Logistic Regression
Logistic regression predicts the value of a binary dependent variable based on one or more independent variables measured on a metric or binary scale. Researchers use it instead of linear regression whenever the outcome of interest is dichotomous (0/1), for example whether a customer churns or not, because linear regression assumes a dependent variable measured on a continuous metric scale. SmartPLS supports the estimation of logistic regression models and provides comprehensive result reports for evaluating the outcomes.
This algorithm is in beta stage. Changes and additions are likely and feedback is welcome.
Understanding Logistic Regression
As described by Hair, Black, Babin, and Anderson (2018), logistic regression is a specialized form of regression designed to predict and explain a binary dependent variable rather than a metric-dependent variable. Its structure resembles that of multiple regression, representing a single multivariate relationship with coefficients that indicate the relative influence of each predictor. However, unlike linear regression, the coefficients are interpreted differently: they reflect effects on the logit (log odds) rather than linear relationships. Logistic regression can accommodate both metric and non-metric (categorical) independent variables, with categorical variables typically represented using dummy-coded binary indicators.
Logistic regression in SmartPLS is based on the multiple regression framework used for linear regression but requires a binary dependent variable. The software provides estimates of the logistic regression coefficients, their significance, and various metrics for evaluating the model's predictive accuracy. Estimation is performed using a maximum likelihood approach with Newton-Raphson iterations. Accordingly, the output also includes standard information on model fit.
When specified (i.e., in the graphical regression model), an intercept is included in the model estimation. To estimate a regression model without an intercept in SmartPLS, the intercept must be removed from the graphical specification of the regression model (i.e., select the intercept in the graphic and delete it).
Logistic Regression Settings in SmartPLS
| Setting | What it controls |
|---|---|
| Test type | Specifies whether a one-sided or two-sided significance test is conducted. |
| Significance level | Specifies the significance level of the test statistic. |
| Maximum iterations | Specifies how many times the maximum likelihood (ML) estimation algorithm will run, which prevents the algorithm from running indefinitely in cases of nonconvergence. In most instances, the algorithm converges within a few iterations, depending on the precision specified by the stopping criterion. ML algorithms can occasionally encounter convergence issues, in which case increasing the maximum number of iterations may help achieve convergence. |
| Stop criterion | The algorithm terminates when the change in the log-likelihood (LnL) between two consecutive iterations falls below the specified stopping criterion, 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.
Frequently Asked Questions
When should I use logistic regression instead of linear regression?
Use logistic regression whenever your dependent variable is dichotomous (0/1) rather than measured on a continuous metric scale. Linear regression assumes a continuous dependent variable, while logistic regression explicitly accommodates and requires a binary outcome.
How does SmartPLS estimate logistic regression models?
SmartPLS estimates logistic regression coefficients using a maximum likelihood approach with Newton-Raphson iterations, building on the same multiple regression framework used for linear regression. The output includes the coefficients, their significance, metrics for predictive accuracy, and standard model fit information.
How do I estimate a model without an intercept?
By default, an intercept is included whenever it is specified in the graphical regression model. To exclude it, select the intercept in the graphical model specification and delete it.
What do the "maximum iterations" and "stop criterion" settings do?
These settings control the maximum likelihood estimation process. Maximum iterations limits how many times the algorithm runs to avoid indefinite runs in case of nonconvergence, while the stop criterion defines the threshold for the change in log-likelihood between iterations at which the algorithm terminates.
What does it mean that logistic regression in SmartPLS is in beta?
It means the implementation should already produce correct results and has undergone basic testing, but extensive testing is not yet complete. Additional results and outputs are planned, and the structure of the results reports may still change considerably.
Related SmartPLS Methods
References
- Backhaus, K., Erichson, B., Gensler, S., Weiber, R., & Weiber, T. (2021). Multivariate analysis: An application-oriented introduction. Springer.
- Hair, J. F., Black, W. C., Babin, B. J., & Anderson, R. E. (2018). Multivariate data analysis (8th ed.). Cengage Learning.
- More literature ...
Cite correctly
Please always cite the use of SmartPLS!
Ringle, Christian M., Wende, Sven, & Becker, Jan-Michael. (2024). SmartPLS 4. Bönningstedt: SmartPLS. Retrieved from https://www.smartpls.com
