Overview

TETRAD II

TETRAD III

TETRAD IV

Educational Software

CausalityLab

DSep Tutor

Publications

Researchers

What is TETRAD?

TETRAD is a program for

- creating,
- simulating data from,
- estimating,
- testing,
- predicting with, and
- searching for

causal/statistical models.

The aim of the program is to provide sophisticated methods in a friendly interface requiring very little statistical sophistication of the user and no programming knowledge. It is not intended to replace flexible statistical programming systems such as Matlab, Splus or R. TETRAD is freeware that performs many of the functions in commercial programs such as Netica, Hugin, LISREL, EQS and other programs, and many discovery functions these commercial programs do not perform.

TETRAD is unique in the suite of principled search ("exploration," "discovery") algorithms it provides--for example its ability to search when there may be unobserved confounders of measured variables, to search for models of latent structure, and to search for linear feedback models--and in the ability to calculate predictions of the effects of interventions or experiments based on a model. All of its search procedures are "pointwise consistent"--they are guaranteed to converge almost certainly to correct information about the true structure in the large sample limit, provided that structure and the sample data satisfy various commonly made (but not always true!) assumptions.

TETRAD is limited to models of categorical data (which can also be used for ordinal data) and to linear models
("structural equation models') with a Normal probability distribution, and to a very limited class of time series models. The TETRAD programs describe causal models in three distinct parts or stages: a picture, representing a directed graph specifying hypothetical causal relations among the variables; a specification of the family of probability distributions and kinds of parameters associated with the graphical model; and a specification of the numerical values of those parameters.

The program and its search algorithms have been developed over several years with support from the National Aeronautics and Space Administration and the Office of Naval Research.

The TETRAD suite of programs permits the user to do any of the following:

1. Generate a graphical statistical/causal model of any of the following kinds:
   1. Models for categorical data (Bayes networks);
   2. Models for continuous data with variables having a Gaussian (Normal) joint probability distribution;
   3. Models for a limited class of time-series representing genetic regulatory networks..
2. Estimate parameters of models of the following kinds:
   1. Models for categorical data in which all variables are recorded in the data (no "latent" variables);
   2. Models for continuous data with or without latent variables;
3. Test the fit of models of any of the kinds listed in 2. above.
4. Simulate data from a model. or any of the kinds listed in 1. above.
5. Update models of categorical data; i.e.,, compute the probability of any variable in the model conditional on any set of values for other variables in the model.
6. Predict the probability of a variable in a model (without latent variables) from interventions that fix or randomize values for any set of other variables in the model.
7. Search for models:
   1. Of categorical data with or without latent variables;
   2. Of continuous, Gaussian data with or without latent variables.
8. Compare graphical features of two models.
9. Select variables within a dataset for classifying values of cases of another variable in the dataset
10. Classify new (or old) cases using the variables selected in 9. above.
11. Assess the accuracy of classification.

scheines@andrew.cmu.edu