Price Elasticity of Demand

Price elasticity of demand (PED) is a measure that has been used in econometric to show how demand of a particular product changes when the price of the product is changed. More particularly, it measures the % change in demand of a product when the price changes by 1%.

It can be expressed as the following formula-

PED

Let’s look at example- Let’s say that demand of a particular Bluetooth headset decreases by 2% when the price is increased by 1%. In this case the PED will be defined as = -2%/1% or -2.

Now, let’s talk about how we interpret PED-

PED of greater than 1 (absolute value) shows highly elastic product. In other words, the change in price will cause a more than proportionate change in demand. This is generally the case with non-essential or luxury products such as the example shown above. On the other hand, PED of less than 1 shows relatively inelastic products such as groceries and daily necessities. Furthermore, for most product PED will be negative, i.e. when the price is increased demand falls.

There are few other practical applications of PED that we should be aware of-

  • PED for a given product or product category can change over time and hence it’s imperative to measure PED over of time.
  • PED for a given product or product category can vary by customer segments. For example, low income customers may have higher PED for the same product
  • Pricing of a product should be optimized taking in account the PED. For example, if a product is showing lower price elasticity or inelasticity, pricing can be increased on the product to maximize revenue

Here is an article that gives some examples from the retail world.

Let’s now step into how we can estimate PED in Python. For this, we will working with the beef price and demand data from USDA Red Meat Yearbook-

http://usda.mannlib.cornell.edu/MannUsda/viewDocumentInfo.do?documentID=1354

You can download the data from here

We will be building a log-log linear model to estimate PED. Please see here for the theoretical discussion on this topic. The coefficient from the log-log linear model shows the PED between two factors.

Let the Python show begin! In the below example PED comes out to be -0.53. It shows that when the price of beef is increased by 1% the demand for beef falls by 0.53%

PED1PED2PED3

Cheers!

 

 

Recommender Engines

Recommendation engines or systems are all around us. Few common examples are-

  • Amazon- People who buy this also buy this or who viewed this also viewed this
  • Facebook- Friends recommendation
  • Linkedin- Jobs that match you or network recommendation or who viewed this profile also viewed this profile
  • Netflix- Movies recommendation
  • Google- news recommendation, youtube videos recommendation

and so on…

The main objective of these recommendation systems is to do following-

  • Customization or personalizaiton
  • Cross sell
  • Up sell
  • Customer retention
  • Address the “Long Tail” phenomenon seen in Online stores vs Brick and Mortar stores

etc..

There are three main approaches for building any recommendation system-

  • Collaborative Filtering

Users and items matrix is built. Normally this matrix is sparse, i.e. most of the cells will be empty. The goal of any recommendation system is to find similarities among the users and items and recommend items which have high probability of being liked by a user given the similarities between users and items.

Similarities between users and items can be assessed using several similarity measures such as Correlation, Cosine Similarities, Jaccard Index, Hamming Distance. The most commonly used similarity measures are Cosine Similarity and Jaccard Index in a recommendation engine

  • Content Based-

This type of recommendation engine focuses on finding the characteristics, attributes, tags or features of the items and recommend other items which have some of the same features. Such as recommend another action movie to a viewer who likes action movies.

  • Hybrid- 

These recommendation systems combine both of the above approaches.

Read more here

Build Recommendation System in Python using ” Scikit – Surprise”-

Now let’s switch gears and see how we can build recommendation engines in Python using a special Python library called Surprise.

This library offers all the necessary tools such as different algorithms (SVD, kNN, Matrix Factorization),  in built datasets, similarity modules (Cosine, MSD, Pearson), sampling and models evaluations modules.

Here is how you can get started

  • Step 1- Switch to Python 2.7 Kernel, I couldn’t make it work in 3.6 and hence needed to install 2.7 as well in my Jupyter notebook environment
  • Step 2- Make sure you have Visual C++ compilers installed on your system as this package requires Cython Wheels. Here are couple of links to help you in this effort

Please note that if you don’t do the Step 2 correctly, you will get errors such as shown below – ” Failed building wheel for Scikit-surprise” or ” Microsoft Visual C++ 14 is required”c1c2

  • Step 3- Install Scikit- Surprise. Please make sure that you have Numpy installed before this

pip install numpy

pip install scikit-surprise

  • Step 4- Import scikit-surprise and make sure it’s correctly loaded

from surprise import Dataset

  • Step 5- Follow along the below examples

Examples

Getting Started

Movie Example

Cheers!

 

Market Basket Analysis or Association Rules or Affinity Analysis or Apriori Algorithm

First of all, if you are not familiar with the concept of Market Basket Analysis (MBA), Association Rules or Affinity Analysis and related metrics such as Support, Confidence and Lift, please read this article first.

Here is how we can do it in Python. We will look at two examples-

Example 1-

Data used for this example can be found here Retail_Data.csv

mba1mba2mba3

Example 2-

MBA4MBA5MBA6

Cheers!

Linear Discriminant Analysis ( LDA) with Scikit

Linear Discriminant Analysis (LDA) is similar to Principal Component Analysis (PCA) in reducing the dimensionality. However, there are certain nuances with LDA that we should be aware of-

  • LDA is supervised (needs categorical dependent variable) to provide the best linear combination of original variables while providing the maximum separation among the different groups. On the other hand, PCA is unsupervised
  • LDA can be used for classification also, whereas PCA is generally used for unsupervised learning
  • LDA doesn’t need the numbers of discriminant to be passed on ahead of time. Generally speaking the number of discriminant will be lower of the number of variables or number of categories-1.
  • LDA is more robust and can be conducted without even standardizing or normalizing the variables in certain cases
  • LDA is preferred for bigger data sets and machine learning

Let the action begin now-

lda1LDA2LDA3LDA4LDA5

Cheers!

Principal Component Analysis ( PCA) using Scikit

Principal Component Analysis ( PCA) is generally used as an unsupervised algorithm for reducing the data dimensions to address Curse of Dimensionality, detecting outliers, removing noise, speech recognition and other such areas.

The underlying algorithm in PCA is generally a linear algebra technique called Singular Value Decomposition (SVD). PCAs take the original data and create orthogonal components (uncorrelated components) that capture the information contained in the original data however with significantly less number of components.

Either the components themselves or  key loading of the components can be plugged in any further modeling work, rather than the original data to minimize information redundancy and noise.

There are three main ways to select the right number of components-

  1. Number of components should explain at least 80% of the original data variance or information [Preferred One]
  2. Eigen value of each PCA component should be more than or equal to 1. This means that they should express at least one variable worth of information
  3. Elbow or Scree method- look for the elbow in the percentage of variance explained by each components and select the components where an elbow or kink is visible.

You can use any one of the above or combination of the above to select the right number of components. It is very critical to standardize or normalize data before conducting PCA.

In the below case study we will use the first criterion shown above, i.e. 80% or more of the original data variance should be explained by the selected number of components.

PCA1PCA2PCA3PCA4PCA5PCA6

Decision Tree using Python Scikit

If you are not familiar with Decision Trees, please read this article first.

First let’s look at a very simple example on the Iris data-

Decision Tree in Python

Decision Tree in Python

Now let’s look at slightly more complex data-

Let’s first build a logistic regression model in Python using machine learning library Scikit. Please read here about the dataset and dummy coding.

clf1clf2clf3clf4clf5clf6clf7

dt1dt2dt3dt4

 

 

Cheers!

Logistic Regression using Scikit Python

If you are not familiar with logistics regression, please read this article first. Moreover, if you are not familiar with the sklearn machine learning model building process, please read this article also.

Assuming you are now familiar, this is how you can build a logistic regression model in Python using machine learning library Scikit.  Please read here about the dataset and dummy coding. 

clf1clf2clf3clf4clf5clf6clf7

clf8clf9clf10

Cheers!

Categorical Variables Dummy Coding

Converting categorical variables into numerical dummy coded variable is generally a requirement in machine learning libraries such as Scikit as they mostly work on numpy arrays.

In this blog, let’s look at how we can convert bunch of categorical variables into numerical dummy coded variables using four different methods-

  1. Scikit learn preprocessing LabelEncoder
  2.  Pandas getdummies
  3. Looping
  4. Mapping

We will work with a dataset from IBM Watson blog as this has plenty of categorical variables. You can find the data here.  In this data, we are trying to build a model to predict “churn”, which has two levels “Yes” and “No”.

We will convert the dependent variable using Scikit LabelEncoder and the independent categorical variables using Pandas getdummies. Please note that LabelEncoder will not necessarily create additional columns, whereas the getdummies will create additional columns in the data. We will see that in the below example-

clf1clf2clf3clf4clf5clf6clf7

Here are few other ways to dummy coding-

dummy_coding1dummy_coding2dummy_coding3

Here is an excellent Kaggle Kernel for detailed feature engineering.

Cheers!

Hierarchical Clustering with Python

As highlighted in the article, clustering and segmentation play an instrumental role in Data Science. In this blog, we will show you how to build a Hierarchical Clustering with Python.

For this purpose, we will work with a R dataset called “Cheese”. Please install package called “Bayesm” in R and export this data set in csv format to be imported in Python. More on this dataset can be found here.

Let’s begin with the clustering in Python then. hclust1hclust2hclust3hclust4hclust5hclust6hclust7

hclust8

Cheers!