Code review

When reviewing student’s scripts ensure:

• They load tidyverse (and BayesFactor) at the top of the file
• They don’t load it again further down (this can cause weirdness)
• They are including sufficient vertical white space to make the file readable
• They break up long lines of code (e.g. > 100 characters, and after every pipe %>%) with a line break

Read CSV

Read a CSV file stored in the current working directory:

mydata <- read_csv('filename.sav')

Download a file from the internet

#extension

This downloads supplementary data from a paper in PlosOne (https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0212482#sec016)

download.file('https://ndownloader.figstatic.com/files/14532419', 'egger.sav')

Read all the csv files stored in a directory:

If you have a folder full of data files you can list them like so:

list.files('multifile-data/')

##  [1] "participant1.csv"  "participant10.csv" "participant2.csv"  "participant3.csv"  "participant4.csv" 
##  [6] "participant5.csv"  "participant6.csv"  "participant7.csv"  "participant8.csv"  "participant9.csv"

You can read all the csv files like so:

combined.data <- tibble(file = list.files('multifile-data/')) %>% 
  rowwise() %>% 
  do(
    {
      fn = .$file;
      read_csv(paste0("multifile-data/", fn)) %>% 
        mutate(file = fn)
    }
  )

## Parsed with column specification:
## cols(
##   participant = col_double(),
##   rt = col_double(),
##   condition = col_double()
## )
## Parsed with column specification:
## cols(
##   participant = col_double(),
##   rt = col_double(),
##   condition = col_double()
## )
## Parsed with column specification:
## cols(
##   participant = col_double(),
##   rt = col_double(),
##   condition = col_double()
## )
## Parsed with column specification:
## cols(
##   participant = col_double(),
##   rt = col_double(),
##   condition = col_double()
## )
## Parsed with column specification:
## cols(
##   participant = col_double(),
##   rt = col_double(),
##   condition = col_double()
## )
## Parsed with column specification:
## cols(
##   participant = col_double(),
##   rt = col_double(),
##   condition = col_double()
## )
## Parsed with column specification:
## cols(
##   participant = col_double(),
##   rt = col_double(),
##   condition = col_double()
## )
## Parsed with column specification:
## cols(
##   participant = col_double(),
##   rt = col_double(),
##   condition = col_double()
## )
## Parsed with column specification:
## cols(
##   participant = col_double(),
##   rt = col_double(),
##   condition = col_double()
## )
## Parsed with column specification:
## cols(
##   participant = col_double(),
##   rt = col_double(),
##   condition = col_double()
## )

# by-participant summary
combined.data %>% 
  group_by(participant) %>% 
  summarise(mean(rt), sd(rt))

## `summarise()` ungrouping output (override with `.groups` argument)

## # A tibble: 10 x 3
##    participant `mean(rt)` `sd(rt)`
##          <dbl>      <dbl>    <dbl>
##  1           1       250.     198.
##  2           2       243.     189.
##  3           3       250.     200.
##  4           4       244.     190.
##  5           5       251.     200.
##  6           6       249.     204.
##  7           7       243.     197.
##  8           8       257.     199.
##  9           9       246.     205.
## 10          10       259.     202.

Read from SPSS, Excel

#extension We don’t yet teach students this, but the rio package has a flexible interface for importing SPSS/SAV files, Excel and many other formats.

egger <- rio::import('egger.sav')

egger %>%
  select(ID:height_cm) %>%
  glimpse

## Rows: 142
## Columns: 6
## $ ID           <dbl> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25…
## $ vpn          <dbl> 3, 4, 5, 6, 7, 8, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34,…
## $ condition    <dbl> 2, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4,…
## $ age_in_years <dbl> 7.916667, 7.583333, 7.416667, 7.916667, 8.083333, 7.666667, 8.250000, 7.333333, 7.333333,…
## $ gender       <dbl> 2, 2, 1, 1, 1, 1, 2, 2, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 2, 2, 2, 1, 2, 1, 1, 2, 2, 1,…
## $ height_cm    <dbl> 127.0, 121.0, 119.0, 123.0, 129.0, 127.5, 122.0, 121.0, 132.0, 135.0, 130.0, 126.0, 132.0…

Reading of different file type works, based on the file extension:

rio::import('sleep.xlsx') %>% 
  glimpse

## New names:
## * `` -> ...1

## Rows: 241
## Columns: 12
## $ ...1                                                                                        <chr> "1", "2", …
## $ uniqueid                                                                                    <chr> "60120734e…
## $ `Start time`                                                                                <dttm> 2020-11-2…
## $ `Completion time`                                                                           <dttm> 2020-11-2…
## $ `My sleep is affected by my study commitments`                                              <chr> "Agree", "…
## $ `I achieve good quality sleep`                                                              <chr> "Agree", "…
## $ `My electronic device usage negatively affects my sleep`                                    <chr> "Disagree"…
## $ `Tiredness interferes with my concentration`                                                <chr> "Strongly …
## $ `My sleep is disturbed by external factors e.g. loud cars, housemates, lights, children...` <chr> "Strongly …
## $ `I often achieve eight hours of sleep`                                                      <chr> "Disagree"…
## $ `I regularly stay up past 11pm`                                                             <chr> "Disagree"…
## $ `My other personal commitments affect my sleep`                                             <chr> "Disagree"…

If reading an existing SPSS file which has factor (category) labels that you would like to preserve you can also use the haven package. The code below shows how to converts all labelled category data to factors. This avoids some errors later when pivoting or mutating:

egger.labelled <- haven:::read_sav('egger.sav') %>%
  mutate_if(haven::is.labelled, factor)
  
egger.labelled %>%
  select(ID:height_cm) %>%
  glimpse

## Rows: 142
## Columns: 6
## $ ID           <dbl> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25…
## $ vpn          <dbl> 3, 4, 5, 6, 7, 8, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34,…
## $ condition    <fct> 2, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4,…
## $ age_in_years <dbl> 7.916667, 7.583333, 7.416667, 7.916667, 8.083333, 7.666667, 8.250000, 7.333333, 7.333333,…
## $ gender       <fct> 2, 2, 1, 1, 1, 1, 2, 2, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 2, 2, 2, 1, 2, 1, 1, 2, 2, 1,…
## $ height_cm    <dbl> 127.0, 121.0, 119.0, 123.0, 129.0, 127.5, 122.0, 121.0, 132.0, 135.0, 130.0, 126.0, 132.0…

Visually there is not much difference, but the variables of type <dbl+lbl> (haven’s labelled data type) are now <fct> (boring old R factors). If you have any other trouble with SPSS labels read the Haven documentation.

Fix file path errors

read_csv('doesntexist.csv')

If the file you want to read in can’t be found, check the current working directory (also displayed in the error message), or list the files in the directory to check what is actually there

getwd()

## [1] "/Users/ben/dev/cheatR"

list.files()

##  [1] "_build.R"                              "cheatR.Rproj"                         
##  [3] "complete-cheat.rmd"                    "docs"                                 
##  [5] "egger.sav"                             "index.rmd"                            
##  [7] "lifesavr_cheatsheet.rmd"               "multifile-data"                       
##  [9] "README.md"                             "references.bib"                       
## [11] "sleep.xlsx"                            "staff-cheatsheet_files"               
## [13] "staff-project-students-cheatsheet.rmd"

Tidying messy names

#extension

The janitor package has a really great function to tidy messy names as they come from online survey systems. This is a real example:

rio::import('sleep.xlsx') %>% 
  glimpse

## New names:
## * `` -> ...1

## Rows: 241
## Columns: 12
## $ ...1                                                                                        <chr> "1", "2", …
## $ uniqueid                                                                                    <chr> "60120734e…
## $ `Start time`                                                                                <dttm> 2020-11-2…
## $ `Completion time`                                                                           <dttm> 2020-11-2…
## $ `My sleep is affected by my study commitments`                                              <chr> "Agree", "…
## $ `I achieve good quality sleep`                                                              <chr> "Agree", "…
## $ `My electronic device usage negatively affects my sleep`                                    <chr> "Disagree"…
## $ `Tiredness interferes with my concentration`                                                <chr> "Strongly …
## $ `My sleep is disturbed by external factors e.g. loud cars, housemates, lights, children...` <chr> "Strongly …
## $ `I often achieve eight hours of sleep`                                                      <chr> "Disagree"…
## $ `I regularly stay up past 11pm`                                                             <chr> "Disagree"…
## $ `My other personal commitments affect my sleep`                                             <chr> "Disagree"…

rio::import('sleep.xlsx') %>% 
  janitor::clean_names() %>%
  glimpse

## New names:
## * `` -> ...1

## Rows: 241
## Columns: 12
## $ x1                                                                                 <chr> "1", "2", "3", "4",…
## $ uniqueid                                                                           <chr> "60120734ec", "d0a9…
## $ start_time                                                                         <dttm> 2020-11-27 14:21:2…
## $ completion_time                                                                    <dttm> 2020-11-27 14:22:4…
## $ my_sleep_is_affected_by_my_study_commitments                                       <chr> "Agree", "Somewhat …
## $ i_achieve_good_quality_sleep                                                       <chr> "Agree", "Agree", "…
## $ my_electronic_device_usage_negatively_affects_my_sleep                             <chr> "Disagree", "Strong…
## $ tiredness_interferes_with_my_concentration                                         <chr> "Strongly agree", "…
## $ my_sleep_is_disturbed_by_external_factors_e_g_loud_cars_housemates_lights_children <chr> "Strongly agree", "…
## $ i_often_achieve_eight_hours_of_sleep                                               <chr> "Disagree", "Somewh…
## $ i_regularly_stay_up_past_11pm                                                      <chr> "Disagree", "Disagr…
## $ my_other_personal_commitments_affect_my_sleep                                      <chr> "Disagree", "Neithe…

This makes working with the dataset much easier:

• Everything is lower case, so no guessing whether you need to capitalise names
• No spaces (so no escaping of spaces needed with back ticks)
• No special characters which can mess things up

Renaming programatically

#extension You can do similar things yourself by doing string replacements and the set_names function.

# here the dot refers to the data coming from the pipe
rio::import('sleep.xlsx') %>% names(.)

## New names:
## * `` -> ...1

##  [1] "...1"                                                                                     
##  [2] "uniqueid"                                                                                 
##  [3] "Start time"                                                                               
##  [4] "Completion time"                                                                          
##  [5] "My sleep is affected by my study commitments"                                             
##  [6] "I achieve good quality sleep"                                                             
##  [7] "My electronic device usage negatively affects my sleep"                                   
##  [8] "Tiredness interferes with my concentration"                                               
##  [9] "My sleep is disturbed by external factors e.g. loud cars, housemates, lights, children..."
## [10] "I often achieve eight hours of sleep"                                                     
## [11] "I regularly stay up past 11pm"                                                            
## [12] "My other personal commitments affect my sleep"

So this can be more flexible, but does still need some more work to remove special characters like parentheses:

rio::import('sleep.xlsx') %>%
  set_names(tolower(str_replace_all(names(.), " ", "_"))) %>%
  glimpse

## New names:
## * `` -> ...1

## Rows: 241
## Columns: 12
## $ ...1                                                                                        <chr> "1", "2", …
## $ uniqueid                                                                                    <chr> "60120734e…
## $ start_time                                                                                  <dttm> 2020-11-2…
## $ completion_time                                                                             <dttm> 2020-11-2…
## $ my_sleep_is_affected_by_my_study_commitments                                                <chr> "Agree", "…
## $ i_achieve_good_quality_sleep                                                                <chr> "Agree", "…
## $ my_electronic_device_usage_negatively_affects_my_sleep                                      <chr> "Disagree"…
## $ tiredness_interferes_with_my_concentration                                                  <chr> "Strongly …
## $ `my_sleep_is_disturbed_by_external_factors_e.g._loud_cars,_housemates,_lights,_children...` <chr> "Strongly …
## $ i_often_achieve_eight_hours_of_sleep                                                        <chr> "Disagree"…
## $ i_regularly_stay_up_past_11pm                                                               <chr> "Disagree"…
## $ my_other_personal_commitments_affect_my_sleep                                               <chr> "Disagree"…

Summarising multiple variables

#extension It’s also possible to use pivot_longer to simplify summarising multiple variables. We don’t show this technique explicitly, but we do teach pivot_longer and pivot_wider, so students could combine the ideas for themselves:

mtcars %>%
  select(cyl, mpg, wt, disp, drat) %>%
  pivot_longer(-cyl) %>%
  group_by(name) %>%
  summarise(M=mean(value), SD=sd(value), Med = median(value), IQR = IQR(value))

## `summarise()` ungrouping output (override with `.groups` argument)

## # A tibble: 4 x 5
##   name       M      SD    Med     IQR
##   <chr>  <dbl>   <dbl>  <dbl>   <dbl>
## 1 disp  231.   124.    196.   205.   
## 2 drat    3.60   0.535   3.70   0.840
## 3 mpg    20.1    6.03   19.2    7.38 
## 4 wt      3.22   0.978   3.32   1.03

Comparing variables in tables

#extension Using pivot_longer and pivot_wider you can compare variables in a table side by side:

mtcars %>%
  select(cyl, am, mpg, wt) %>%
  # note here we have to select multiple columns to exclude (cyl and am) by adding a hyhen in front of the name
  pivot_longer(c(-cyl, -am)) %>%
  # recode am to have nice labels in the table below
  mutate(am=factor(am, levels=c(0,1), labels=c("Manual", "Auto"))) %>%
  group_by(am, name) %>%
  summarise(M=mean(value), SD=sd(value)) %>%
  pivot_wider(names_from=am, values_from=c(M, SD)) %>%
  # replace underscores in column names with spaces
  set_names(str_replace(names(.), "_", " "))

## `summarise()` regrouping output by 'am' (override with `.groups` argument)

## # A tibble: 2 x 5
##   name  `M Manual` `M Auto` `SD Manual` `SD Auto`
##   <chr>      <dbl>    <dbl>       <dbl>     <dbl>
## 1 mpg        17.1     24.4        3.83      6.17 
## 2 wt          3.77     2.41       0.777     0.617

See reshaping data below for a guide to pivot_longer and pivot_wider. See also various techniques for renaming columns.

Reshaping to long form

mtcars %>%
  select(mpg, wt) %>%
  pivot_longer(cols=everything())

## # A tibble: 64 x 2
##    name  value
##    <chr> <dbl>
##  1 mpg   21   
##  2 wt     2.62
##  3 mpg   21   
##  4 wt     2.88
##  5 mpg   22.8 
##  6 wt     2.32
##  7 mpg   21.4 
##  8 wt     3.22
##  9 mpg   18.7 
## 10 wt     3.44
## # … with 54 more rows

mtcars %>%
  select(cyl, mpg, wt) %>%
  pivot_longer(cols = -cyl) %>%
  sample_n(6)

## # A tibble: 6 x 3
##     cyl name  value
##   <dbl> <chr> <dbl>
## 1     8 wt     3.57
## 2     8 wt     5.25
## 3     4 mpg   30.4 
## 4     8 mpg   13.3 
## 5     4 mpg   32.4 
## 6     4 wt     3.15

mtcars %>%
  select(cyl, am, mpg, wt) %>%
  pivot_longer(cols = c(-cyl, -am)) %>%
  sample_n(6)

## # A tibble: 6 x 4
##     cyl    am name  value
##   <dbl> <dbl> <chr> <dbl>
## 1     4     1 mpg   27.3 
## 2     4     1 wt     1.94
## 3     4     0 wt     3.19
## 4     4     1 wt     2.78
## 5     6     0 wt     3.22
## 6     4     1 wt     2.2

mtcars %>%
  select(cyl, am, mpg, wt) %>%
  pivot_longer(cols = c(mpg, wt)) %>%
  sample_n(6)

## # A tibble: 6 x 4
##     cyl    am name  value
##   <dbl> <dbl> <chr> <dbl>
## 1     4     1 wt     1.94
## 2     4     1 mpg   32.4 
## 3     6     0 mpg   18.1 
## 4     8     0 mpg   10.4 
## 5     8     0 mpg   15.2 
## 6     8     1 wt     3.17

Reshape to wider form

Use pivot_wider. With a simple table like this:

mpg.summary <- mtcars %>%
  group_by(cyl) %>%
  summarise(M = mean(mpg))

## `summarise()` ungrouping output (override with `.groups` argument)

mpg.summary

## # A tibble: 3 x 2
##     cyl     M
##   <dbl> <dbl>
## 1     4  26.7
## 2     6  19.7
## 3     8  15.1

We can spread the data wide to enable comparison (and the table is more in line with expected APA format):

mpg.summary %>%
  pivot_wider(names_from=cyl, values_from=M)

## # A tibble: 1 x 3
##     `4`   `6`   `8`
##   <dbl> <dbl> <dbl>
## 1  26.7  19.7  15.1

This is especially useful when you have more rows in the table:

diamonds %>%
  # this is a quick way of renaming color to be capitalised
  group_by(cut, Color=color) %>%
  summarise(M = mean(price)) %>%
  pivot_wider(names_from=cut, values_from=M) %>% 
  pander::pander()

## `summarise()` regrouping output by 'cut' (override with `.groups` argument)

Scatter plots

iris %>%
  ggplot(aes(x = Sepal.Length, y=Petal.Length)) +
  geom_point()

#extension Adding jitter to a plot can be useful. We don’t teach it, but I recommend using geom_jitter rather than geom_point. This is especially helpful with survey data which is not often truly continuous; adding jitter helps show points which overlap on scale boundaries:

iris %>%
  ggplot(aes(x = Sepal.Length, y=Petal.Length)) +
  geom_jitter() + 
  ggtitle("Geom jitter reveals overlapping points in non-scale data.")

Color dimensions

With a categorical color dimension:

diamonds %>%
  ggplot(aes(x = carat, y=price, color=clarity)) +
  geom_point()

Or a continuous color dimension:

iris %>%
  ggplot(aes(x = Sepal.Length, y=Sepal.Width, color=Petal.Length)) +
  geom_jitter()

See also converting continuous and categorical data

Smoothed lines

We show students how to add a smoothed line:

iris %>%
  ggplot(aes(x = Sepal.Length, y=Sepal.Width, color=Species)) +
  geom_jitter() +
  geom_smooth(se=F)

## `geom_smooth()` using method = 'loess' and formula 'y ~ x'

And also how to use a linear fit for the lines:

iris %>%
  ggplot(aes(x = Sepal.Length, y=Sepal.Width, color=Species)) +
  geom_jitter() +
  geom_smooth(se=F, method=lm)

## `geom_smooth()` using formula 'y ~ x'

Facets/panels

Create a grid of plots using a single faceting variable:

diamonds %>%
  ggplot(aes(x = carat, y=price)) +
  geom_point() +
  facet_wrap(~clarity)

#extension Or a two-way grid of facets using two variables:

diamonds %>%
  ggplot(aes(x = carat, y=price)) +
  # note adding alpha=.1 makes points partly transparent and makes it easier to see
  # where most of the density is in large datasets. The term alpha refers to the alpha-channel
  # in computer graphics which controls the transparency of images
  geom_point(alpha=.1) +
  facet_grid(cut~clarity)

plot1 <- diamonds %>%
  ggplot(aes(x = carat, y=price)) +
  geom_point(alpha=.1) +
  facet_wrap(~clarity)

plot2 <- iris %>%
  ggplot(aes(x = Sepal.Length, y=Sepal.Width, color=Species)) +
  geom_jitter(alpha=.7) +
  geom_smooth(se=F, method=lm)

cowplot::plot_grid(plot1, plot2) 

## `geom_smooth()` using formula 'y ~ x'

Boxplots (and similar)

Where the x axis is a categorical variable we teach students to use a boxplot (in preference to bar plots):

diamonds %>%
  ggplot(aes(x = cut, y=log(price))) +
  geom_boxplot()

#extension If you don’t like boxplots you can use a point-range plot. Bar charts are not recommended because of the ‘within-bar bias’, whereby readers perceive points inside the bar (e.g. the bottom of an error bar) as more likely than those outside the bar (e.g. the top of an error bar), even though this is not the case.

diamonds %>%
  ggplot(aes(x = cut, y=price)) +
  # set the error bars to be 95% CI. Default is the SE.
  # could also use the median_hilow function here
  stat_summary(fun.data=mean_cl_normal)

#extension Combining boxplots and facets can be useful for experimental data:

warpbreaks %>%
  ggplot(aes(wool, breaks)) +
  geom_boxplot() +
  # note the dot here means 'skip the horizontal-facet`
  facet_grid(.~tension)

#extension Some people like violin plots + boxplots. Day 9 in this data is a good example of why:

lme4::sleepstudy %>%
  ggplot(aes(factor(Days), Reaction)) +
  geom_violin() +
  geom_boxplot(width=.2)

Labelling axes

#extension

• xlab() and ylab() change x and y axis labels
• Color labels can also be changed
• Labels in facets are fiddly but also possible

Model ‘formula’

Most model functions in R accept a formula which describes the outcome and predictor variables (we avoid using dependent and independent variable nomenclature because researchers frequently misuse it when some or all variables are observed rather than manipulated).

Some functions, like t-test, have an alternative method for wide-format data, but this is relatively rare and it is better for students to get used to using model formulae.

A formula always has three parts:

y ~ x

1. The ‘left hand side’, y, which is the outcome
2. The tilde symbol, ~, which means “is predicted by”
3. The ‘right hand side’, x, which is the predictor(s)

You can add multiple additive predictors using the + symbol:

y ~ x1 + x2 ...

Or add interactions between variables with the *:

y ~ x1 * x2 * x3

If you write it this way all 2nd and 3rd-level interactions would be included.

Some more complex models require more than one variable on the left hand side, or can combine more than once formula (e.g. for SEM) but we don’t teach these on any of the programmes.

Compare two groups

ttestBF(formula= mpg ~ am, data=mtcars)

## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 86.58973 ±0%
## 
## Against denominator:
##   Null, mu1-mu2 = 0 
## ---
## Bayes factor type: BFindepSample, JZS

t.test(mpg ~ am, data=mtcars)

## 
##  Welch Two Sample t-test
## 
## data:  mpg by am
## t = -3.7671, df = 18.332, p-value = 0.001374
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -11.280194  -3.209684
## sample estimates:
## mean in group 0 mean in group 1 
##        17.14737        24.39231

paired.data <- lme4::sleepstudy %>%
  filter(Days==1 | Days==9) %>%
  mutate(Days=paste0('day', Days)) %>%
  pivot_wider(names_from=Days, values_from=Reaction)

paired.data

## # A tibble: 18 x 3
##    Subject  day1  day9
##    <fct>   <dbl> <dbl>
##  1 308      259.  466.
##  2 309      205.  237.
##  3 310      194.  248.
##  4 330      300.  354.
##  5 331      285   372.
##  6 332      243.  254.
##  7 333      290.  362.
##  8 334      276.  377.
##  9 335      274.  237.
## 10 337      314.  459.
## 11 349      230.  352.
## 12 350      243.  389.
## 13 351      300.  348.
## 14 352      298.  389.
## 15 369      268.  367.
## 16 370      235.  372.
## 17 371      272.  369.
## 18 372      273.  364.

with(paired.data, ttestBF(day1, day9, paired=TRUE))

## Bayes factor analysis
## --------------
## [1] Alt., r=0.707 : 3966.803 ±0%
## 
## Against denominator:
##   Null, mu = 0 
## ---
## Bayes factor type: BFoneSample, JZS

with(paired.data, t.test(day1, day9, paired=TRUE))

## 
##  Paired t-test
## 
## data:  day1 and day9
## t = -6.5205, df = 17, p-value = 5.236e-06
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -114.29724  -58.41369
## sample estimates:
## mean of the differences 
##               -86.35547

wool.anova <- anovaBF(breaks ~ wool * tension, data=warpbreaks)

## 
  |                                                                                                             
  |                                                                                                       |   0%
  |                                                                                                             
  |==========================                                                                             |  25%
  |                                                                                                             
  |====================================================                                                   |  50%
  |                                                                                                             
  |=============================================================================                          |  75%
  |                                                                                                             
  |=======================================================================================================| 100%

wool.anova

## Bayes factor analysis
## --------------
## [1] wool                          : 0.8184672 ±0.01%
## [2] tension                       : 21.451    ±0.01%
## [3] wool + tension                : 22.56884  ±1.4%
## [4] wool + tension + wool:tension : 69.5478   ±1.46%
## 
## Against denominator:
##   Intercept only 
## ---
## Bayes factor type: BFlinearModel, JZS

wool.anova[4]/wool.anova[3]

## Bayes factor analysis
## --------------
## [1] wool + tension + wool:tension : 3.081585 ±2.03%
## 
## Against denominator:
##   breaks ~ wool + tension 
## ---
## Bayes factor type: BFlinearModel, JZS

car::Anova(lm(breaks ~ wool * tension, data=warpbreaks), type=3)

## Anova Table (Type III tests)
## 
## Response: breaks
##               Sum Sq Df  F value    Pr(>F)    
## (Intercept)  17866.8  1 149.2757 2.426e-16 ***
## wool          1200.5  1  10.0301 0.0026768 ** 
## tension       2468.5  2  10.3121 0.0001881 ***
## wool:tension  1002.8  2   4.1891 0.0210442 *  
## Residuals     5745.1 48                       
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

sleep <- lme4::sleepstudy %>%
  mutate(Days=ordered(Days))

anovaBF(Reaction ~ Days + Subject, whichRandom="Subject", data=sleep)

## 
  |                                                                                                             
  |                                                                                                       |   0%
  |                                                                                                             
  |====================================================                                                   |  50%
  |                                                                                                             
  |=======================================================================================================| 100%

## Bayes factor analysis
## --------------
## [1] Days + Subject : 5.116887e+17 ±0.5%
## 
## Against denominator:
##   Reaction ~ Subject 
## ---
## Bayes factor type: BFlinearModel, JZS

ez::ezANOVA(sleep, dv = Reaction, wid = Subject, within=Days) %>%
  pander::pander()

Regression and Ancova

# calculate a base model with the covariate
h0 <- lmBF(Petal.Length ~ Sepal.Width ,  data=iris)
# an model of interest with the factor added
h1 <- lmBF(Petal.Length ~ Sepal.Width * Species,  data=iris)

h1 / h0

## Bayes factor analysis
## --------------
## [1] Sepal.Width * Species : 7.386454e+86 ±3.51%
## 
## Against denominator:
##   Petal.Length ~ Sepal.Width 
## ---
## Bayes factor type: BFlinearModel, JZS

iris.ancova <- lm(Petal.Length ~ Sepal.Width * Species,  data=iris)
car::Anova(iris.ancova)

## Anova Table (Type II tests)
## 
## Response: Petal.Length
##                     Sum Sq  Df   F value    Pr(>F)    
## Sepal.Width           3.89   1   26.1913 9.726e-07 ***
## Species             355.76   2 1198.2894 < 2.2e-16 ***
## Sepal.Width:Species   1.96   2    6.5973  0.001814 ** 
## Residuals            21.38 144                        
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

iris.ancova %>%
  broom::tidy() %>%
  pander::pander(caption="Ancova covariate and dummy coded parameters.")

Multiple regression

h1 <- lmBF(mpg ~ wt + hp, data=mtcars)
h0 <- lmBF(mpg ~ wt, data=mtcars)

h1/h0

## Bayes factor analysis
## --------------
## [1] wt + hp : 17.27075 ±0.01%
## 
## Against denominator:
##   mpg ~ wt 
## ---
## Bayes factor type: BFlinearModel, JZS

step1 <- lmBF(rating ~ complaints, data=attitude)
step2 <- lmBF(rating ~ complaints + learning + raises + critical, data=attitude)

step2 / step1

## Bayes factor analysis
## --------------
## [1] complaints + learning + raises + critical : 0.02517264 ±0.01%
## 
## Against denominator:
##   rating ~ complaints 
## ---
## Bayes factor type: BFlinearModel, JZS

mpg.m <- lm(mpg ~ wt + disp, data=mtcars)

summary(mpg.m)

## 
## Call:
## lm(formula = mpg ~ wt + disp, data = mtcars)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.4087 -2.3243 -0.7683  1.7721  6.3484 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 34.96055    2.16454  16.151 4.91e-16 ***
## wt          -3.35082    1.16413  -2.878  0.00743 ** 
## disp        -0.01773    0.00919  -1.929  0.06362 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.917 on 29 degrees of freedom
## Multiple R-squared:  0.7809, Adjusted R-squared:  0.7658 
## F-statistic: 51.69 on 2 and 29 DF,  p-value: 2.744e-10

# the `statistic` column is the t statstic here
broom::tidy(mpg.m)

## # A tibble: 3 x 5
##   term        estimate std.error statistic  p.value
##   <chr>          <dbl>     <dbl>     <dbl>    <dbl>
## 1 (Intercept)  35.0      2.16        16.2  4.91e-16
## 2 wt           -3.35     1.16        -2.88 7.43e- 3
## 3 disp         -0.0177   0.00919     -1.93 6.36e- 2

step1 <- lm(rating ~ complaints, data=attitude)
step2 <- lm(rating ~ complaints + learning + raises + critical, data=attitude)

anova(step2, step1)

## Analysis of Variance Table
## 
## Model 1: rating ~ complaints + learning + raises + critical
## Model 2: rating ~ complaints
##   Res.Df    RSS Df Sum of Sq      F Pr(>F)
## 1     25 1253.2                           
## 2     28 1369.4 -3   -116.16 0.7724 0.5204

# note + vs * in formula
h1 <- lmBF(mpg ~ wt * hp, data=mtcars)
h0 <- lmBF(mpg ~ wt + hp, data=mtcars)

h1/h0

## Bayes factor analysis
## --------------
## [1] wt * hp : 30.43604 ±0%
## 
## Against denominator:
##   mpg ~ wt + hp 
## ---
## Bayes factor type: BFlinearModel, JZS

# note + vs * in formula
h1 <- lm(mpg ~ wt * hp, data=mtcars)
h0 <- lm(mpg ~ wt + hp, data=mtcars)

anova(h1, h0)

## Analysis of Variance Table
## 
## Model 1: mpg ~ wt * hp
## Model 2: mpg ~ wt + hp
##   Res.Df    RSS Df Sum of Sq      F    Pr(>F)    
## 1     28 129.76                                  
## 2     29 195.05 -1   -65.286 14.088 0.0008108 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

anova(h1)

## Analysis of Variance Table
## 
## Response: mpg
##           Df Sum Sq Mean Sq F value    Pr(>F)    
## wt         1 847.73  847.73 182.923 8.428e-14 ***
## hp         1  83.27   83.27  17.969 0.0002207 ***
## wt:hp      1  65.29   65.29  14.088 0.0008108 ***
## Residuals 28 129.76    4.63                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

mtcars %>%
  ggplot(aes(wt, mpg)) +
  geom_jitter()

# it's annoying but we have to add the column to the df first
# because lmBF won't allow arithmetic inside it's formula

mtcars.poly <- mtcars %>%
  mutate(wt_2 = poly(wt,2))

h1 <- lmBF(mpg ~ wt + wt_2, data=mtcars.poly)
h0 <- lmBF(mpg ~ wt, data=mtcars.poly)

h1/h0

## Bayes factor analysis
## --------------
## [1] wt + wt_2 : 9.502005 ±0.01%
## 
## Against denominator:
##   mpg ~ wt 
## ---
## Bayes factor type: BFlinearModel, JZS

h1 <- lm(mpg ~ poly(wt, 2), data=mtcars)
summary(h1) # look at the p value for the second poly term

## 
## Call:
## lm(formula = mpg ~ poly(wt, 2), data = mtcars)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -3.483 -1.998 -0.773  1.462  6.238 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   20.0906     0.4686  42.877  < 2e-16 ***
## poly(wt, 2)1 -29.1157     2.6506 -10.985 7.52e-12 ***
## poly(wt, 2)2   8.6358     2.6506   3.258  0.00286 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.651 on 29 degrees of freedom
## Multiple R-squared:  0.8191, Adjusted R-squared:  0.8066 
## F-statistic: 65.64 on 2 and 29 DF,  p-value: 1.715e-11

Model statistics

Extract R² and other statistics from any linear model:

iris.ancova %>%
  broom::glance() %>%
  pivot_longer(everything())

## # A tibble: 11 x 2
##    name              value
##    <chr>             <dbl>
##  1 r.squared      9.54e- 1
##  2 adj.r.squared  9.52e- 1
##  3 sigma          3.85e- 1
##  4 statistic      5.97e+ 2
##  5 p.value        2.44e-94
##  6 df             6.00e+ 0
##  7 logLik        -6.67e+ 1
##  8 AIC            1.47e+ 2
##  9 BIC            1.69e+ 2
## 10 deviance       2.14e+ 1
## 11 df.residual    1.44e+ 2

Plotting model results

# standardise first
mtcars.z <- scale(mtcars) %>% as_tibble()
h1.z <- lmBF(mpg ~ wt + hp, data=mtcars.z)

## Warning: data coerced from tibble to data frame

chains = posterior(h1.z, iterations = 5000, progress = FALSE) %>% as_tibble()

chains %>%
  pivot_longer(c(wt, hp)) %>%
  ggplot(aes(value)) +
  geom_density(aes(y=..scaled..)) +
  facet_wrap(~name, ncol=1) +
  geom_vline(xintercept = 0)

chains %>%
  pivot_longer(c(wt, hp)) %>%
  ggplot(aes(name, value)) +
  # 95th highest density posterior interval, see Krushke book but
  # where these don't cross zero the parameter is 'significant'
  stat_summary(fun.data=tidybayes::mean_hdci) +
  coord_flip() +
  geom_hline(yintercept = 0)

Recoding categorical data

TODO

Taught in stage 2 here: https://benwhalley.github.io/rmip/data.html

Converting continuous and categorical data

mtcars %>%
  select(wt) %>%
  mutate(wt_categ = cut(wt, 5)) %>%
  sample_n(10)

##       wt    wt_categ
## 1  5.424 (4.64,5.43]
## 2  2.780  (2.3,3.08]
## 3  1.513  (1.51,2.3]
## 4  3.440 (3.08,3.86]
## 5  3.190 (3.08,3.86]
## 6  2.140  (1.51,2.3]
## 7  3.730 (3.08,3.86]
## 8  3.435 (3.08,3.86]
## 9  3.780 (3.08,3.86]
## 10 2.320  (2.3,3.08]

mtcars %>%
  select(wt) %>%
  mutate(wt_categ = cut(wt, breaks = c(-1,1,3,5,Inf))) %>%
  sample_n(10)

##       wt wt_categ
## 1  3.840    (3,5]
## 2  3.780    (3,5]
## 3  2.780    (1,3]
## 4  3.170    (3,5]
## 5  1.935    (1,3]
## 6  5.345  (5,Inf]
## 7  3.730    (3,5]
## 8  3.520    (3,5]
## 9  1.835    (1,3]
## 10 3.570    (3,5]