Scale Scores & PCA

Get set up
  1. Create a new .Rmd file for this week’s exercises.
  2. Save it somewhere you can find it again.
  3. Give it a clear name (for example, dapr3_lab07.Rmd).
  4. In the first code chunk, load the packages you’ll need this week:
    • tidyverse
    • psych

Gambler’s Fallacies

Dataset: gamblers.csv

A researcher is interested in assessing if people who gamble will tend to lose more if they are more ‘impulsive’, and whether this might depend on whether they are gambling online or in a casino.

They recruited 482 participants (248 in a casino, and 234 on an online gambling site). Each participant filled out a 6 question measure of “impulsivity”, and then their total net gains (or losses) for the day were recorded (in £). All people were only playing the game BlackJack.

Our research question: is greater impulsivity associated with bigger losses when comparing online gamblers to casino gamblers?

Dataset: The data can be found at https://uoepsy.github.io/data/gamblers.csv

Table 1: gamblers.csv Data Dictionary
variable description
online whether the person was gambling in a casino or online
imp_1 I often act on the spur of the moment without thinking.
imp_2 I find it hard to resist temptations.
imp_3 I make decisions quickly, even when they have serious consequences.
imp_4 I find it hard to stay focused on tasks that take a long time to finish.
imp_5 I prefer safe activities rather than risky things just for fun.
imp_6 I am usually patient and can wait for what I want.
gain net losses or gains upon leaving/logging out
Question 1

First things first, our questionnaire software has given us the responses all in the descriptors used for each point of the likert scale, which is a bit annoying.

What we have What we want
Strongly Agree 5
Agree 4
Agree 4
Strongly Disagree 1
Neither Disagree nor Agree 3
Agree 4
Disagree 2
… …

Task: Convert them all to numbers, which we can then work with.

The code to achieve this is quite a lot, so we’ll give you the structure that will work.

In this case, we want to recode from words to numbers, and we want to do that operation across lots of variables.
In the code below, wou’ll want to change:

  • lines 1 and 2 to use the name of your dataset.
  • line 4 needs to specify the set of variables you want to do the operation to. it currently says “all the variables from variable1 to variablex (and everything in between)”.
  • lines 6-11 need to give the current values and what you want them to change to. Currently it will turn any entry of “?” to a 1, and any entry of “??” to a 2, and so on.
data <- 
  data |> 
  mutate(
    across(c(variable1:variablex),
           ~case_match(.,
                      "?" ~ 1,
                      "??" ~ 2,
                      "???" ~ 3,
                      ...
                      ...
                      ...
          ))
    )

🗂️ For a more in depth explanation of this and lots of other common data wrangling tasks for questionnaire data, see the Questionnaire Data Wrangling flash card.

Question 2

Just looking at the impulsivity questions, create a correlation matrix of the 6 variables.
What do you notice? Does it make sense given the wording of the questions?

To get a correlation matrix, we just select the columns we want, and then pass it to cor() function:

data |>
  select(variable1:variablex) |>
  cor()

We can even visualise this by passing it to something like heatmap():

data |>
  select(variable1:variablex) |>
  cor() |> 
  heatmap()

🗂️ See the Refresher: Variance, Covariance, Correlation flash card for how to read a correlation matrix.

Question 3

Reverse score questions 5 and 6, and then examine how the correlation matrix has changed.

🗂️ See the Questionnaire Data Wrangling flash card for how to reverse score variables.

  • Be careful!! if you have some code that reverse scores a question, and you run it twice, you will essentially reverse-reverse score the question, and it goes back to the original ordering!

Question 4

Create a score for “impulsivity” and add it as a new column onto the existing data frame.

The description of the questionnaire says that we should take the sum of the scores on each question, to get an overall measure of impulsivity.

🗂️ See the How to: Calculate Scale Scores flash card for how to calculate scale scores in R.

Question 5

Is greater impulsivity associated with bigger losses when comparing online gamblers to casino gamblers?

Using the scale scores that you just computed, create a plot to show how impulsivity is associated with gains/losses of gamblers in the two places (casino vs online).

Based on the plot you make, what do you predict the coefficients from the model below will look like (where impulsivity is the scale score). Will the sign of each coefficient be positive or negative?

lm(gain ~ impulsivity * online)

Once you’ve made a good effort to predict the answers to these questions, fit the model and see if your predictions are borne out. (If your predictions are different from the outcomes, reflect on why the outcomes are the way they are.)

Question 6

Take a look again at the wordings of the questions on impulsivity. Do you think they equally represent the construct of ‘impulsivity’?

If you’re stuck, think about whether each question might be measuring something else, in addition to (or instead of?) impulsivity.

variable description
imp_1 I often act on the spur of the moment without thinking.
imp_2 I find it hard to resist temptations.
imp_3 I make decisions quickly, even when they have serious consequences.
imp_4 I find it hard to stay focused on tasks that take a long time to finish.
imp_5 I prefer safe activities rather than risky things just for fun.
imp_6 I am usually patient and can wait for what I want.

This is a very subjective question. “Impulsivity” will mean subtly different things to each one of us. The idea is that we want to get at whatever idea it is that is shared across us when we use this word. To me, one of these questions feels a little less closely linked to being an ‘impulsive’ behaviour than the others.

Question 7

Okay, so if we’re not very happy that our 6 questions are equally representative of “impulsivity” (or maybe groups of questions capture distinct aspects of the construct?), we might not want to work with the plain old sum of impulsivity scores that we used above.

What are we going to do?

Let’s start by doing a Principal Component Analysis (PCA) on the 6 original items, and extracting 6 components.

🗂️ See the How to: Get PCA Scores flash card for all things conducting PCA

Question 8

Take a look at the ‘variance accounted for’ by each component (you could use a scree plot to show this too!), and think back to our research question, which has absolutely nothing to do with whether “impulsivity” is one thing, or two things, or 6 things…

How many components do you want to keep?

🗂️ See the How to: Decide on the Number of Components/Factors flash card.

Question 9

Extract the scores for the first principal component, and attach them to your dataset as a new set of scores for “impulsivity”.

Attend also to the loadings for that first component - is it related more to the questions you felt were more clearly asked about ‘impulsivity’?

🗂️ See the How to: Get PCA Scores flash card for all things conducting PCA and extracting scores.

Question 10

Using your PCA scores, not the old summed scale scores, create a plot that shows the association between impulsivity and financial loss or gain in the two different locations (casino and online). What changes, compared to the old plot?

Next, fit a new linear model that uses the PCA scores, not the old summed scale scores, to address the question of how impulsivity might affect gains in different locations. What changes, compared to the previous model that used the summed scale scores?