These functions can be used to generate simulated data for supervised (classification and regression) and unsupervised modeling applications.
Usage
sim_classification(
num_samples = 100,
method = "caret",
intercept = -5,
num_linear = 10
)
sim_regression(
num_samples = 100,
method = "sapp_2014_1",
std_dev = NULL,
factors = FALSE
)
sim_noise(
num_samples,
num_vars,
cov_type = "exchangeable",
outcome = "none",
num_classes = 2,
cov_param = 0
)Arguments
- num_samples
Number of data points to simulate.
- method
A character string for the simulation method. For classification, the single current option is "caret". For classification, values can be "sapp_2014_1", "sapp_2014_2", "van_der_laan_2007_1", or "van_der_laan_2007_2". See Details below.
- intercept
The intercept for the linear predictor.
- num_linear
Number of diminishing linear effects.
- std_dev
Gaussian distribution standard deviation for residuals. Default values are shown below in Details.
- factors
A single logical for whether the binary indicators should be encoded as factors or not.
- num_vars
Number of noise predictors to create.
- cov_type
The multivariate normal correlation structure of the predictors. Possible values are "exchangeable" and "toeplitz".
- outcome
A single character string for what type of independent outcome should be simulated (if any). The default value of "none" produces no extra columns. Using "classification" will generate a
classcolumn withnum_classesvalues, equally distributed. A value of "regression" results in anoutcomecolumn that contains independent standard normal values.- num_classes
When
outcome = "classification", the number of classes to simulate.- cov_param
A single numeric value for the exchangeable correlation value or the base of the Toeplitz structure. See Details below.
Details
These functions provide several supervised simulation methods (and one
unsupervised). Learn more by method:
method = "caret"
This is a simulated classification problem with two classes, originally
implemented in caret::twoClassSim() with all numeric predictors. The
predictors are simulated in different sets. First, two multivariate normal
predictors (denoted here as two_factor_1 and two_factor_2) are created
with a correlation of about 0.65. They change the log-odds using main
effects and an interaction:
intercept - 4 * two_factor_1 + 4 * two_factor_2 + 2 * two_factor_1 * two_factor_2 The intercept is a parameter for the simulation and can be used to control the amount of class imbalance.
The second set of effects are linear with coefficients that alternate signs and have a sequence of values between 2.5 and 0.025. For example, if there were four predictors in this set, their contribution to the log-odds would be
-2.5 * linear_1 + 1.75 * linear_2 -1.00 * linear_3 + 0.25 * linear_4(Note that these column names may change based on the value of num_linear).
The third set is a nonlinear function of a single predictor ranging between
[0, 1] called non_linear_1 here:
(non_linear_1^3) + 2 * exp(-6 * (non_linear_1 - 0.3)^2) The fourth set of informative predictors are copied from one of Friedman's
systems and use two more predictors (non_linear_2 and non_linear_3):
2 * sin(non_linear_2 * non_linear_3) All of these effects are added up to model the log-odds.
method = "sapp_2014_1"
This regression simulation is from Sapp et al. (2014). There are 20 independent Gaussian random predictors with mean zero and a variance of 9. The prediction equation is:
predictor_01 + sin(predictor_02) + log(abs(predictor_03)) +
predictor_04^2 + predictor_05 * predictor_06 +
ifelse(predictor_07 * predictor_08 * predictor_09 < 0, 1, 0) +
ifelse(predictor_10 > 0, 1, 0) + predictor_11 * ifelse(predictor_11 > 0, 1, 0) +
sqrt(abs(predictor_12)) + cos(predictor_13) + 2 * predictor_14 + abs(predictor_15) +
ifelse(predictor_16 < -1, 1, 0) + predictor_17 * ifelse(predictor_17 < -1, 1, 0) -
2 * predictor_18 - predictor_19 * predictor_20The error is Gaussian with mean zero and variance 9.
method = "sapp_2014_2"
This regression simulation is also from Sapp et al. (2014). There are 200
independent Gaussian predictors with mean zero and variance 16. The
prediction equation has an intercept of one and identical linear effects of
log(abs(predictor)).
The error is Gaussian with mean zero and variance 25.
method = "van_der_laan_2007_1"
This is a regression simulation from van der Laan et al. (2007) with ten random Bernoulli variables that have a 40% probability of being a value of one. The true regression equation is:
2 * predictor_01 * predictor_10 + 4 * predictor_02 * predictor_07 +
3 * predictor_04 * predictor_05 - 5 * predictor_06 * predictor_10 +
3 * predictor_08 * predictor_09 + predictor_01 * predictor_02 * predictor_04 -
2 * predictor_07 * (1 - predictor_06) * predictor_02 * predictor_09 -
4 * (1 - predictor_10) * predictor_01 * (1 - predictor_04)The error term is standard normal.
method = "van_der_laan_2007_2"
This is another regression simulation from van der Laan et al. (2007) with twenty Gaussians with mean zero and variance 16. The prediction equation is:
predictor_01 * predictor_02 + predictor_10^2 - predictor_03 * predictor_17 -
predictor_15 * predictor_04 + predictor_09 * predictor_05 + predictor_19 -
predictor_20^2 + predictor_09 * predictor_08The error term is also Gaussian with mean zero and variance 16.
sim_noise()
This function simulates a number of random normal variables with mean zero.
The values can be independent if cov_param = 0. Otherwise the values are
multivariate normal with non-diagonal covariance matrices. For
cov_type = "exchangeable", the structure has unit variances and covariances
of cov_param. With cov_type = "toeplitz", the covariances have an
exponential pattern (see example below).
References
van der Laan, Mark J., Polley, Eric C and Hubbard, Alan E.. "Super Learner" Statistical Applications in Genetics and Molecular Biology, vol. 6, no. 1, 2007. DOI: 10.2202/1544-6115.1309.
Stephanie Sapp, Mark J. van der Laan & John Canny (2014) Subsemble: an ensemble method for combining subset-specific algorithm fits, Journal of Applied Statistics, 41:6, 1247-1259, DOI: 10.1080/02664763.2013.864263
Examples
set.seed(1)
sim_regression(100)
#> # A tibble: 100 × 21
#> outcome predictor_01 predictor_02 predictor_03 predictor_04
#> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 8.49 -1.88 -1.86 1.23 2.68
#> 2 19.3 0.551 0.126 5.07 -3.14
#> 3 57.7 -2.51 -2.73 4.76 5.91
#> 4 -8.41 4.79 0.474 -0.993 -1.15
#> 5 43.0 0.989 -1.96 -6.86 4.96
#> 6 72.3 -2.46 5.30 7.49 4.54
#> 7 -3.36 1.46 2.15 2.00 0.249
#> 8 -3.82 2.21 2.73 1.62 1.70
#> 9 22.7 1.73 1.15 -0.0402 -3.07
#> 10 25.7 -0.916 5.05 1.53 0.969
#> # … with 90 more rows, and 16 more variables: predictor_05 <dbl>,
#> # predictor_06 <dbl>, predictor_07 <dbl>, predictor_08 <dbl>,
#> # predictor_09 <dbl>, predictor_10 <dbl>, predictor_11 <dbl>,
#> # predictor_12 <dbl>, predictor_13 <dbl>, predictor_14 <dbl>,
#> # predictor_15 <dbl>, predictor_16 <dbl>, predictor_17 <dbl>,
#> # predictor_18 <dbl>, predictor_19 <dbl>, predictor_20 <dbl>
sim_classification(100)
#> # A tibble: 100 × 16
#> class two_factor_1 two_factor_2 non_linear_1 non_linear_2 non_linear_3
#> <fct> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 class… -2.27 -1.18 -0.245 0.888 0.354
#> 2 class… -0.537 0.420 0.621 0.170 0.374
#> 3 class… 3.23 2.39 0.163 0.957 0.840
#> 4 class… 3.42 0.236 0.110 0.788 0.134
#> 5 class… 0.571 -0.100 -0.487 0.377 0.541
#> 6 class… -1.61 -0.0701 0.393 0.789 0.515
#> 7 class… 2.74 2.51 -0.751 0.459 0.931
#> 8 class… 0.0763 -0.679 0.307 0.220 0.771
#> 9 class… 0.0591 -2.35 0.402 0.566 0.712
#> 10 class… -1.39 -2.10 -0.887 0.0154 0.0784
#> # … with 90 more rows, and 10 more variables: linear_01 <dbl>,
#> # linear_02 <dbl>, linear_03 <dbl>, linear_04 <dbl>, linear_05 <dbl>,
#> # linear_06 <dbl>, linear_07 <dbl>, linear_08 <dbl>, linear_09 <dbl>,
#> # linear_10 <dbl>