Market Response Modelling.R

---
title: "**Market Response Modelling**"
author: "Cheryl Isabella"
output:
  html_document:
    toc: true
    toc_float: true
    toc_depth: 2
    theme: cosmo
    df_print: paged
editor_options: 
  markdown: 
    wrap: 72
---

```{r setup , warning=FALSE, fig.align='center', echo= FALSE, include = FALSE}
knitr::opts_chunk$set(echo = TRUE)
knitr::opts_chunk$set(fig.width=6, fig.height=4) 
library(dplyr)
library(ggplot2)
library(tidyr)
library(caret)
library(tidyverse)
library(radiant)
library(conjoint)
library(Metrics)
mrm <- read.csv("/Users/Isabella/Documents/GitHub/Market-Response-Modelling--Marketing/Data_Market Response Modeling.csv", sep = ";", stringsAsFactors = FALSE, dec = ",")
head(mrm)
```

# Data

This project will analyse how effective the current channels are in
acquiring new customers. Therefore, the following data were collected:

-   number of newly acquired customers across 118 weeks
-   the investment in traditional advertising
-   the number of impressions of Facebook posts initiated by the
    telecommunications provider
-   information about media and buzz events, holiday periods, promotions
-   marketing buzz about the telecommunications provider on Twitter.

The variables and their descriptions are shown below:

![](mrm%20variables.png)

# Categorisation

We commence by categorising all variables in the form of a market
response framework. ![](market%20response%20framework.png)

# Linear regression analysis

The data has been cleaned prior to its upload into R. Therefore, we can
proceed with a linear regression analysis on the data.

```{r, linear regression}
#normalise function
normalize <- function(x) {
  return((x-min(x))/ (max(x)-min(x)))
}

mrm1 = mrm %>% mutate(
  acquisition_n = normalize(acquisition),
  promotions_n = normalize(promotions),
  lag_traditional.advertising_n = normalize(lag_traditional.advertising),
  lag_Twitter_valence_n = normalize(lag_Twitter_valence),
  lag_Twitter_volume_n = normalize(lag_Twitter_volume),
  lag_FB_impressions_n = normalize(lag_FB_impressions)
)

model = lm(acquisition_n ~ buzz.event + media.event + holidays + promotions_n + lag_traditional.advertising_n + lag_Twitter_valence_n + lag_Twitter_volume_n + lag_FB_impressions_n, mrm1)
summary(model)
```

## Regression model performance

The performance of the linear regression model will be evaluated in 3
ways:

1.  Model Assumptions
2.  Model fit
3.  Significance of coefficients (via T-tests)

### Model Assumptions

Diagnostic plots:

```{r, model assumptions}
par(mfrow = c(2, 2))
plot(model)
```

**Results:**

1.  Linearity of the data: A linear relationship between the predictors
    and outcome variables can be assumed as the Residuals vs Fitted plot
    shows no fitted pattern, and the red line is approximately
    horizontal at zero.
2.  Homoscedasticity: residuals can be assumed to have a constant
    variance since the residuals in the Scale-Location plot are spread
    rather equally along the ranges of predictors.
3.  Independence: can be assumed between and within the customers since
    each customer is a unique individual (ratings by an individual
    customer are not expected to be dependent on ratings by other
    customer(s)).
4.  Normality: can be assumed since the normal probability plot of
    residuals approximately follow a straight line.
5.  Metric scale: all variables are on the metric scale.

### Model Fit

-   The adjusted R-Squared is only 0.3857 meaning that only
    approximately 38.6% of the variance of the dependent variable is
    explained by the model ⇒ This suggests that this model is not a good
    fit.
-   The p-value associated to the F-statistic is \< 0.05 ⇒ this means at
    least 1 independent variable is significantly related to
    Acquisition.
-   The F-statistic of 10.18 is relatively small given the size of our
    data.
-   The model has an RSME of 0.314 which is relatively good as there is
    little variation in the spread of data.

### Significance of coefficients (via T-tests)

-   Before evaluating the significance of coefficients, I did a two-fold
    cross validation and split the dataset into a training subgroup with
    88 observations and a test set with 30 observations.
-   The two-sample T-test for difference in means was used to validate
    the partitions as the dataset is entirely numerical.

H0: The means between test and training sets are the same

HA: The means between test and training sets are different

```{r}
#Two fold cross-validation
split <- round(nrow(mrm1)*0.75)
split
nrow(mrm1) - split
```

```{r}
set.seed(1)
#Function for two-sample t-test
ttest <- function(training, testing) {
  x1_mean <- mean(testing)
  x2_mean <- mean(training)
  s1 <- sd(testing)
  s2 <- sd(training)
  n1 <- length(testing)
  n2 <- length(training)
  dfs <- min(n1-1, n2-1)
  tdata <- (x1_mean - x2_mean) / sqrt((s1^2/n1)+(s2^2/n2))
  tdata
  pvalue <- 2*pt(abs(tdata), df = dfs, lower.tail = FALSE)
  return(pvalue)
}

trainindex <- createDataPartition(mrm1$acquisition_n, p = .75, 
                                  list = FALSE, 
                                  times = 1)
trainmrm <- mrm1[trainindex,]
testmrm  <- mrm1[-trainindex,]
```

Derivation of coefficients can be found in the associated .rmd file

```{r, t-test coefficients, include = FALSE}
ttest(training = trainmrm$buzz.event, testing = testmrm$buzz.event)
ttest(training = trainmrm$media.event, testing = testmrm$media.event)
ttest(training = trainmrm$holidays, testing = testmrm$holidays)
ttest(training = trainmrm$promotions_n, testing = testmrm$promotions_n)
ttest(training = trainmrm$lag_traditional.advertising_n, testing = testmrm$lag_traditional.advertising_n)
ttest(training = trainmrm$lag_Twitter_valence_n , testing = testmrm$lag_Twitter_valence_n )
ttest(training = trainmrm$lag_Twitter_volume_n , testing = testmrm$lag_Twitter_volume_n )
ttest(training = trainmrm$lag_FB_impressions_n, testing = testmrm$lag_FB_impressions_n)

rmsemrm <- rmse(trainmrm$acquisition_n, testmrm$acquisition_n)
```

![](mrm%20coefficients.png)

**Results:** Since the p-value of the t-statistic for all explanatory
variables are much larger than the 5% significance level, we do not have
enough evidence to reject the null hypothesis, meaning that the means of
explanatory variables in the Training and Test sets are similar.

<br>

# Dynamic effects

-   The effort put into marketing sometimes influences sales in future
    periods. This is known as the carryover effect.
-   One type of carryover effect is the delayed-response effect. Some of
    the variables (e.g., traditional advertising and Twitter volume) are
    delayed by one week. This has been done to account for the delayed
    effect this action might have on acquisition.
-   This model takes into account some dynamic effects that are relevant
    to this case.
-   However, the inclusion of information from past observations of a
    series does not necessarily include other omitted variables that may
    explain some of the historical variations, and that may lead to more
    accurate forecasts.

# Influence of traditional advertising on acquisition

-   The coefficient for traditional advertising is 0.297 (3sf). This
    means that traditional advertising and acquiring new customers are
    positively correlated.
-   That is, when traditional gross media expenditures increase, the
    number of newly acquired customers is likely to increase.
-   Note: 0.297 is a proportional effect.

# Influence of FB impressions on acquisition

-   The coefficient for Facebook impressions is 0.084, which indicates
    that like traditional advertising, Facebook impressions and
    acquiring new customers are positively correlated, albeit to a
    relatively smaller extent.
-   This means that increasing number of impressions on Facebook will
    likely lead to increase in the number of newly acquired customers.

# Conclusion

Most effective communication channel (traditional advertising, Facebook,
Twitter) in stimulating customer acquisition:

![](mrm%20conclusion.png)

**Results:**

-   The model indicated that the most effective communication channel is
    Twitter as it has the highest coefficient.
-   The difference between the most effective and second most effective
    communication channel - traditional advertising - is relatively
    small. However, the difference between Facebook, which turns out to
    be least effective, and traditional advertising is fairly large.
-   The influence of Twitter is more than three times as large as the
    influence of Facebook impressions. This insight is useful for the
    company to decide on how to divide their resources.
-   It is surprising that traditional advertising is remains impactful
    in this day and age.\
-   It can be concluded that digital advertisings' impact is higher when
    coupled with traditional advertising, because they need the
    credibility traditional advertising provides.

**Recommendations for telecommunication provider**

-   As seen from the quantitative evaluation of coefficients, the use of
    more modern advertising, notably Twitter, is recommended for the
    telecommunication provider . This "digital first" approach would be
    a more holistic marketing communication campaign as it meet the
    changing consumer landscape of tech savvy consumers.
-   Further, the telecommunication provider could consider reaching
    prospective consumers through personal communication channels (eg
    face-to-face pitches) and buzz marketing to capitalise on
    word-of-mouth influence for higher acquisition and profits.
-   Lastly, the firm should also evaluate the return on advertising
    investment through the sales and profits effects. This can be done
    by comparing past sales and profits with past advertising
    expenditures, or through experiments(eg varying the amount it spends
    on advertising in different market areas and measuring the
    differences in the resulting sales/acquisition and profit levels.