<commit_before><commit_msg>added help doc for regression analysis<commit_after>Summary Stats - Bayesian Linear Regression
==========================

Bayesian Linear regression allows you to model a linear relationship between one or more explanatory variable(s) (predictors) and a continuous dependent (response) variable.
This analysis, based on the classical (unadjusted) R^2 statistic, allows you to compute the corresponding Bayes factor test. The Bayes factor is computed using Gaussian quadrature.


Input options and restrictions
----------------
### Behavior
- If only alternative model values are specified, then the analysis uses the default null model to calculate the Bayes factor
- Model comparison - both models are specified
    - If number of covariates for alternative model is higher than the number of covariates for the null model, then R^2 value for null model should be less than that of alternative model
- If only null model values are specified, the analysis is not carried out.    


Input Box
-------
- Sample size
- Null model:
    - Covariates: Number of predictors in model (excluding intercept)
    - Unadjusted R-squared: Proportion of variance accounted by the predictors
- Alternative model:
    - Covariates
    - Unadjusted R-squared
- r scale (prior scale)

Default Options
-------
### Bayes Factor:
- BF10: Bayes factor to quantify evidence for the alternative hypothesis relative to the null hypothesis
- BF01: Bayes factor to quantify evidence for the null hypothesis relative to the alternative hypothesis
- Log(BF10): Natural logarithm of BF10

### Prior:
- Cauchy prior width: Scale of the Cauchy prior density on effect size under the alternative hypothesis; the default is 0.5

Default Output
-------

### Model Comparison
- If Null model not specified (default option)
    - n: sample size.
    - Number of covariates.
    - unadjusted R^2 .
    - BF10: Bayes factor in favor of the model compared to the null model (i.e., intercept only).
    - % error: Proportional error of the computation of the Bayes factor.
- If Null model is specified, above output is given for both the null and alternative models

Additional Options
-------
- specification of r Scale
- Plots
    - Bayes factor robustness plot: Displays the Bayes factor as a function of the width of the Cauchy prior on effect size. The scale of the Cauchy prior is varied between 0 and 1.5 (between 0 and 2 if user prior width is greater than 1.5), creating progressively more uninformative priors




References
-------
- <NAME>., <NAME>., <NAME>., <NAME>., & <NAME>. (2008). Mixtures of g-priors for Bayesian variable selection. *Journal of the American Statistical Association, 103*, 410-423.
- <NAME>., & <NAME>. (2012). Default Bayes factors for model selection in regression. *Multivariate Behavioral Research, 47*, 877-903.
- <NAME>., & <NAME>. (1980) Posterior odds ratios for selected regression hypotheses. In <NAME>, <NAME>, & <NAME> (Eds), *Bayesian statistics: Proceedings of the first international meeting held in Valencia (Spain)* (pp. 585-603). University of Valencia.
- Perception and Cognition Lab (University of Missouri): Bayes factor calculators. http://pcl.missouri.edu/bayesfactor
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