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Friday, October 21, 2022

Dichotomous variables


There are several ways in which a model with an endogenous dichotomous variable can be analyzed in PLS-SEM - via the logistic regression variables technique, without any additional treatment, and via the conditional probabilistic queries technique. Below we discuss the first two options.

Logistic regression variables technique

Starting in version 8.0 of WarpPLS, the menu option “Explore logistic regression” allows you to create a logistic regression variable as a new indicator that has both unstandardized and standardized values. Logistic regression is normally used to convert an endogenous variable on a non-ratio scale (e.g., dichotomous) into a variable reflecting probabilities. You need to choose the variable to be converted, which should be an endogenous variable, and its predictors. 

The new logistic regression variable is meant to be used as a replacement for the endogenous variable on which it is based. Two algorithms are available: probit and logit. The former is recommended for dichotomous variables; the latter for non-ratio variables where the number of different values (a.k.a. “distinct observations”) is greater than 2 but still significantly smaller than the sample size; e.g., 10 different values over a sample size of 100. The unstandardized values of a logistic regression variable are probabilities; going from 0 to 1. 

Since a logistic regression variable can be severely collinear with its predictors, you can set a local full collinearity VIF cap for the logistic regression variable. Predictor-criterion collinearity, or lateral collinearity, is rarely assessed or controlled in classic logistic regression algorithms. 

For more on this topic, see the links below.

Explore Logistic Regression in WarpPLS

Using Logistic Regression in PLS-SEM with Composites and Factors

Without any additional treatment

Models with dichotomous endogenous variables can also be tested with WarpPLS without any additional treatment, although this may lead to path coefficient suppression as well as other problems. Based on preliminary Monte Carlo simulations, the following combination of algorithm and P value calculation method seems to be the most advisable, if users want to analyze models with composite-based algorithms: PLS regression and stable.

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 (as in logistic regression), 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.

13 comments:

Unknown said...

I have an independent variable in my model which is measured by a nominal scale with only two categories. Now, I just wanna know that how I can analyze this variable in warp pls?

Ned Kock said...

Hi Sayema. These two posts should be quite useful in the context of your question:

http://warppls.blogspot.com/2010/02/how-do-i-control-for-effects-of-one-or.html

http://warppls.blogspot.com/2011/08/using-warppls-in-e-collaboration.html

Btw, are you attending our whole-day workshop in the PLS Appls. Symposium?

http://plsas.net

Unknown said...

Dear Prof.
Many thanks for your prompt reply.
I would love to attend the workshop, but, I am not residing in USA.
I am Ph. D student and in my last colloquium, the accessors were asking, why I have used Warp PLS not, Smart PLS. Can you please point out some of the advantages of using Warp PLS over Smart PLS?

Thanks again
Best regards

Unknown said...

Dear Prof.
Many thanks for your prompt reply.
I would love to attend the workshop, but, I am not residing USA.
I am Ph. D student and in my colloquium, the accessors were asking, why I have used Warp PLS not, Smart PLS. Can you please point out some of the advantages of using Warp PLS over Smart PLS?

Thanks again
Best regards

Ned Kock said...

The text below can be used to justify the use of WarpPLS. Some of its features, such as the ability to conduct a factor-based SEM and model nonlinear relationships, are, to the best of my knowledge, unique among SEM software.

--------------

WarpPLS has been used to study a number of topics in a variety of disciplines and fields, including: accounting, anthropology, clinical psychology, ecology, economics, education, global environmental change, epidemiology, evolutionary psychology, exercise physiology, information systems, international business, finance, management, marketing, medicine, nursing, organizational psychology, and sociology. Articles presenting empirical studies employing WarpPLS as the main data analysis tool have been published in journals that are highly ranked in their respective fields, such as: Global Environmental Change, Journal of Advanced Nursing, Journal of Management Information Systems, International Business Review, Journal of the Association for Information Systems, Decision Support Systems, and Management Information Systems Quarterly.[3]

Main features
Among the main features of WarpPLS is its ability to identify and model non-linearity among variables in path models, whether these variables are measured as latent variables or not, yielding parameters that take the corresponding underlying heterogeneity into consideration.[4][5] This and other notable features are summarized through the list below.

Guides SEM analysis flow via a step-by-step user interface guide.[6]
Implements classic (composite-based) as well as factor-based PLS algorithms.
Identifies nonlinear relationships, and estimates path coefficients accordingly.
Also models linear relationships, using classic and factor-based PLS algorithms.
Models reflective and formative variables, as well as moderating effects.
Calculates P values, model fit and quality indices, and full collinearity coefficients.
Calculates effect sizes and Q-squared predictive validity coefficients.
Calculates indirect effects for paths with 2, 3 etc. segments; as well as total effects.
Calculates several causality assessment coefficients.
Provides zoomed 2D graphs and 3D graphs.

References
Kock, N., & Mayfield, M. (2015). PLS-based SEM algorithms: The good neighbor assumption, collinearity, and nonlinearity. Information Management and Business Review, 7(2), 113-130.
Kock, N. (2015). A note on how to conduct a factor-based PLS-SEM analysis. International Journal of e-Collaboration, 11(3), 1-9.
Google Scholar list of links to academic publications using or discussing WarpPLS
Gountas, S., & Gountas, J. (2016). How the ‘warped’ relationships between nurses' emotions, attitudes, social support and perceived organizational conditions impact customer orientation. Journal of Advanced Nursing, 72(2), 283-293.
Guo, K.H., Yuan, Y., Archer, N.P., & Connelly, C.E. (2011). Understanding nonmalicious security violations in the workplace: A composite behavior model. Journal of Management Information Systems, 28(2), 203-236.
Short YouTube video illustrating step-by-step user interface guide

Anonymous said...

Dear Professor Kock
I have a model that involves 1 exogenous variable (two items, binary yes/no), 2 mediating variables (both single item, yes/no binary) and one dependent variable (single item, continuous percentage).

Questions:
1. Can WarpPLS handle binary (yes/now) single item variables like in the model above? I saw that SmartPLS cannot handle binary variables.
2. The link from independent to mediating variable is Sig, and the one from mediating variable to dependent also sig. However, the indirect effect is non-sig. What does this mean in practice? can I say the influence of independent variable on dependent variable takes place through the mediator?

Your help is much appreciated
Best regards
Mohamed

Ned Kock said...

Yes, but some information is lost when a ratio var. is modeled as a binary var. Have you seen the link below? It addresses a new feature of WarpPLS that can be useful in cases like this.

https://warppls.blogspot.com/2017/03/model-with-endogenous-dichotomous.html

Anonymous said...

Thank you Professor Kock! This is much appreciated. I have indeed seen this post but wanted to confirm with you re my model. I will definitely use this to add some practical relevance. What about the practical interpretation of The following:

"2. The link from independent to mediating variable is Sig, and the one from mediating variable to dependent also sig. However, the indirect effect is non-sig. What does this mean in practice? can I say the influence of independent variable on dependent variable takes place through the mediator?

Your help is much appreciated!

Ned Kock said...

It does not look like you can make that claim, since the ind. eff. is non-sig. Still, here are two pubs to take a look at, regarding this.

https://www.scriptwarp.com/warppls/pubs/Kock_2014_UseSEsESsLoadsWeightsSEM.pdf

https://scriptwarp.com/dapj/2020_DAPJ_1_3/Moqbel_2020_etal_DAPJ_1_3_IndirectMediation.pdf

Anonymous said...

Dear Professor Kock

Can we have a latent variable with 2 binary indicators (1/0) as an independent variable?

Many thanks
Mohamed

Ned Kock said...

Generally, I would say yes, but it is important to keep these in mind:

http://warppls.blogspot.com/search/label/dichotomous%20variables

Abhisek Dutta said...

Hi Prof,
Your software Warp PLS has been a life saver in many aspects. But, I am confused over the algo used for inner model analysis, to whether use linear or warp. Could you point me out to any of your tutorials where you may have discussed this with some examples. Thanks

Ned Kock said...

Thanks. A full latent growth analysis, in addition to high-quality theory development work, should be useful in defining the types of algorithms to be used. See:

Kock, N. (2020). Full latent growth and its use in PLS-SEM: Testing moderating relationships. Data Analysis Perspectives Journal, 1(1), 1-5.