factor.scoreslibrary('dplyr') #data wrangling
library("nFactors") #parts of factor analyses##
## Attaching package: 'nFactors'## The following object is masked from 'package:lattice':
##
## parallellibrary('factoextra') #parts of factor analysis
library('magrittr') #piping
library('psych') #stats/data analysis
StudyOne_IJHCS <- read.csv("StudyOne_IJHCS.csv", header = T)
head(StudyOne_IJHCS) # so here we have 10 columns, each are a different scale## MPPUS NS ES Sat SAS SABAS PMPUQ MTUAS SUQ_G SUQ_A
## 1 126 93 23 21 124 17 29 6.111111 42 54
## 2 154 124 18 20 98 13 28 6.444444 48 58
## 3 121 70 26 20 99 17 28 6.000000 43 54
## 4 102 89 23 22 94 16 27 5.666667 44 48
## 5 132 106 18 17 108 22 36 6.222222 50 59
## 6 77 74 16 13 87 10 27 6.222222 57 57When running a PCA, we need to be aware of correlations, often when doing a PCA we check that things are not highly correlated. We know that some these scales are well-correlated and generally you’d even drop some before running the PCA as it already suggests they’re measuring something similar (if not the same thing)…
Anyway, for the purposes of the study, we kept in all 10 scales and we create a correlation matrix as this is the data type required for the analysis. As a note, we are also doing whats known as a parallel analysis too to ensure our results are robust. A parallel analysis creates simulated random datasets (we used N=100) to then compare the eigenvalues from the simulated datastes against our dataset. (To be expanded…)
Prior to doing a PCA analysis, it is important to check sampling adequacy (MSA), which is done via the Kaiser-Meyer-Olkin (KMO) test. The average MSA for our sample was 0.9, more than sufficient to proceed (generally anything above 0.6 is good, see paper for more info).
PCA = cor(StudyOne_IJHCS)# for the parallel analysis, this needs to be a correlation matrix
# checking sampling adequacy (KMO)
KMO(PCA) #overall MSA = 0.9, which is "marvelous"## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = PCA)
## Overall MSA = 0.9
## MSA for each item =
## MPPUS NS ES Sat SAS SABAS PMPUQ MTUAS SUQ_G SUQ_A
## 0.90 0.96 0.87 0.86 0.92 0.93 0.96 0.83 0.86 0.90From here, everything looks OK for us to proceed with a PCA analysis. This is quite a simple set of code and includes the parallel analysis in there. Just be careful to adapt the numbers in the code to fit your dataset…
PCAParallel <- fa.parallel(PCA,
n.obs=238, #make sure this is correct for your sample
fm="minres",
fa="pc", #pc = PCA, both = PCA and Factor Analysis, fa = Factor analysis only
nfactors=1,
main="Parallel Analysis Scree Plots",
n.iter=100, #how many simulated datasets?
error.bars=FALSE,
se.bars=FALSE,
SMC=FALSE,
ylabel=NULL,
show.legend=TRUE,
sim=T,
quant=.95,
cor="cor",
use="pairwise",
plot=TRUE,correct=.5)
## Parallel analysis suggests that the number of factors = NA and the number of components = 1print(PCAParallel)## Call: fa.parallel(x = PCA, n.obs = 238, fm = "minres", fa = "pc", nfactors = 1,
## main = "Parallel Analysis Scree Plots", n.iter = 100, error.bars = FALSE,
## se.bars = FALSE, SMC = FALSE, ylabel = NULL, show.legend = TRUE,
## sim = T, quant = 0.95, cor = "cor", use = "pairwise", plot = TRUE,
## correct = 0.5)
## Parallel analysis suggests that the number of factors = NA and the number of components = 1
##
## Eigen Values of
##
## eigen values of factors
## [1] 5.33 0.57 0.30 0.04 -0.03 -0.04 -0.11 -0.14 -0.25 -0.33
##
## eigen values of simulated factors
## [1] NA
##
## eigen values of components
## [1] 5.75 1.15 0.81 0.61 0.44 0.32 0.30 0.25 0.21 0.16
##
## eigen values of simulated components
## [1] 1.33 1.23 1.15 1.09 1.02 0.96 0.90 0.84 0.78 0.70So, how do we interpret this? Well, if the eigenvalues from our dataset exceed the simulated average eigenvalues, we retain them as a component. The PA here revealed only one component, which you can also see in the figure plotted. Our simulated eigenvalue was 1.33 in comparison to 5.75 (our dataset). You can see the rest of the eigen values in our dataset are lower than the simulated and are therefore dropped.
We can also create other visualizations from a PCA, for instance a biplot:
#biplot viz
res.pca <- prcomp(StudyOne_IJHCS, scale = TRUE)
fviz_eig(res.pca)
fviz_pca_var(res.pca,
col.var = "contrib", # Color by contributions to the PC
gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
repel = TRUE # Avoid text overlapping
)
A biplot allows us to visualize and assess the quality of representation (cosine2) across all scales by plotting the amount of variance explained across two components. Most scales aligned with component one (57.5% variance explained) (x-axis) with few aligning with component two (y-axis) (11.5% variance explained).
This essentially further shows the lack of the existence of more than one component. The cosine2 value/coloring of the lines for each scale reveals which scale(s) contribute the most to each component… what we can see here is that the SAS (smartphone addiction scale) is the most representative scale across the whole sample.
Generally what this overall shows is that these scales all fall into one cluster and appear to measure a very similar, if not identical, construct.
# Bonus Content: More Advanced Topic Modelling
As I had mentioned earlier in the textbook, I wanted to also provide real-life examples using real and noisy data (that sometimes makes you want to cry and reconsider why we wanted to do this work in the first place!) – I’m kidding, although, the more you get into data science, you will encounter projects, data, or types of analysis that test your resilience!
Here, we will look at another way to approach topic modelling. The entire concept is the same as had been shown earlier in the textbook, but we will be using a new package: text2vec and LDAvis. text2vec is an R package that provides a pretty efficient way of doing NLP in R. They have a nice website that shows you everything this package can do here (https://text2vec.org/topic_modeling.html). We are only focusing on Topic Modelling.
All right, let’s get started…
library('dplyr')
library('text2vec')
library('data.table')
library('readr')
library('SnowballC')So we’ve loaded some packages to get us started. I am using a dataset that contains social media posts from extreme right-wing social media sites. If you’re interested in knowing more, please drop me an email with your questions. Of course, due to the nature of the data… I will NOT be showing any dataviz showing the topics, however, when the final article is out on this, I will create a link to it so you can see them there.
To follow the analysis, please
## Warning: Missing column names filled in: 'X1' [1]##
## ── Column specification ─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
## cols(
## X1 = col_double(),
## PPT_ID = col_double(),
## platform = col_character(),
## prosecuted = col_double(),
## arrested = col_character(),
## username = col_character(),
## date = col_character(),
## server = col_character(),
## message = col_character(),
## links = col_double(),
## questionmarks = col_double(),
## exclaimation = col_double(),
## all_punc = col_double(),
## word_count = col_double()
## )##
## ── Column specification ─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
## cols(
## X1 = col_character()
## )# This data has lots of columns, but we are only interested the message here.
# Our first step is to clean the data up a little bit...
#going to get rid of abbreviations in text, as shown in the function:
fix.contractions <- function(doc) {
doc <- gsub("won't", "will not", doc)
doc <- gsub("can't", "can not", doc)
doc <- gsub("n't", " not", doc)
doc <- gsub("'ll", " will", doc)
doc <- gsub("'re", " are", doc)
doc <- gsub("'ve", " have", doc)
doc <- gsub("'m", " am", doc)
doc <- gsub("'d", " would", doc)
doc <- gsub("'s", "", doc)
doc <- gsub("they'r", "they are", doc)
doc <- gsub("they'd", "they had", doc)
doc <- gsub("they'v", "they have", doc)
return(doc)
}
#then we can apply this to our message column
final_data$message = sapply(final_data$message, fix.contractions)
# function to remove special characters throughout the text - so this will be a nicer/easier base to tokenise and analyse
removeSpecialChars <- function(x) gsub("[^a-zA-Z0-9 ]", "", x)
removeNumbers <- function(x) gsub('[[:digit:]]+', '', x)
final_data$message = sapply(final_data$message, removeSpecialChars)
final_data$message = sapply(final_data$message, removeNumbers)
# convert everything to lower case
final_data$message <- sapply(final_data$message, tolower)
#this is never perfect (and is not here!) but you need to check things out iteratively
#until you are happy enough with the cleaningOnce we have finished some cleaning (you can always do more, as the above is a very BASIC form of cleaning)… we can get started with preparation for the topic modelling….
10.2 Data Prep
setDT(final_data) #this forces data into a datatable format
setkey(final_data, X1) #this is setting an ID column First, we need to create tokens from our messages… we can also use in-built functions like ‘tolower’, which I have shown here (not necessary as this was already done before). We can also attempt (as these do not always work brilliantly) to stem words (aka, if we had running, ran, and runner, these would all revert to run).
tokens = final_data$message %>%
tolower %>%
word_tokenizer #making tokens
tokens = lapply(tokens, SnowballC::wordStem, language="en") #stemming words to help with duplication
it = itoken(tokens, ids = final_data$X1, progressbar = T) #iterating over tokens to build a vocab (see below)While also loading the dataset, I have also loaded in a smaller csv file of a collection of stop words that I have collected. You can find these online, which I did, and I added my own words, too. This is speciifc to this dataset, as of course, when doing topic modelling we need to remove any words that may be irrelevant and actually just add noise into the topics. One thing to notice is that file formats (and sometimes the langauges themselves like R or python) cannot handle all characters, especially non-ascii ones… so I have a copied list I also put into my stop words based on doing this coding iteratively to remove nonsense characters that add noise to my topic models…
#sorting out stop words (manual and list)
#the stop words list was imported already... and we are making this a vector so then we can add additional
#words and characters to remove
stop_list = as.vector(stop_words[[1]])
#additional characters to manually remove
remove = c("ª",
"á",
"å",
"ä",
"ç",
"æ",
"é",
"ê",
"ë",
"ñ",
"º",
"ô",
"ø",
"òö",
"tt",
"û",
"ü",
"µ",
"ω",
'ï',
'ïë',
'u',
'ïê',
'ñì',
'äî',
'îå',
"I'm",
'im',
"Im",
"ð",
"â",
"ã",
"i've",
"you're",
"don't",
"ð_ð",
"ã_ã",
"NA",
'yea',
'yeah',
'gonna',
'dont',
'oh',
'org',
'name',
'lol',
'guy',
'guys',
'literally',
'am',
'actually',
'getting',
'lot',
'little',
'probably',
'yes',
'√§√',
',Äç',
'äù',
'äì',
'äôs',
'äôt',
'01',
'02',
'03',
'04',
'05',
'06',
'07',
'08',
'09')
stop_list = c(stop_list, remove) #merged into one list to remove from modelNext, we create a vocabulary from our tokens, and we can prune this down and remove our stop words. When we prune, this is a manual number we select, and this is based on knowledge of the dataset, so you might need to do this a few times. We have set this to 50, where each term has to appear a minimum of 50 times otherwise it is not included in the vocabulary. Similarly, we ensure that the word is not a obscenely high proportion of the data, so we have set this to 0.1 (aka 10% of the data maximum). We then create a document term matrix (dtm).
v = create_vocabulary(it, stopwords = stop_list) %>%
prune_vocabulary(term_count_min = 50, doc_proportion_max = 0.1)
vectorizer = vocab_vectorizer(v)
dtm = create_dtm(it, vectorizer, type = "dgTMatrix") #this is just using words (you can use bigrams, for example, too!)Here, we can proceed with doing our topic modelling! There are a couple ways we can do this…
We can iteratively figure out what the right number of topics is by manually inspecting it…
Or, we can check whats known as topic coherence, which is a data-driven method to see which topics appear to be the most coherent
Both of these are valid topics and often give very different answers.
10.3 Manually testing different numbers of topics
Here we are testing n=4 topics in our dataset.
# note it is really important to set seed here...
#otherwise this will not reproduce each time...!
set.seed(127)
lda_model = LDA$new(n_topics =4, doc_topic_prior = 0.1, topic_word_prior = 0.01)
doc_topic_distr = lda_model$fit_transform(x = dtm, n_iter = 500,
convergence_tol = 0.001, n_check_convergence = 25,
progressbar = T)##
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|=======================================================================================================================================| 100%INFO [14:54:18.874] early stopping at 225 iteration
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|=======================================================================================================================================| 100%INFO [14:54:21.588] early stopping at 75 iterationHere, we can select a given document (aka a row in the dataset), and see the topics distribtion in each one….
#little data viz...
#this is looking at the proportion of topics in the dataset
barplot(doc_topic_distr[127, ], xlab = "topic",
ylab = "proportion", ylim = c(0, 1),
names.arg = 1:ncol(doc_topic_distr))
10.4 Topic Coherence Measures
There are a number of different types of topic coherence, but this is one way we used. We were calculating the normalized pointwise mutual information (NPMI), but there are others you can use (e.g., https://search.r-project.org/CRAN/refmans/text2vec/html/coherence.html). Here, in the following code we iterate between 3 to 20 topics by 1 (aka every single number and not skipping any). Note: the code for the coherence metrics was written by Daniel Racek, I tried and panicked, so he helped me figure it out.
Do note, if you run a version of this code (aka please copy cat it if you want to), this will take a while to code as it is literally running a topic model for each of the number of topics between 3 to 20. So give it time and don’t panic!
RcppParallel::setThreadOptions(1)
coh_results = tibble()
for(i in seq(3,20, by = 1)){
print(i)
set.seed(127)
lda_model = LDA$new(n_topics =i, doc_topic_prior = 0.1, topic_word_prior = 0.01)
doc_topic_distr = lda_model$fit_transform(x = dtm, n_iter = 500,
convergence_tol = 0.001, n_check_convergence = 25,
progressbar = T)
tcm = create_tcm(it, vectorizer
,skip_grams_window = 110
,weights = rep(1, 110)
,binary_cooccurence = TRUE
)
diag(tcm) = attributes(tcm)$word_count
n_skip_gram_windows = sum(sapply(tokens, function(x) {length(x)}))
tw = lda_model$get_top_words(n = 50, lambda = 0.4)
# check coherence
res = coherence(tw, tcm, metrics = "mean_npmi_cosim2", n_doc_tcm = n_skip_gram_windows)
coh_results = bind_rows(coh_results, tibble("topic_n" = i, "coh" = mean(res)))
}## [1] 3
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|=======================================================================================================================================| 100%INFO [14:54:27.292] early stopping at 150 iteration
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|=======================================================================================================================================| 100%INFO [14:54:29.038] early stopping at 50 iteration
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|=======================================================================================================================================| 100%INFO [14:54:44.813] early stopping at 225 iteration
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|=======================================================================================================================================| 100%INFO [14:54:47.637] early stopping at 75 iteration
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|=======================================================================================================================================| 100%INFO [14:55:02.679] early stopping at 200 iteration
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|=======================================================================================================================================| 100%INFO [14:55:05.852] early stopping at 75 iteration
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## [1] 6
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|=======================================================================================================================================| 100%INFO [14:55:23.151] early stopping at 250 iteration
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|=======================================================================================================================================| 100%INFO [14:55:26.419] early stopping at 75 iteration
##
## [1] 7
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|=======================================================================================================================================| 100%INFO [14:55:42.669] early stopping at 225 iteration
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|=======================================================================================================================================| 100%INFO [14:55:45.863] early stopping at 75 iteration
##
## [1] 8
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|=======================================================================================================================================| 100%INFO [14:56:03.605] early stopping at 250 iteration
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|=======================================================================================================================================| 100%INFO [14:56:06.697] early stopping at 75 iteration
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## [1] 9
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|=======================================================================================================================================| 100%INFO [14:56:23.765] early stopping at 250 iteration
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|=======================================================================================================================================| 100%INFO [14:56:26.905] early stopping at 75 iteration
##
## [1] 10
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|=======================================================================================================================================| 100%INFO [14:56:47.917] early stopping at 300 iteration
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|=======================================================================================================================================| 100%INFO [14:56:51.340] early stopping at 75 iteration
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|=======================================================================================================================================| 100%INFO [14:57:08.184] early stopping at 225 iteration
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|=======================================================================================================================================| 100%INFO [14:57:11.590] early stopping at 75 iteration
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## [1] 12
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|=======================================================================================================================================| 100%INFO [14:57:32.263] early stopping at 300 iteration
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|=======================================================================================================================================| 100%INFO [14:57:35.644] early stopping at 75 iteration
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## [1] 13
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|=======================================================================================================================================| 100%INFO [14:57:56.448] early stopping at 325 iteration
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|=======================================================================================================================================| 100%INFO [14:57:59.636] early stopping at 75 iteration
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## [1] 14
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|=======================================================================================================================================| 100%INFO [14:58:21.325] early stopping at 350 iteration
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|=======================================================================================================================================| 100%INFO [14:58:24.516] early stopping at 75 iteration
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## [1] 15
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|=======================================================================================================================================| 100%INFO [14:58:44.079] early stopping at 300 iteration
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|=======================================================================================================================================| 100%INFO [14:58:47.225] early stopping at 75 iteration
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|=======================================================================================================================================| 100%INFO [14:59:10.430] early stopping at 375 iteration
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|=======================================================================================================================================| 100%INFO [14:59:13.713] early stopping at 75 iteration
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|=======================================================================================================================================| 100%INFO [14:59:36.038] early stopping at 325 iteration
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|=======================================================================================================================================| 100%INFO [14:59:39.545] early stopping at 75 iteration
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|=======================================================================================================================================| 100%INFO [15:00:04.423] early stopping at 375 iteration
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|=======================================================================================================================================| 100%INFO [15:00:08.006] early stopping at 75 iteration
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|=======================================================================================================================================| 100%INFO [15:00:31.364] early stopping at 350 iteration
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|=======================================================================================================================================| 100%INFO [15:00:34.756] early stopping at 75 iteration
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|=======================================================================================================================================| 100%INFO [15:00:59.160] early stopping at 375 iteration
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|=======================================================================================================================================| 100%INFO [15:01:02.636] early stopping at 75 iteration#here we are creating a plot at the most coherent topics... (we know it is 3, 6, 15 based on the above and the plot)
library('ggplot2')
library('ggthemes')
ggplot(data = coh_results) +
geom_point(aes(topic_n, coh)) +
geom_line(aes(topic_n, coh)) +
geom_vline(xintercept=c(3,6,15), color='red',linetype = "longdash")+
xlab("Number of Topics") +
ylab("Coherence")+
theme_classic()
# 3, 6, 15 are the number of topics we will go ahead with DATA DRIVEN