Machine Learning-Logistic Regression

Another post starts with you beautiful people!
I appreciate that you have shown your interest in Machine Learning track and enjoyed my previous post about Linear Regression where we learned the concept with the case study of bike sharing system.
Today we will continue our Data Science journey and learn about Logistic Regression.
Like all regression analyses, the logistic regression is a predictive analysis.
The fact is that linear regression works on a continuum of numeric estimates. In order to classify correctly, we need a more suitable measure, such as the probability of class ownership.
Thanks to the following formula, we can transform a linear regression numeric estimate into a probability that is more apt to describe how a class fits an observation:

probability of a class = exp(r) / (1+exp(r))

• r is the regression result (the sum of the variables weighted by the coefficients) 
• exp is the exponential function. 
• exp(r) corresponds to Euler’s number e elevated to the power of r. 
• A linear regression using such a formula (also called a link function) for transforming its results into probabilities is a logistic regression.

Logistic regression is similar to linear regression, with the only difference being the y data, which should contain integer values indicating the class relative to the observation.
Agenda of this exercise-

• loading a dataset from statsmodels into a pandas dataframe
• exploring the data using pandas
• visualizing the data using matplotlib
• preparing the data for logistic regression using patsy
• building a logistic regression model using scikit-learn
• model evaluation using cross validation from scikit-learn

For this exercise we will work on a very interesting dataset- Affair Dataset

In this dataset: Extramarital affair data is used to explain the allocation of an individual’s time among work, time spent with a spouse, and time spent with a paramour. The data is used as an example of regression with censored data.

It was derived from a survey of women in 1974 by Redbook magazine, in which married women were asked about their participation in extramarital affairs.

It was derived from a survey of women in 1974 by Redbook magazine, in which married women were asked about their participation in extramarital affairsDescription of Variables

The dataset contains 6366 observations of 9 variables:

Dataset description:-

• rate_marriage: woman's rating of her marriage (1 = very poor, 5 = very good)
• age: woman's age
• yrs_married: number of years married
• children: number of children
• religious: woman's rating of how religious she is (1 = not religious, 4 = strongly religious)
• educ: level of education (9 = grade school, 12 = high school, 14 = some college, 16 = college graduate, 17 = some graduate school, 20 = advanced degree)
• occupation: woman's occupation (1 = student, 2 = farming/semi-skilled/unskilled, 3 = "white collar", 4 = teacher/nurse/writer/technician/skilled, 5 = managerial/business, 6 = professional with advanced degree)
• occupation_husb: husband's occupation (same coding as above)
• affairs: time spent in extra-marital affairs

Problem Statement:-

We will treat this as a classification problem by creating a new binary variable affair (did the woman have at least one affair?) and trying to predict the classification for each woman.

Importing the required modules-

Data Pre-Processing-

First, let's load the dataset and add a binary 'affair' column.

Data Exploration-

We can see that on average, women who have affairs rate their marriages lower, which is to be expected. 

Let's take another look at the rate_marriage variable.

It seems an increase in age, yrs_married, and children appears to correlate with a declining marriage rating.

Data Visualization-

Result-

Result-

Let's take a look at the distribution of marriage ratings for those having affairs versus those not having affairs.

Let's use a stacked barplot to look at the percentage of women having affairs by number of years of marriage.

Prepare Data for Logistic Regression-

To prepare the data, we will add an intercept column as well as dummy variables for occupation and occupation_husb, since we are treating them as categorial variables. 

The dmatrices function from the patsy module can do that using formula language.

The column names for the dummy variables are ugly, so let's rename those-

We also need to flatten y into a 1-D array, so that scikit-learn will properly understand it as the response variable.

Logistic Regression-

Let's go ahead and run logistic regression on the entire data set, and see how accurate it is!

73% accuracy seems good, but what's the null error rate?

Only 32% of the women had affairs, which means that we could obtain 68% accuracy by always predicting "no". 

So we're doing better than the null error rate, but not by much.

Let's examine the coefficients to see what we learn-

From the above output we can say-Increases in marriage rating and religiousness correspond to a decrease in the likelihood of having an affair. 

For both the wife's occupation and the husband's occupation, the lowest likelihood of having an affair corresponds to the baseline occupation (student), since all of the dummy coefficients are positive.

Model Evaluation Using a Validation Set-

So far, we have trained and tested on the same set. Let's instead split the data into a training set and a testing set.

We now need to predict class labels for the test set. We will also generate the class probabilities, just to take a look.

As you can see, the classifier is predicting a 1 (having an affair) any time the probability in the second column is greater than 0.5.

Now let's generate some evaluation metrics-

The accuracy is 73%, which is the same as we experienced when training and predicting on the same data.

We can also see the confusion matrix and a classification report with other metrics-

Model Evaluation Using Cross-Validation-

Now let's try 10-fold cross-validation, to see if the accuracy holds up more rigorously.

Looks good. It's still performing at 73% accuracy.So our model is ready for prediction!

Can we predict the probability of an affair using our model?

Let's predict the probability of an affair for a random woman not present in the dataset. 

Assume she's a 25-year-old house wife who graduated college, has been married for 3 years, has 1 child, rates herself as strongly religious, rates her marriage as fair, and her husband is a farmer.

From our model we can predict that probability of an affair is 23%.

Looks cool right! we can make many improvement like below to improve our model-

• including interaction terms
• removing features
• regularization techniques
• using a non-linear model

It's time to try yourself and improve our model.

In my next post I will share you When and Where to use Linear or Logistic regression?