Investigate Model Behavior

# MODULE IMPORTS ----
import hddm

From version HDDM >= 0.9.0, you have access to multiple new sequential sampling models. You can simulate from these models, perform parameter estimation and moreover you have some extended plotting capabilities which can be useful to visualize model fits, or simply to investigate the behavior of models across parameter settings.

Metadata

Lets take a look at the new hddm.model_config.model_config dictionary, which allows you to investigate metadata for all the new (and old) models which are available through the HDDM-LAN extension.

# List all available models
list(hddm.model_config.model_config.keys())[:10]

['ddm_hddm_base',
 'full_ddm_hddm_base',
 'ddm',
 'angle',
 'weibull',
 'levy',
 'full_ddm',
 'ornstein',
 'ddm_sdv',
 'ddm_par2']

# Take an example to list data available for a given model
model_tmp = 'ornstein'
hddm.model_config.model_config[model_tmp]

{'doc': 'Model formulation is described in the documentation under LAN Extension.Meant for use with the extension.',
 'params': ['v', 'a', 'z', 'g', 't'],
 'params_trans': [0, 0, 1, 0, 0],
 'params_std_upper': [1.5, 1.0, None, 1.0, 1.0],
 'param_bounds': [[-2.0, 0.3, 0.2, -1.0, 0.001], [2.0, 2.0, 0.8, 1.0, 2]],
 'boundary': <function hddm.simulators.boundary_functions.constant(t=0)>,
 'params_default': [0.0, 1.0, 0.5, 0.0, 0.001],
 'hddm_include': ['z', 'g'],
 'choices': [-1, 1],
 'slice_widths': {'v': 1.5,
  'v_std': 0.1,
  'a': 1,
  'a_std': 0.1,
  'z': 0.1,
  'z_trans': 0.2,
  't': 0.01,
  't_std': 0.15,
  'g': 0.1,
  'g_trans': 0.2,
  'g_std': 0.1}}

You have access to the following data (we focus on the parts important for the user):

params, the names of paramaters for a given model (order matters)
params_trans whether HDDM should internally transform a parameter to an unconstrained domain
param_bounds the range of parameter values that the respective LAN was trained on (order as in params)
boundary the boundary function, which corresponds to the model (access the available boundary functions through the hddm.simulators.boundary_functions module.
params_default, defaults settings for the parameters of the model
hddm_include, list to supply to hddm to include all model parameters (you may want to drop some)
slide_widths, slice sampler settings parameter by parameter (changing these can improve / deteriorate sampler behavior)

You can change these settings as you see fit.

Simulate

The new simulator_h_c() function lets you generate complex datasets using the models available under hddm.model_config.model_config. The function is especially useful for parameter recovery studies. It can generate fully synthetic data, or you can supply an empirial dataset and it’s structure can be used to generate simulation based replicas. Find more information using the help() function. Here we give a simple example.

# test regressors only False
# add p_outliers to the generator !
model = 'angle'
n_subjects = 1
n_samples_by_subject = 500

data, full_parameter_dict = hddm.simulators.hddm_dataset_generators.simulator_h_c(n_subjects = n_subjects,
                                                                                  n_samples_by_subject = n_samples_by_subject,
                                                                                  model = model,
                                                                                  p_outlier = 0.00,
                                                                                  conditions = None,
                                                                                  depends_on = None,
                                                                                  regression_models = None,
                                                                                  regression_covariates = None,
                                                                                  group_only_regressors = False,
                                                                                  group_only = None,
                                                                                  fixed_at_default = None)

# A look at the data generated
data

	rt	response	subj_idx	v	a	z	t	theta
0	0.770753	1.0	0	0.380409	0.839763	0.479834	0.515753	0.959683
1	0.812753	1.0	0	0.380409	0.839763	0.479834	0.515753	0.959683
2	0.707753	0.0	0	0.380409	0.839763	0.479834	0.515753	0.959683
3	0.616753	1.0	0	0.380409	0.839763	0.479834	0.515753	0.959683
4	0.746753	1.0	0	0.380409	0.839763	0.479834	0.515753	0.959683
...	...	...	...	...	...	...	...	...
95	0.696753	0.0	0	0.380409	0.839763	0.479834	0.515753	0.959683
96	0.778753	1.0	0	0.380409	0.839763	0.479834	0.515753	0.959683
97	0.708753	1.0	0	0.380409	0.839763	0.479834	0.515753	0.959683
98	0.848752	0.0	0	0.380409	0.839763	0.479834	0.515753	0.959683
99	0.817753	1.0	0	0.380409	0.839763	0.479834	0.515753	0.959683

100 rows × 8 columns

The full_parameter_dic returned plays well with HDDM and some plots that give you the option to provide ground truth parameters. In our case the output is simple. More complicated datasets, will make this much more interesting.

full_parameter_dict

{'z': 0.4798341238342858,
 'theta': 0.9596826258981702,
 'v': 0.3804088421388936,
 't': 0.51575296339607,
 'a': 0.8397625801445228}