Solutions to integrated exercise

Introduction

During this workshop you have learned to import, manipulate, visualise and analyse data. Time to use all these skills and create a research report!

This research report will focus upon the relation of motivation with math scores. We will use data that was collected in 2010 during a large project on the transition of secondary to higher education or the labour market. We followed almost 4000 students for two years and collected data during 5 waves. If you want to know more about the project, you can have a look at this or this article. Today, we only use the data collected during the first two measurement waves. Students were in their final year of secondary education.

The data set contains information on 15 variables:
- ID_School: ID of the school
- ID_Class: ID of the class
- ID_Student: ID of the student
- Educ_level: educational track of the studion (1: general education, 2: technical education, 3: vocational education, 4: arts education)
- Gender: gender of student (0: female, 1: male)
- SES_language: language indicator of social-economic status that was used by the government to indicate whether or not a student was at risk (0: does not apply, 1: applies)
- SES_neighbourhood: neighbourhood indicator of social-economic status that was used by the government to indicate whether or not a student was at risk (0: does not apply, 1: applies)
- SES_educ_level: education indicator of social-economic status that was used by the government to indicate whether or not a student was at risk (0: does not apply, 1: applies)
- IQ_score: raw score on a non-verbal IQ-test (min. score: 0, max. score: 40) - Math_score: raw score on a math test (problem-solving) (min. score: 0, max. score: 24)
- Reading_score: raw score on a reading comprehension test (min. score: 0, max. score: 24)
- Autonomous_motivation: autonomous motivation for studying (based on average score on 6 items, min. score: 0, max. score: 5)
- Controlled_motivation: controlled motivation for studying (based on average score on 6 items, min. score: 0, max. score: 5)
- Amotivation: amotivation for studying (based on average score on 3 items, min. score: 0, max. score: 5)

💡 Don’t forget to load the necessary packages: tidyverse and here.

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1. Import and clean data

1.1 Import the data

Import the data

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1.2 Check data

Check all variables:

Are they correctly defined (numeric, character, …)?
Which variables should be converted to another ‘type’ (numeric, character, …)?

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What is your conclusion?

Most categorical variables (ID_Class, ID_Student, Educ_level, Gender, SES_language, SES_neighbourhood, SES_educ_level) are defined as ‘integer’. These variables should be converted to type ‘character’. The variable X contains row numbers and should be removed.

You might have already noticed that several variables contain missing values (NA’s). However, it is always save to check this for all variables and also to look for ‘strange’ values. Get an overview of the variables using the function summary().

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What is your conclusion?

Almost all variables have missing values. The maximum value of the motivation variables (Autonomous_motivation, Controlled_motivation, Amotivation) is 99. This is, of course, an impossible value (maximum was 5). To be sure that these variables don’t contain other strange values, you make a quick barplot of the distribution of each of these variables. You save the plots as objects P1, P2 and P3.
(A barplot is most of the time not a good choice to visualise quantitative variables. However, to get an idea of every value in a quantitative variable, a barplot is more informative than a histogram or density plot.)

💡 Attention! You have to create three barplots. These plots can be combined into one plot using the package patchwork. You have to load this package and add code to combine the three plots. This code has already been included in the code block below. This code now has a # in front of it. Remove that # so the code will be executed.

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What is your conclusion?

The motivation variables (Autonomous_motivation, Controlled_motivation, Amotivation) don’t contain other strange values.

You decide to also visualise the distribution of the categorical variables: Educ_level, Gender, SES_language, SES_neighbourhood en SES_educ_level (using a barplot).

You already know that these variables are included as numeric variables, while they are of type character. To make sure that you get correct values on the x-axis of your barplots, specify the x aesthetic as follows ggplot(aes(x = as.character(Educ_level))).

💡 Attention! You have to create five barplots. These plots can be combined into one plot using the package patchwork. You have to add code to combine the five plots. This code has already been included in the code block below. This code now has a # in front of it. Remove that # so the code will be executed.

# CODE HERE

What is your conclusion?

The distribution of the five categorical variables looks fine. (They all have missing values!) Category 4 of the variable Educ_level contains little observations compared to that of the three other categories. It would be nice if the categories of all these variables would be appropriately labelled. (In that case, you would immediately know what category 4 of the variable Educ_level refers to.)

1.3 Clean data

After having checked the data, you know that the following actions needs to be performed:

convert all categorical variables to a character variable
label the categories of the variables Educ_level, Gender, SES_language, SES_neighbourhood and SES_educ_level and store them as new variables
recode the values 99 in the motivation variables (Autonomous_motivation, Controlled_motivation, and Amotivation) to NA and store them as new variables
remove the first column

Write the code to perform the actions listed above and save as a new data frame transition_data_cleaned

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Don’t forget to check your recoding work!

First, check whether each variable is defined correctly. (Are all categorical variables defined as a character variable? Is the redundant variable removed from the data?)

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Check whether you labelled the categorical variables correct using the function table().

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1.4 Prepare data for analysis

Create a data frame transition_data_for_analysis that only contains the following variables:

ID_School
ID_Class
ID_Student
Educ_level and Educ_level_cat
Gender and Gender_cat
all SES-indicators (original and recoded variables)
IQ_score, Reading_score, Wisk_score
the motivation variables (only the ones that you recoded)

To select these variables efficiently, the ‘selection helpers’ of the select()-function are handy. More information on these helpers can be found here. Also include a standardized version of every quantitative variable in your data set. To standardize a variable, you can use the function scale(). Finally, you decide to exclude all students in the arts education track (based on the results of the barplot you created in 1.2).

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Check you new data frame transition_data_for_analysis.

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Check if the data is filtered correctly.

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3. Some descriptives

Before doing the analysis, you want to check some things.

First, you want to get an idea of the number of observations per school. To do so, you create a lollipop plot. To help the reader of your rapport, you make sure that the ‘bars’ are arranged in ascending order. Color bars with counts less than 20 in red. (You first have to create a new variable color_ID to be avble to do that!) Use your ggplot2-skills to make the plot “publication-ready”.

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You also create a table with the descriptive statistics (mean, SD, min, max) of the raw (unstandardized) variables IQ_score, Reading_score and Math_score. To so, you first create a vector per variable (using the function c()) that contains those four values. To calculate these values you use the functions mean(), sd(), min() and max(). Then, you combine the three vectors into one tibble (descriptives) using the function bind_rows(). (This function pastes the rows below each other.) Don’t forget to print the resulting tibble.

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Before turning the tibble into a real table, you must round all numbers to two places after the decimal combining the functions mutate_all and round(). After that, you also create a new column Name that contains the names of the variables. Make sure it appears before the column mean.

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Reuse the code you wrote and turn your tibble into a real table by using the function kable().** Check out the help-page of the kable()-function to find out how you can align the five columns! Center all but the first columns. (The first one can be “left” aligned.)

💡 Attention! To use the function kable() you have to install and load the package knitr.

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Much more options are available when you also install the package kableExtra. This website provides more information on the use of that package: https://cran.r-project.org/web/packages/kableExtra/vignettes/awesome_table_in_html.html One of the many nice features of kableExtra are the built-in themes:
- kable_classic()
- kable_classic2()
- kable_paper()
- kable_minimal()
- kable_material()
- kable_material_dark()

Reuse the code your wrote above and add a theme. Play around with these themes to get to know them.

💡 Attention! To use these functions you have to install and load the package kableExtra.

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4. Analyse the data

Fit a first linear regression model with math score as dependent variable and the thee motivation variables as independent variables.

Use standardized variables. Save your model as an object Model_lm1 and print the model summary.

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Fit a second linear regression model that builds on the previous one but adds gender, educational level, IQ-score and reading-score as control variables.

Use standardized variables. Save your model as an object Model_lm2 and print the model summary.

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Before reporting on the results, **you have to check the assumptions of both models. Several R-packages perform these kind of tasks. One example is the performance package. Install this package and use the function check_model() to do a visual check of the assumptions.

💡 Attention! To use the function check_model() you have to install and load the package performance.

Check the assumptions of the model Model_lm1 first.

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Do the same for the other model.

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These results look quite good. However, you also want to do an additional check for outliers. Go to this website and look for the function that you need to do an additional check on outliers.

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Another important assumption concerns the distribution of the dependent variable (should be normally distributed). You do not need a package to check on that distribution, but use your ggplot2-skills to make a histogram of the distribution of the dependent variable. ‘Style’ the histogram so you can use it in a publication.

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The tail on the left-hand side of the distribution worries you a bit. You decide to discuss this with your supervisor.

To finish up the report, you create a nice table of the estimates of both models. To create this table, you use the function tab_model() of the package sjPlot. Go the help-page of this function and figure out how to turn off the printing of p-values, print a 90% confidence interval, rename the column names to ‘Variables’, ‘Est.’ and ‘90% CI’ and remove the brackets around Intercept.

💡 Attention! To use the function tab_model() you have to install and load the package sjPlot.

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Before sending the report to your supervisor, you compare both models. To do so, you first make a data set transition_data_omitted that excludes all missing values for the variables included in Model_lm2. (This is necessary in order to compare the models.)

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Then, you refit both models using the new data set.

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Finally, you compare both models using the function compare_performance of the package performance.

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To be able to sent the report to your supervisor, you render it as an html-file

A Quarto tip!

Please note, if you Render the document to send it to someone else you want to have all the information in one single file so that you can send the .html file to that person. To make sure all the figures etc are in the file, specify the option self-contained: true in the YAML. See it in action in the .qmd file for this exercise.