## Thursday, May 22, 2014

### Dichotomous variables

Models with dichotomous variables can be tested with WarpPLS. Based on preliminary Monte Carlo simulations, the following combination of algorithm and P value calculation method seems to be the most advisable: PLS regression and stable.

A model with a dichotomous dependent variable can also be tested with WarpPLS; another technique that can be used is logistic regression, which is a variation of ordinary multiple regression.

Below is a model with a dichotomous dependent variable - Effe. The variable assumes two values, 0 or 1, to reflect low or high levels of "effectiveness".

The graph below shows the expected values of Effe given Effi. The latter is one of the LVs that point at Effe in the model. The values of Effe and Effi are unstandardized.

Arguably a model with a dichotomous dependent variable cannot be viably tested with ordinary multiple regression because the dependent variable is not normally distributed (as it assumes only two values).

The graph below shows a histogram with the distribution of values of Effe. This variable's skewness is -0.423 and excess kurtosis is -1.821.

This is not a problem for WarpPLS because P values are calculated via nonparametric techniques that do not assume in their underlying design that any variables in the model meet parametric expectations; such as the expectations of univariate and multivariate unimodality and normality.

If a dependent variable refers to a probability, and is expected to be associated with a predictor according to a logistic function, you should use the Warp3 or Warp3 basic inner model algorithms to relate the two variables.

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