Search for conditions that provide significant differences between paired variables

Paired baseline contrast patterns identify conditions under which there is a significant difference in some statistical feature between two paired numeric variables.

Scheme:: (xvar - yvar) != 0 | C

There is a statistically significant difference between paired variables xvar and yvar under the condition C.
Example:: (daily_ice_cream_income - daily_tea_income) > 0 | sunny

Under the condition of sunny weather, the paired test shows that daily ice-cream income is significantly higher than the daily tea income.

The paired baseline contrast is computed using a paired version of a statistical test, which is specified by the method argument. The function computes the paired contrast between all pairs of variables, where the first variable is specified by the xvars argument and the second variable is specified by the yvars argument. Paired baseline contrasts are computed in sub-data corresponding to conditions generated from the condition columns. Function dig_paired_baseline_contrasts() supports crisp conditions only, i.e., the condition columns in x must be logical.

Usage

dig_paired_baseline_contrasts(
  x,
  condition = where(is.logical),
  xvars = where(is.numeric),
  yvars = where(is.numeric),
  disjoint = var_names(colnames(x)),
  min_length = 0L,
  max_length = Inf,
  min_support = 0,
  max_support = 1,
  method = "t",
  alternative = "two.sided",
  h0 = 0,
  conf_level = 0.95,
  max_p_value = 1,
  t_var_equal = FALSE,
  wilcox_exact = FALSE,
  wilcox_correct = TRUE,
  wilcox_tol_root = 1e-04,
  wilcox_digits_rank = Inf,
  max_results = Inf,
  verbose = FALSE,
  threads = 1
)

Arguments

x: a matrix or data frame with data to search the patterns in.
condition: a tidyselect expression (see tidyselect syntax) specifying the columns to use as condition predicates
xvars: a tidyselect expression (see tidyselect syntax) specifying the columns to use for computation of contrasts
yvars: a tidyselect expression (see tidyselect syntax) specifying the columns to use for computation of contrasts
disjoint: an atomic vector of size equal to the number of columns of x that specifies the groups of predicates: if some elements of the disjoint vector are equal, then the corresponding columns of x will NOT be present together in a single condition. If x is prepared with partition(), using the var_names() function on x's column names is a convenient way to create the disjoint vector.
min_length: the minimum size (the minimum number of predicates) of the condition to be generated (must be greater or equal to 0). If 0, the empty condition is generated in the first place.
max_length: The maximum size (the maximum number of predicates) of the condition to be generated. If equal to Inf, the maximum length of conditions is limited only by the number of available predicates.
min_support: the minimum support of a condition to trigger the callback function for it. The support of the condition is the relative frequency of the condition in the dataset x. For logical data, it equals to the relative frequency of rows such that all condition predicates are TRUE on it. For numerical (double) input, the support is computed as the mean (over all rows) of multiplications of predicate values.
max_support: the maximum support of a condition to trigger the callback function for it. See argument min_support for details of what is the support of a condition.
method: a character string indicating which contrast to compute. One of "t", for parametric, or "wilcox", for non-parametric test on equality in position.
alternative: indicates the alternative hypothesis and must be one of "two.sided", "greater" or "less". "greater" corresponds to positive association, "less" to negative association.
h0: a numeric value specifying the null hypothesis for the test. For the "t" method, it is the difference in means. For the "wilcox" method, it is the difference in medians. The default value is 0.
conf_level: a numeric value specifying the level of the confidence interval. The default value is 0.95.
max_p_value: the maximum p-value of a test for the pattern to be considered significant. If the p-value of the test is greater than max_p_value, the pattern is not included in the result.
t_var_equal: (used for the "t" method only) a logical value indicating whether the variances of the two samples are assumed to be equal. If TRUE, the pooled variance is used to estimate the variance in the t-test. If FALSE, the Welch (or Satterthwaite) approximation to the degrees of freedom is used. See t.test() and its var.equal argument for more information.
wilcox_exact: (used for the "wilcox" method only) a logical value indicating whether the exact p-value should be computed. If NULL, the exact p-value is computed for sample sizes less than 50. See wilcox.test() and its exact argument for more information. Contrary to the behavior of wilcox.test(), the default value is FALSE.
wilcox_correct: (used for the "wilcox" method only) a logical value indicating whether the continuity correction should be applied in the normal approximation for the p-value, if wilcox_exact is FALSE. See wilcox.test() and its correct argument for more information.
wilcox_tol_root: (used for the "wilcox" method only) a numeric value specifying the tolerance for the root-finding algorithm used to compute the exact p-value. See wilcox.test() and its tol.root argument for more information.
wilcox_digits_rank: (used for the "wilcox" method only) a numeric value specifying the number of digits to round the ranks to. See wilcox.test() and its digits.rank argument for more information.
max_results: the maximum number of generated conditions to execute the callback function on. If the number of found conditions exceeds max_results, the function stops generating new conditions and returns the results. To avoid long computations during the search, it is recommended to set max_results to a reasonable positive value. Setting max_results to Inf will generate all possible conditions.
verbose: a logical scalar indicating whether to print progress messages.
threads: the number of threads to use for parallel computation.

Value

A tibble with found patterns in rows. The following columns are always present:

condition: the condition of the pattern as a character string in the form {p1 & p2 & ... & pn} where p1, p2, ..., pn are x's column names.
support: the support of the condition, i.e., the relative frequency of the condition in the dataset x.
xvar: the name of the first variable in the contrast.
yvar: the name of the second variable in the contrast.
estimate: the estimated difference of variable var.
statistic: the statistic of the selected test.
p_value: the p-value of the underlying test.
n: the number of rows in the sub-data corresponding to the condition.
conf_int_lo: the lower bound of the confidence interval of the estimate.
conf_int_hi: the upper bound of the confidence interval of the estimate.
alternative: a character string indicating the alternative hypothesis. The value must be one of "two.sided", "greater", or "less".
method: a character string indicating the method used for the test.
comment: a character string with additional information about the test (mainly error messages on failure).

For the "t" method, the following additional columns are also present (see also t.test()):

df: the degrees of freedom of the t test.
stderr: the standard error of the mean difference.

Author

Michal Burda

Examples

# Compute ratio of sepal and petal length and width for iris dataset
crispIris <- iris
crispIris$Sepal.Ratio <- iris$Sepal.Length / iris$Sepal.Width
crispIris$Petal.Ratio <- iris$Petal.Length / iris$Petal.Width

# Create predicates from the Species column
crispIris <- partition(crispIris, Species)

# Compute paired contrasts for ratios of sepal and petal length and width
dig_paired_baseline_contrasts(crispIris,
                              condition = where(is.logical),
                              xvars = Sepal.Ratio,
                              yvars = Petal.Ratio,
                              method = "t",
                              min_support = 0.1)
#> # A tibble: 4 × 15
#>   condition  support xvar  yvar  estimate statistic    df  p_value     n conf_lo
#>   <chr>        <dbl> <chr> <chr>    <dbl>     <dbl> <dbl>    <dbl> <int>   <dbl>
#> 1 {}           1     Sepa… Peta…   -2.36      -10.5   149 1.31e-19   150  -2.80 
#> 2 {Species=…   0.333 Sepa… Peta…   -5.44      -13.5    49 4.41e-18    50  -6.25 
#> 3 {Species=…   0.333 Sepa… Peta…   -1.08      -25.6    49 5.13e-30    50  -1.17 
#> 4 {Species=…   0.333 Sepa… Peta…   -0.550     -11.1    49 4.85e-15    50  -0.649
#> # ℹ 5 more variables: conf_hi <dbl>, stderr <dbl>, alternative <chr>,
#> #   method <chr>, comment <chr>