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Intent-Satisfaction Modeling – From Music to Video Streaming

Gabriel Bénédict

This repository contains the supporting material for the paper Intent-based Satisfaction Modeling – From Music to Video Streaming. A reproducibility study of Mehrotra et. al. 2019.

The plots shown here are made with real Videoland data. In order to run the code yourself, download the repo and run the .Rmd file. Trivial data simulation is provided below instead of real user data (GDPR compliance). You can expect therefore the plots to change.

Change this value to false, to make the code executable with fake data

realData = T

1 libraries

# data wrangling
library(data.table) # faster and arguably nice syntax
library(magrittr) # allows piping such as %>% or %<>%
library(stringr) # for string operations like str_replace
library(tidyr) # separate
library(knitr) # especially to make tables with kable
library(dplyr)
library(purrr)
library(MASS)

# plotting
library(ggcorrplot)
library(ggplot2)

# Bayes
library(tidybayes)
library(bayesplot) # plot bayesian model
library(brms)

2 Data prep

2.1 Trivial Fake Data

This is probably a research topic of its own. This data is only there for the code to run. We thus go with the simplest approach, without considering correlations between variables.

possibleIntents <- c('Decisive - catch-up' , 'Decisive - continuewatching' , 'Decisive - livetv' , 'Decisive - specifictitle' , 'Explorative - addwatchlist' , 'Explorative - genre' , 'Explorative - new' , 'Explorative - watchlist')

behaviorNames <- c('numPlays' , 'timeToFirstPlay' , 'numTrailerPlays' , 'timeToFirstTrailer' , 'nBookmarks' , 'nProfileClicks' , 'nAccounts' , 'nStrips' , 'nSearches' , 'nSeriesDescr' , 'nMoviesDescr' , 'sessionLength')
  
possibleIntentsOrigNames <- c("Decisive_catch-up", "Decisive_continuewatching", "Decisive_livetv", "Decisive_specifictitle", "Inspiration_addwatchlist",  "Inspiration_genre", "Inspiration_new", "Inspiration_watchlist")

N <- 3000

responded <- data.frame(satisfaction = sample(1:5, N, replace = T)) %>% setDT
for(i in 1:length(possibleIntents)){
  responded[,  (possibleIntents[i]) := sample(0:1, N, replace = T)]
}
for(i in 1:length(behaviorNames)){
  responded[,  (behaviorNames[i]) := rnegbin(N, mu = 1, theta = 1)]
}
responded[, sessionId := 1:N]

measureVars <- names(responded) %>% .[grep("-",.)]
idVars <- names(responded) %>% .[-grep("-",.)]

intentsLong <- melt(responded, id.vars = idVars, measure.vars = measureVars, 
                      variable.name = "intent")[order(sessionId)][value == 1, !"value"] %>%
                      separate(intent, c("group", "intent"), "-")

behaviorLong <- melt(responded, id.vars = c("sessionId", "satisfaction"),
                     measure.vars = behaviorNames,
                     variable.name = "behavioral variable")

2.2 Behavioral data

If you are running a website and are tracking users with Google Analytics, the Bigquery code here, will allow you to retrieve the same behavioral data as ours. Custom dimensions are proper to our platform and will differ depending on your setup.

2.3 available Vars

behaviors <- behaviorNames %>% paste(., collapse =" + ") # useful for modelling

possibleIntents <- names(responded[,`Decisive - catch-up`:`Explorative - watchlist`])

kable(list(data.frame("intents" = possibleIntents), data.frame("behaviorals" = behaviorNames)))
intents
Decisive - catch-up
Decisive - continuewatching
Decisive - livetv
Decisive - specifictitle
Explorative - addwatchlist
Explorative - genre
Explorative - new
Explorative - watchlist
behaviorals
numPlays
timeToFirstPlay
numTrailerPlays
timeToFirstTrailer
nBookmarks
nProfileClicks
nAccounts
nStrips
nSearches
nSeriesDescr
nMoviesDescr
sessionLength

3 Vizualizations

3.1 Descriptive stats on Behavioral Vars

We show log values given the skewness of the data

responded[, ..behaviorNames] %>% gather %>% ggplot(aes(log(value))) + 
  facet_wrap(~ key, scales = "free") + geom_histogram()

# d[, ..behaviorNames] %>% gather %>% ggplot(aes(log(value))) + 
#   facet_wrap(~ key, scales = "free") + geom_histogram()

3.1.1 for the quite satisfied (y >= 4)

responded[satisfaction >= 4, sessionLength:nStrips] %>%
  keep(is.numeric) %>% 
  gather() %>% 
  ggplot(aes(log(value))) +
    facet_wrap(~ key, scales = "free") +
    geom_histogram()

# intents[satisfactionBin == 1, sessionLengthByHit:nStrips] %>%
#   keep(is.numeric) %>% 
#   gather() %>% 
#   ggplot(aes(log(value))) +
#     facet_wrap(~ key, scales = "free") +
#     geom_histogram()

3.1.2 for the less satisfied (y<4)

responded[satisfaction < 4, sessionLength:nStrips] %>%
  keep(is.numeric) %>% 
  gather() %>% 
  ggplot(aes(log(value))) +
    facet_wrap(~ key, scales = "free") +
    geom_histogram()

# intents[satisfactionBin == 0, sessionLengthByHit:nStrips] %>%
#   keep(is.numeric) %>% 
#   gather() %>% 
#   ggplot(aes(log(value))) +
#     facet_wrap(~ key, scales = "free") +
#     geom_histogram()

3.2 The Satisfaction histogram

# Daltonian palette https://jfly.uni-koeln.de/color/
cbp1 <- c("#999999", "#E69F00", "#56B4E9", "#009E73",
          "#F0E442", "#0072B2", "#D55E00", "#CC79A7")

blue <-  cbp1[6]
orange <-  cbp1[2]

# hist
ggplot(responded, aes(x=satisfaction, y = ..count.., fill = satisfaction)) +
  geom_bar(width = 0.5, fill = blue) + theme_classic() +
  theme(text = element_text(size = 18))

# ggplot(responded, aes(x=..count.., y = satisfaction, fill = satisfaction)) +
#   geom_bar(width = 0.5, fill = blue) + theme_classic() +
#   scale_x_continuous(expand = c(0, 0)) +
#   theme(text = element_text(size = 18))

3.3 Violin Plots

3.3.1 Violins of Satisfaction and Intents

ggplot(intentsLong, aes(intent, satisfaction, fill = factor(group))) +
  # stat_summary(fun.y=mean, geom="point", shape=23, size=2) +
  geom_violin() +
  stat_summary(fun.y=mean, geom="point", color = "white") +
  # geom_jitter(shape=16, position=position_jitter(0.2), alpha = 1) +
  # geom_boxplot(width=0.1) +
  theme_classic() +
  theme(axis.text.x = element_text(size = 14)) +
  # theme(axis.text.x = element_text(angle = 45, hjust=1, size = 14)) +
  theme(axis.text.y = element_text(size = 14)) +
  theme(legend.position="none") +
  facet_grid(~group, 
             scales = "free_x", # Let the x axis vary across facets.
             space = "free_x",  # Let the width of facets vary and force all bars to have the same width.
             switch = "x") +
  theme(strip.placement = "outside",                      # Place facet labels outside x axis labels.
        strip.background = element_rect(fill = "grey90", color = "white"),
        strip.text = element_text(size = 14),# Make facet label background white.
        axis.title.x=element_blank(),
        axis.title.y=element_text(size = 14),
        text = element_text(size = 18))  +
  scale_fill_manual(values = c(blue, orange))

# ggplot(intentsPure, aes(intent, satisfaction, fill = factor(group))) + 
#   # stat_summary(fun.y=mean, geom="point", shape=23, size=2) +
#   geom_violin() +
#   stat_summary(fun.y=mean, geom="point") +
#   # geom_jitter(shape=16, position=position_jitter(0.2), alpha = 1) +
#   # geom_boxplot(width=0.1) +
#   theme_classic() +
#   theme(axis.text.x = element_text(angle = 45, hjust=1, size = 14)) +
#   theme(axis.text.y = element_text(size = 14)) +
#   theme(legend.position="none") +
#   facet_grid(~group, 
#              scales = "free_x", # Let the x axis vary across facets.
#              space = "free_x",  # Let the width of facets vary and force all bars to have the same width.
#              switch = "x") +
#   theme(strip.placement = "outside",                      # Place facet labels outside x axis labels.
#         strip.background = element_rect(fill = "grey90", color = "white"),
#         strip.text = element_text(size = 14),# Make facet label background white.
#         axis.title.x=element_blank(),
#         axis.title.y=element_text(size = 14))  +
#   scale_fill_manual(values = cbp1[c(7,8)])

3.3.2 Violins of Satisfaction and Behavioral Variables

ggplot(behaviorLong[value >= 1], 
       aes(x= log(value), y = satisfaction, group = satisfaction, fill = as.factor(satisfaction))) +
  geom_violin() +
  facet_wrap(~`behavioral variable`, scales = "free") +
  theme_classic() +
  theme(legend.position="none") +
  scale_fill_brewer(palette="Set1")

# ggplot(satBehavLong[value >= 1], 
#        aes(x= log(value), y = satisfaction, group = satisfaction, fill = as.factor(satisfaction))) +
#   geom_violin() +
#   facet_wrap(~`behavioral variable`, scales = "free") +
#   theme_classic() +
#   theme(legend.position="none") +
#   scale_fill_brewer(palette="Set1")

3.4 Corrplots

## cor plot data prep

corrIntentBehav <- cor(responded[, `Decisive - catch-up`:`Explorative - watchlist`],
                       responded[, ..behaviorNames])

p.mat <- psych::corr.test(responded[, `Decisive - catch-up`:`Explorative - watchlist`],
                       responded[, ..behaviorNames]) #, adjust="none")

scaledCorr <- corrIntentBehav * 10

The original corrplot

if(realData){
  ggcorrplot(scaledCorr, show.legend=T) + # lab = TRUE
    theme(text = element_text(size = 18)) +
    scale_fill_gradientn("",
                         colours = c("darkblue","white","red"),
                         values = scales::rescale(c(min(scaledCorr), 0, max(scaledCorr))),
                         labels = c(round(min(scaledCorr), 1), -0.60, 0,
                                    0.60, round(max(scaledCorr), 1)))
} else {
  ggcorrplot(scaledCorr, show.legend=T)
}

The corrplot with significance testing (corrected for multiple testing, significance level 0.05). A cross indicates insignificant correlations.

if(realData){
  ggcorrplot(scaledCorr, show.legend=T, p.mat = p.mat$p, pch.cex = 2) + # lab = TRUE
    theme(text = element_text(size = 18)) +
  scale_fill_gradientn("",
                       colours = c("darkblue","white","red"),
                       values = scales::rescale(c(min(scaledCorr), 0, max(scaledCorr))),
                       labels = c(round(min(scaledCorr), 1), -0.60, 0,
                                  0.60, round(max(scaledCorr), 1)))
} else {
  ggcorrplot(scaledCorr, show.legend=T, p.mat = p.mat$p, pch.cex = 2)
}

4 Modelling

5-fold trainval / test (80 / 20 %). For each trainval set, 5-fold tain / val (80 / 20 %).

source("source/utils.R")

methodsParams <- list("w/o intent" = list(m = "logistic", withIntent = F, RE = F),
                      "w intent"  = list(m = "logistic", withIntent = T, RE = F),
                      "multilevel"  = list(m = "logistic", withIntent = T, RE = T),
                      "xgboost w/o intent" = list(m = "xgboost", withIntent = F, RE = F),
                      "xgboost w intent" = list(m = "xgboost", withIntent = T, RE = F))

overallResults <-
  rbind(
    crossT(5, 5, responded, response = "satisfactionBin", methodsParams),
    crossTByIntent(5,5, response = "satisfactionBin")
  )

satResults <-
  rbind(
    crossT(5, 5, responded, response = "satisfied", methodsParams),
    crossTByIntent(5,5, response = "satisfied")
  )


unsatResults <-
  rbind(
    crossT(5, 5, responded, response = "dissatisfied", methodsParams),
    crossTByIntent(5,5, response = "dissatisfied")
  )

results <- cbind(overallResults[,1],
                 overallResults[,Accuracy:F1],
                 satResults[,Accuracy:F1],
                 unsatResults[,Accuracy:F1])

kbl(results, format="latex", booktabs = T, escape = F, linesep = linesep(11)) %>%
  add_header_above(
    c(" " = 1,
      "Overall ($\\\\mathds{1}_{\\\\hat{\\\\mathbf{y}} \\\\geq 4}$)" = 4,
      "Satisfied ($\\\\mathds{1}_{\\\\hat{\\\\mathbf{y}} = 5}$)" = 4,
      "Unsatisfied ($\\\\mathds{1}_{\\\\hat{\\\\mathbf{y}} = 1}$)" = 4),
    escape = F)

4.1 per intent logistic Bayes regression

4.1.1 modelling

for (i in possibleIntents){
  logisticBayes <- brm(
    formula = as.formula(paste("satisfactionBin ~", behaviors)),
    data = responded[intent == i],
    family = bernoulli(link = logit),
    file = paste0("models/logistic_", i, ".rds"),
    chains = 4, cores = 4, backend = "cmdstanr"
  )
}

logisticBayes <- do.call('rbind', lapply(list.files("models", full.names = TRUE, pattern = "logistic_"), readRDS))

4.1.2 Goodness of Fit example

fit <- readRDS("models/logistic_Decisive_catch-up.rds")

loo <- loo_subsample(fit, merge_chains = FALSE)
loo
## 
## Computed from 4000 by 400 subsampled log-likelihood
## values from 544 total observations.
## 
##          Estimate   SE subsampling SE
## elpd_loo   -249.8 15.0            1.2
## p_loo        14.2  2.6            1.5
## looic       499.5 30.0            2.5
## ------
## Monte Carlo SE of elpd_loo is NA.
## 
## Pareto k diagnostic values:
##                          Count Pct.    Min. n_eff
## (-Inf, 0.5]   (good)     391   97.8%   1024      
##  (0.5, 0.7]   (ok)         4    1.0%   215       
##    (0.7, 1]   (bad)        1    0.2%   61        
##    (1, Inf)   (very bad)   4    1.0%   576       
## See help('pareto-k-diagnostic') for details.

4.1.3 plotting

posteriors <- list()

j <- 1
for (i in possibleIntentsOrigNames){
  thisBayes <- readRDS(paste0("models/logistic_", i, ".rds"))
  thisPosterior <- thisBayes %>% as.array
  thisBayes %<>% tidy_draws()
  notConverged <- thisBayes %>% summarise_draws() %>%
    setDT() %>% .[rhat > 1.05 & grepl("b_", variable) , variable]

  posteriors[[j]] <- thisPosterior %>% .[,,!dimnames(.)$variable %in% c(notConverged, "lp__", "Intercept")]
  
  thisBayes %<>%
    gather_variables() %>%
    setDT() %>% .[!.variable %in% notConverged] %>%
    .[, var := str_replace(.variable, "b_", "")] %>%
    .[var %in% behaviorNames, ] %>%
    .[, satisfaction := .value] %>%
      .[, intent := i] %>%
    .[]

  if(j == 1){
    logisticBayes <- thisBayes
  } else {
    logisticBayes <- rbind(logisticBayes, thisBayes)
  }
  j <- j + 1
}

logisticBayes[, index := .I]
logisticBayes[, varIntent := paste0(var, intent)]

medians <- logisticBayes[!var %in% c("numTrailerPlays")] %>% # "timeToFirstTrailer", 
  .[, .(intent = intent, median = abs(median(satisfaction))), by = .(varIntent)]
medians <- unique(medians)
topVars <- setorder(medians, intent, -median)[, head(.SD, 3), by = intent][, varIntent]

logisticBayes$intent %<>% str_replace("Inspiration", "Explorative") %>% str_replace("_", " - ")

logisticBayes[varIntent %in% topVars] %>%
  ggplot(aes(y = var, x = satisfaction, fill = var)) +
  facet_wrap(~intent, ncol = 4, scales = "free") +
  ## stat_gradientinterval() +
  stat_halfeye(scale = 1.5, point_size = 1.5) +
  geom_vline(xintercept = 0, linetype="dashed") +
  theme_classic() +
  theme(axis.title.y=element_blank()) +
  scale_fill_manual(values=cbp1) +
  theme(legend.position="none", strip.background = element_rect(fill = "white", color = "white")) +
  scale_x_continuous(labels = scales::number_format(accuracy = 0.1))

4.2 Chain PLots

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