Introduction to faux

It is useful to be able to simulate data with a specified structure. The faux package provides some functions to make this process easier.

sim_design

This function creates a dataset with a specific between- and within-subjects design. see vignette

For example, the following creates a 2w*2b design with 100 observations in each cell. The between-subject factor is pet with twolevels of cat and dog. The within-subject factor is time with two levels of day and night. The mean for the cat_day cell is 10, the mean for the cat_night cell is 20, the mean for the dog_day cell is 15, and the mean for the dog_night cell is 25. All cells have a SD of 5 and all within-subject cells are correlated r = 0.5. The resulting data has exactly these values (set empirical = FALSE to sample from a population with these values).

between <- list("pet" = c("cat", "dog"))
within <- list("time" = c("day", "night"))
mu <- data.frame(
  cat = c(10, 20),
  dog = c(15, 25),
  row.names = within$time
)
df <- sim_design(within, between, 
                 n = 100, cors = 0.5, mu = mu, sd = 5,
                 empirical = TRUE)

Sample `sim_design()` stats
pet	n	var	day	night	mean	sd
cat	100	day	1.0	0.5	10	5
cat	100	night	0.5	1.0	20	5
dog	100	day	1.0	0.5	15	5
dog	100	night	0.5	1.0	25	5

rnorm_multi

This function makes multiple normally distributed vectors with specified parameters and relationships.see vignette

For example, the following creates a sample that has 100 observations of 3 variables, drawn from a population where where A correlates with B and C with r = 0.5, and B and C correlate with r = 0.25. A has a mean of 0 and SD of 1, while B and C have means of 20 and SDs of 5.


dat <- rnorm_multi(
  n = 100, 
  cors = c(0.5, 0.5, 0.25), 
  mu = c(0, 20, 20),
  sd = c(1, 5, 5),
  varnames = c("A", "B", "C"),
  empirical = FALSE
)

Sample `rnorm_multi()` stats
n	var	A	B	C	mean	sd
100	A	1.00	0.62	0.46	-0.05	1.08
100	B	0.62	1.00	0.19	19.95	5.38
100	C	0.46	0.19	1.00	19.81	5.15

sim_df

This function produces a dataframe with the same distributions and correlations as an existing dataframe. It only returns numeric columns and simulates all numeric variables from a continuous normal distribution (for now). see vignette

For example, the following code creates a new sample from the built-in dataset iris with 50 observations of each species.

new_iris <- sim_df(iris, 50, "Species")

Simulated iris dataset

Additional functions

check_sim_stats

If you want to check your simulated stats or just describe an existing dataset, use check_sim_stats().

check_sim_stats(iris)
#> # A tibble: 4 x 8
#>       n var   Sepal.Length Sepal.Width Petal.Length Petal.Width  mean    sd
#>   <dbl> <chr>        <dbl>       <dbl>        <dbl>       <dbl> <dbl> <dbl>
#> 1   150 Sepa…         1          -0.12         0.87        0.82  5.84  0.83
#> 2   150 Sepa…        -0.12        1           -0.43       -0.37  3.06  0.44
#> 3   150 Peta…         0.87       -0.43         1           0.96  3.76  1.77
#> 4   150 Peta…         0.82       -0.37         0.96        1     1.2   0.76

You can also group your data and change the digits to round. Display the table using knitr::kable() by setting usekable to TRUE (remember to set results='asis' in the chunk header.

check_sim_stats(iris, 
                between = "Species", 
                digits = 3, 
                usekable = TRUE)

Species	n	var	Sepal.Length	Sepal.Width	Petal.Length	Petal.Width	mean	sd
setosa	50	Sepal.Length	1.000	0.743	0.267	0.278	5.006	0.352
setosa	50	Sepal.Width	0.743	1.000	0.178	0.233	3.428	0.379
setosa	50	Petal.Length	0.267	0.178	1.000	0.332	1.462	0.174
setosa	50	Petal.Width	0.278	0.233	0.332	1.000	0.246	0.105
versicolor	50	Sepal.Length	1.000	0.526	0.754	0.546	5.936	0.516
versicolor	50	Sepal.Width	0.526	1.000	0.561	0.664	2.770	0.314
versicolor	50	Petal.Length	0.754	0.561	1.000	0.787	4.260	0.470
versicolor	50	Petal.Width	0.546	0.664	0.787	1.000	1.326	0.198
virginica	50	Sepal.Length	1.000	0.457	0.864	0.281	6.588	0.636
virginica	50	Sepal.Width	0.457	1.000	0.401	0.538	2.974	0.322
virginica	50	Petal.Length	0.864	0.401	1.000	0.322	5.552	0.552
virginica	50	Petal.Width	0.281	0.538	0.322	1.000	2.026	0.275

make_id

It is useful for IDs for random effects (e.g., subjects or stimuli) to be character strings (so you don’t accidentally include them as fixed effects) with the same length s(o you can sort them in order like S01, S02,…, S10 rather than S1, S10, S2, …) This function returns a list of IDs that have the same string length and a specified prefix.

make_id(n = 10, prefix = "ITEM_")
#>  [1] "ITEM_01" "ITEM_02" "ITEM_03" "ITEM_04" "ITEM_05" "ITEM_06" "ITEM_07"
#>  [8] "ITEM_08" "ITEM_09" "ITEM_10"

pos_def_limits

Not all correlation matrices are possible. For example, if variables A and B are correlated with r = 1.0, then the correlation between A and C can only be exactly equal to the correlation between B and C.

The function pos_def_limits() lets you know what the possible range of values is for the missing value in a correlation matrix with one missing value. The correlation values are entered just from the top right triangle of the matrix, with a single NA for the missing value.

lims <- pos_def_limits(.8, .2, NA)

min	max
-0.427	0.747

For example, if r_AB = 0.8 and r_AC = 0.2, then -0.427 <= r_BC <= 0.747.

If you enter a correlation matrix that contains impossible combinations, your limits will be NA.

lims <- pos_def_limits(.8, .2,  0,
                          -.5, NA,
                               .2)

min	max
NA	NA

is_pos_def()

If you have a full matrix and want to know if it is positive definite, you can use the following code:

c(.2, .3, .4, .2,
      .3, -.1, .2,
           .4, .5,
               .3) %>%
  cormat_from_triangle() %>%
  is_pos_def()
#> [1] TRUE

matrix(c(1, .3, -.9, .2,
        .3,  1,  .4, .5,
       -.9, .4,   1, .3,
        .2, .5,  .3,  1), 4) %>%
  is_pos_def()
#> [1] FALSE

Lisa DeBruine

2019-05-01