Due date:  5pm, Friday 21st October 2022.

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The purpose of this assessment is to work through all the relevant steps of constructing a predictive model on a given data set.  This will include data cleaning, exploratory analysis, preprocessing, model building and tuning, and finally model evaluation and predicting on new data.  This will assess a variety of skills developed in the course.

Label all question answers clearly.  Include any relevant code in your answers, as there are marks awarded

for code.

The data we are looking at today concerns extramarital activities of readers of Psychology  Today in 1969. Our aim is to build a predictive model that will determine whether an individual is likely to engage in extramarital affairs based on various aspects of their lives. The variables in this dataset are:

• affair - An indicator of whether the participant had engaged in an affair, categorical.

•  sex - the sex of the participant, categorical.

•  age - the age in years of the participant, continuous.

•  ym - the number of years the participant had been married, continuous.

•  child - do they have a child?  Categorical.

•  religious - how religious are they, ranging from 1 = anti-religious to 5 = very religious.

• education - years of education, ranging from 9 = primary school to 20 = PhD.

• occupation - Job status, ranging from 1-7 according to the Hollinghead classification (reverse numbering so 7 is a better level job).

• rate - How do they rate their marriage, ranging from 1 = unhappy to 5 = very happy.

Further information regarding this data can be found in the original paper:

Fair, R. C. (1978). A theory of extramarital affairs. Journal of Political Economy, 86(1), 45-61. This includes a more in depth discussion of the data and variables involved.

Data Cleaning

The questions in this section will involve making sure the data is all good to work with.  Data cleaning

processes include checking for missing data, making sure variables have been read in correctly, and making sure the values of our data are reasonable.

1. Read the data into R, making sure it is a tibble. Display the first 6 rows of the dataset to make sure it has read in correctly (head is a good function for this). [2]

2. What is the outcome variable, and what are the predictor variables? [2]

3. Skim the data.  Is there any missing data?  How many observations and variables do we have?  Have any variables been read in incorrectly? [4]

4. Convert the affair variable to a yes/no response (the function ifelse or case_when will be useful). Change all character variables to factors. [3]

5. Skim the data again and answer the following. [5]

a. How many people responded as having had an affair? How many people responded to having children?

b. What is the mean age of respondents? What is the mean response on the religious scale?

Section Total:  [16]

Exploratory analysis

This section is concerned with the exploratory analysis of the data.  Exploratory analysis is an important part of any model building process.  This is where we will examine possible relationships in our data that may help inform our model. We will look at some of the relationships in our dataset using summary statistics and data visualisation.

1. Of the participants who responded “no” to an affair, what proportion of them are female?   How about for those who responded“yes”to having an affair? Does there appear to be a difference in the proportion of females who will have an affair opposed to those who will not? (Hint: the function count will be useful for this) [3]

2. What proportion of participants who responded “yes”to having an affair had children?  How about those participants who responded“no”? Based on this, are you more likely to have children if you have an affair? [3]

Usually we would  look at  plots to  compare the  relationships  in our  dataset  using  summary

statistics and data visualisation.   To reduce the length of the assignment, we won’t do that this week

Section Total:  [6]

Split and preprocess

In this section, we will look at data splitting and preprocessing in TidyModels. Data slitting is an important

step in the model building process that will help with avoiding over fitting and the evaluation of models. Preprocessing is the generalised term for performing mathematical operations on your data before modelling it to improve the predictive power of the model.

1. Using initial_split, create an rsplit of the affairs data. How many observations are in the train- ing set and how many are in the testing set?  Do not forget to set a seed for reproducibility using set .seed(123). [3]

2. Use the functions training and testing to obtain the test and training sets. Display the first 6 rows of the training set to make sure this has worked properly. [3]

3. What does step_downsample from the themis package do? Why might we want to down sample our data? [4]

4. In tutorial 3 we saw how to use recipes. Create a recipe, based off of our training data, that will: [4]

• Down sample our data on affair.   Do this using themis::step_downsample(  affair  ) in your recipe,

•  Convert all our categorical predictors to dummy variables, and

•  Normalise all of our predictor variables to have mean 0 and standard deviation 1.

•  Print out the recipe to make sure it has worked using prep().

5. Complete the following:

a. Use the function juice (on the recipe) to get your preprocessed training set.  [1]

b. Use the function bake (on the recipe and testing split) to get your preprocessed testing set. This can be both be done in the one function. [1]

6. Skim the preprocessed training data. Explain if the 3 preprocessing steps have done what you expect. [4]

Section Total:  [20]

Tune and fit a model

This section is concerned with the tuning and fitting of the model.   We will be looking at a  k-nearest neighbours model. When considering a k-nearest neighbours model, we need to choose a suitable value for k .

1. Make a model specification for a k-nearest neighbours model.  In the model specification, define that we would like to tune() the neigbors parameter. [2]

2. Create a 5-fold cross validation set from the preprocessed training data.  Be sure to set a seed for reproducibility using set .seed(1223). [3]

3. Use grid_regular to make a grid of k-values to tune our model on. Using levels get 25 unique values for k . You also need to set your neighbors to range from 5 to 75. [2]

4. Use tune_grid to tune your k-nearest neighbours model using your cross validation sets and grid of k-values. [2]