Simulate example data for fitting GAMs

A tidy reimplementation of the functions implemented in mgcv::gamSim() that can be used to fit GAMs. An new feature is that the sampling distribution can be applied to all the example types.

Usage

data_sim(
  model = "eg1",
  n = 400,
  scale = NULL,
  theta = 3,
  power = 1.5,
  dist = c("normal", "poisson", "binary", "negbin", "tweedie", "gamma", "ocat",
    "ordered categorical"),
  n_cat = 4,
  cuts = c(-1, 0, 5),
  seed = NULL,
  gfam_families = c("binary", "tweedie", "normal")
)

Arguments

model: character; either "egX" where X is an integer 1:7, or the name of a model. See Details for possible options.
n: numeric; the number of observations to simulate.
scale: numeric; the level of noise to use.
theta: numeric; the dispersion parameter \(\theta\) to use. The default is entirely arbitrary, chosen only to provide simulated data that exhibits extra dispersion beyond that assumed by under a Poisson.
power: numeric; the Tweedie power parameter.
dist: character; a sampling distribution for the response variable. "ordered categorical" is a synonym of "ocat".
n_cat: integer; the number of categories for categorical response. Currently only used for distr %in% c("ocat", "ordered categorical").
cuts: numeric; vector of cut points on the latent variable, excluding the end points -Inf and Inf. Must be one fewer than the number of categories: length(cuts) == n_cat - 1.
seed: numeric; the seed for the random number generator. Passed to base::set.seed().
gfam_families: character; a vector of distributions to use in generating data with grouped families for use with family = gfam(). The allowed distributions as as per dist.

Details

data_sim() can simulate data from several underlying models of known true functions. The available options currently are:

"eg1": a four term additive true model. This is the classic Gu & Wahba four univariate term test model. See gw_functions for more details of the underlying four functions.
"eg2": a bivariate smooth true model.
"eg3": an example containing a continuous by smooth (varying coefficient) true model. The model is \(\hat{y}_i = f_2(x_{1i})x_{2i}\) where the function \(f_2()\) is \(f_2(x) = 0.2 * x^{11} * (10 * (1 - x))^6 + 10 * (10 * x)^3 * (1 - x)^{10}\).
"eg4": a factor by smooth true model. The true model contains a factor with 3 levels, where the response for the nth level follows the nth Gu & Wabha function (for \(n \in {1, 2, 3}\)).
"eg5": an additive plus factor true model. The response is a linear combination of the Gu & Wabha functions 2, 3, 4 (the latter is a null function) plus a factor term with four levels.
"eg6": an additive plus random effect term true model.
´"eg7": a version of the model in "eg1"`, but where the covariates are correlated.
"gwf2": a model where the response is Gu & Wabha's \(f_2(x_i)\) plus noise.
"lwf6": a model where the response is Luo & Wabha's "example 6" function \(sin(2(4x-2)) + 2 exp(-256(x-0.5)^2)\) plus noise.
"gfam": simulates data for use with GAMs with family = gfam(families). See example in mgcv::gfam(). If this model is specified then dist is ignored and gfam_families is used to specify which distributions are included in the simulated data. Can be a vector of any of the families allowed by dist. For "ocat" %in% gfam_families (or "ordered categorical"), 4 classes are assumed, which can't be changed. Link functions used are "identity" for "normal", "logit" for "binary", "ocat", and "ordered categorical", and "exp" elsewhere.

The random component providing noise or sampling variation can follow one of the distributions, specified via argument dist

"normal": Gaussian,
"poisson": Poisson,
"binary": Bernoulli,
"negbin": Negative binomial,
"tweedie": Tweedie,
"gamma": gamma , and
"ordered categorical": ordered categorical

Other arguments provide the parameters for the distribution.

References

Gu, C., Wahba, G., (1993). Smoothing Spline ANOVA with Component-Wise Bayesian "Confidence Intervals." J. Comput. Graph. Stat. 2, 97–117.

Luo, Z., Wahba, G., (1997). Hybrid adaptive splines. J. Am. Stat. Assoc. 92, 107–116.

Examples

data_sim("eg1", n = 100, seed = 1)
#> # A tibble: 100 x 10
#>          y       x0      x1      x2       x3       f      f0     f1     f2    f3
#>      <dbl>    <dbl>   <dbl>   <dbl>    <dbl>   <dbl>   <dbl>  <dbl>  <dbl> <dbl>
#>  1 14.532  0.26551  0.65472 0.26751 0.67371  13.713  1.4814  3.7041 8.5277     0
#>  2 16.113  0.37212  0.35320 0.21865 0.094858 12.735  1.8408  2.0267 8.8680     0
#>  3  9.5835 0.57285  0.27026 0.51680 0.49260   6.4103 1.9478  1.7169 2.7456     0
#>  4 15.687  0.90821  0.99268 0.26895 0.46155  16.349  0.56879 7.2817 8.4980     0
#>  5  8.2216 0.20168  0.63349 0.18117 0.37522  12.792  1.1841  3.5501 8.0578     0
#>  6  9.9034 0.89839  0.21321 0.51858 0.99110   4.9081 0.62765 1.5318 2.7487     0
#>  7  5.9362 0.94468  0.12937 0.56278 0.17635   4.6020 0.34587 1.2953 2.9609     0
#>  8 10.839  0.66080  0.47812 0.12916 0.81344   9.7565 1.7502  2.6019 5.4045     0
#>  9 16.883  0.62911  0.92407 0.25637 0.068447 16.909  1.8377  6.3481 8.7237     0
#> 10  7.3603 0.061786 0.59876 0.71794 0.40045   6.3401 0.38578 3.3119 2.6424     0
#> # i 90 more rows

# an ordered categorical response
data_sim("eg1", n = 100, dist = "ocat", n_cat = 4, cuts = c(-1, 0, 5))
#> # A tibble: 100 x 11
#>        y      x0        x1      x2       x3         f      f0     f1         f2
#>    <int>   <dbl>     <dbl>   <dbl>    <dbl>     <dbl>   <dbl>  <dbl>      <dbl>
#>  1     1 0.93708 0.21716   0.51711 0.44457  -3.5517   0.39280 1.5439 2.7461    
#>  2     1 0.28614 0.21657   0.85193 0.060386 -4.7654   1.5653  1.5421 0.36166   
#>  3     1 0.83045 0.38895   0.44280 0.32751  -1.7693   1.0157  2.1769 3.2727    
#>  4     4 0.64175 0.94246   0.15788 0.87843   7.2150   1.8050  6.5858 7.0588    
#>  5     3 0.51910 0.96261   0.44232 0.93060   3.8994   1.9964  6.8566 3.2808    
#>  6     1 0.73659 0.73986   0.96773 0.39218  -2.3701   1.4725  4.3917 0.00015734
#>  7     1 0.13467 0.73325   0.48459 0.15885  -0.27657  0.82112 4.3340 2.8028    
#>  8     3 0.65699 0.53576   0.25246 0.31995   5.2247   1.7616  2.9198 8.7777    
#>  9     3 0.70506 0.0022730 0.25969 0.30697   3.0408   1.5991  1.0046 8.6716    
#> 10     2 0.45774 0.60894   0.54202 0.10781  -0.036524 1.9824  3.3800 2.8356    
#> # i 90 more rows
#> # i 2 more variables: f3 <dbl>, latent <dbl>