CS_10.Rmd

---
title: "Brand Perceptual Map (use PCA for data interpretation)"
author: "Mohammad Ali Momen"
date: "05/14/2023"
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```{css, echo=FALSE}
pre {
  max-height: 300px;
  overflow-y: auto;
}

pre[class] {
  max-height: 200px;
}
```

```{r setup, include = FALSE}
knitr::opts_chunk$set(echo = TRUE, warning = FALSE, message = FALSE, attr.source = '.numberLines')
```

***

**Data Analysis methodology**: CRISP-DM

**Dataset**: 100 Customers answered 9 questions about 10 brands by likerd spectrum

**Case Goal**: Knowing market atmosphere and Brand Positioning (know situation of 10 different Brands)

***

# Required Libraries
```{r}
library('pls')
library('ggplot2')
library('corrplot')
```

***

# Read Data from File
```{r}
data <- read.csv('CS_10.csv', header = T)
dim(data)  # 1000 records, 10 variables
```

> We have 10 brands and 9 features (100 persons evaluate each brand in 9 features by likerd spectrum)

***

# Business Understanding

* know business process and issues
* know the context of the problem
* know the order of numbers in the business

***

# Data Understanding
## Data Inspection
Data Understanding from Free Perspective

### Dataset variables definition
```{r}
colnames(data)
```

* **perform**:  Brand has strong performance
* **leader**:   Brand is a leader in the market
* **latest**:   Brand has the latest products in market
* **fun**:      Brand is fun
* **serious**:  Brand is serious
* **bargain**:  Brand products are a bargain (are cheap)
* **value**:    Brand products are a good value
* **trendy**:   Brand is trendy (is trend of market)
* **rebuy**:    I would buy from Brand again


## Data Exploring
Data Understanding from Statistical Perspective

### Overview of Dataframe
```{r}
summary(data)
data$brand <- as.factor(data$brand)
str(data)
```

### Correlation Analysis
```{r}
corr_table <- round(cor(data[, 1:9]), 2)  # calculate correlations between continuous variables
corr_table
corrplot::corrplot(corr_table)
```

### Descriptive Analysis on Brands
```{r}
brand_mean <- aggregate(data[, 1:9], list(data$brand), mean)  # mean score of every brand in each feature
brand_mean  # which brand is better in what?

rownames(brand_mean) <- brand_mean[, 1]
brand_mean <- brand_mean[,-1]  # remove 'brand' column
brand_mean
```

Prepare data for heat-map in ggplot2
```{r}
brand_mean_df <- data.frame(brand = rep(rownames(brand_mean), 9),  # brand names
				var = rep(colnames(brand_mean), each = 10),  # feature names
				mean_value = unlist(brand_mean))  # means
rownames(brand_mean_df) <- NULL  # remove rownames
brand_mean_df
```

Plot heat-map (relative value of numbers are shown by colors)
```{r}
hm_plot <- ggplot(data = brand_mean_df, aes(x = brand, y = var, fill = mean_value)) +
		geom_tile() +
		scale_fill_gradient(low = 'yellow', high = 'dark green')
hm_plot  # try to measure customers emotions about brands (each brand is known as what from customers mindset?), to know our brand's position in the market related to other brands.
```

***


# Data PreProcessing
## Scale data for PCA
```{r}
data_sc <- data
data_sc[, 1:9] <- scale(data[, 1:9])  # can not scale factor variable ('brand' column)
summary(data_sc)  # bring mean = 0 and distribution around mean
```

***

# Modeling
## Model: PCA Analysis
### Run 1
```{r}
pca_res <- prcomp(data_sc[, 1:9])
summary(pca_res)  # we had 9 variables, so PCA gives us 9 PC
```

* But, all of these 9 PCs do not explain same amount of data Variance and we don't want to use all of them. our goal is Dimension Reduction
    + PC1 explains 33% of data Variance 
    + PC2 explains 23% of data Variance
    + we can explain 56.4% of data Variance with PC1 and PC2 (Cumulative Proportion): so we just consider PC1 and PC2

> In Perceptual Map, we just consider 2 or 3 Principal Component to define brand-positions in 2D or 3D plots

Plot the results (each PC explains how much percentage of data Variance?)
```{r}
plot(summary(pca_res)$importance[2,],
	xaxt = 'n',
	yaxt = 'n',
	ylab = 'Proportion of Variance',
	xlab = '# of Components')
axis(1, at = 1:9, labels = 1:9)
axis(2, at = seq(0, 0.35, 0.05), labels = seq(0, 0.35, 0.05))

#Preceptual Map for products (show data in PC1-PC2 space)
 # bottom-horizontal-axis: PC1
 # top-horizontal-axis: weight of PC1 in main variables
 # right-vertical-axis: weight of PC2 in main variables
 # left-vertical-axis: PC2
biplot(pca_res)  
 
```

> According to the bi-plot, the space has been divided to 4 regions (same red-vectors (having same weight in of PC1 and PC2) make a region)
 
* four regions (cluster variables based-on their weight in PC1 and PC2): 
    1. leadership cluster (serious, leader, perform) -> market leadership
    2. value cluster (rebuy, value, bargain) -> benefit/cost ratio
    3. trendiness cluster (trendy, latest)
    4. fun cluster (fun)

Actually, customers are measure different brands in 4 index

### Run 2

Simplify the problem by running PCA on 'brand_mean' (10 row) instead of whole dataset (1000 row)

This helps us to have coordination of brands on bi-plot

```{r}
brand_mean_pca <- prcomp(brand_mean, scale = T)
summary(brand_mean_pca)
```

> We can explain 87.07% of data Variance with PC1 and PC2 (Cumulative Proportion)

```{r}
biplot(brand_mean_pca, main = 'Brand Positioning', cex = c(1.5, 1))  # Perceptual Map for brands
```
Now, we can see that the different brands in PC1-PC2 space, are positioned where (near which feature-clusters)?

Some Questions for analysis results:

* What does the map tell us?
    + brand f and g are valueable brands in customer mindset (are near to value cluster and have good benefit/cost ratio) 
    + brand c and b are leader of market (forerunner) brands in customer mindset
    + brand a and j are fun brands
    + brand d and h and i are innovative brands
* Suppose that you are the brand manager for brand e
    + your brand is famous as nothing! 
    + from marketing aspect, your brand is known as nothing between customers and this is so bad in marketing; because the customers don't know why should choose brand e (for what reason)?
    + customer who looks for leadership brand and performance, chooses c or b brands.
    + customer who looks for low-cost and good-benefit, chooses f or g brands.
    + customer who looks for latest products, chooses d or h or i brands.
* What should you do about the position of your brand e? 
    + two possible solutions:
        * follow other brands (where is other brands position in this industry? choose a position and close yourself to there)
        * fill a gap (position yourself in a gap): value-leadership

***

For more information check the [Github](https://github.com/mamomen1996/R_CS_10) repository.