# Logistic Regression

## Abstract

Logistic regression is a model for predicting the value of a binary
dependent variable based on one or more independent variables of metric
or binary scale. As such it is different from linear regression in that it
allows/requires the dependent variable to be binary (i.e., 0/1) variable,
while in linear regression the dependent variable has to be of metric scale
(i.e., continuous).

This algorithm is in beta stage. Changes and additions are likely and feedback is welcome.

## Brief Description

As described by Hair, Black, Babin, and Anderson (2018), logistic
regression analysis is a specialized form of regression that is designed to
predict and explain a binary dependent variable rather than a metric-
dependent variable. The form of the logistic regression model is similar to
multiple regression, in that it represents a single multivariate relationship,
with regression-like coefficients indicating the relative impact of each
predictor variable. However, unlike linear regression the regression
coefficients are interpreted differently as they do not represent linear
relationships, but a regression on logit values (log odds). For the
independent variables, logistic regression allows both metric and non-
metric (categorical) variables in the form of dummy coded binary
variables.
Logistic regression in SmartPLS builds on the multiple regression model
(i.e., the same that is used for linear regression) but requires a binary
dependent variable to be executable. SmartPLS provides the results for
the logistic regression coefficients, their significance as well as several
metrics for assessing the predictive accuracy of the model. For estimation,
it uses a maximum likelihood approach with Newton Raphson steps.
Accordingly, the outputs also provides typical information regarding model
fit.

## Logistic Regression Settings in SmartPLS

### Test type

Specifies if a one-sided or two-sided significance test is conducted.

### Significance level

Specifies the significance level of the test statistic.

### Maximum Iterations

The maximum number of iterations that the maximum likelihood (ML)
estimation will perform. Ensures in case of nonconvergence that the
algorithm is not running forever. However, in most cases the algorithm will
converges within a couple of iterations (depending on the required
precision of the stop criterion), but sometimes ML algorithms may have
problems to converge. In such cases, allowing higher numbers of iterations
might be useful.

### Stop Criterion

The algorithm stops when the change in the log-likelihood (LnL) between
two consecutive iterations is less than this stop criterion value (or when
the maximum number of iterations is reached).

## Why beta?

SmartPLS has released the Logistic Regression algorithm as beta version
for the following reasons:

- The current implementation should produce correct results and has undergone some basic testing, but extensive testing is not yet completed.
- The current implementation is not yet finished and will include additional results and outputs in the future.
- Considerable changes in the structure of the results reports are possible in the future.

## References

- Backhaus, K., Erichson, B., Gensler, S., Weiber, R., and Weiber, T. (2021).
**Multivariate Analysis: An Application-Oriented Introduction.**Gabler:Wiesbaden. - Hair, J. F., Black, W. C., Babin, B. J., and Anderson, R. E. (2018).
**Multivariate Data Analysis (8 ed.).**Cengage Learning: London. - More literature ...

# Cite correctly

## Please always cite the use of SmartPLS!

Ringle, Christian M., Wende, Sven, & Becker, Jan-Michael. (2024). SmartPLS 4. BÃ¶nningstedt: SmartPLS. Retrieved from https://www.smartpls.com