Using a binary variable (a single-item construct) as DV

[susanna]

Hello,

May I seek your help? In my dataset, I have a single-item construct (that contain one binary variable), this construct is the outcome variable. Can PLS models handle a model with a binary outcome variable? I heard that there is something called "PLS regression" to handle this type of models. Do you have any references / pointers on this?

Thank you very much.

[christian.nitzl]

Hi,

Hair et al. (2012) wrote about this on page 421:

“Several researchers stress that PLS-SEM generally works with nominal, ordinal, interval, and ratio scaled variables (e.g., Fornell and Bookstein 1982; Haenlein and Kaplan 2004; Reinartz et al. 2009). It is therefore not surprising that researchers routinely use categorical (14 studies, 6.86%) or even binary variables (43 studies, 21.08%). However, this practice should be considered with caution. For example, researchers may decide to use a binary single indicator to measure an endogenous construct to indicate a choice situation. In this set-up, however, the latent construct becomes its measure (Fuchs and Diamantopoulos 2009), which proves problematic for approximations in the PLS-SEM algorithm since path coefficients are estimated by OLS regressions. Specifically, OLS requires the endogenous latent variable scores to be continuous, a property that cannot be met in such a set-up. Likewise, using binary indicators in reflective models violates this OLS assumption, because reflective indicators are regressed on the latent variable scores when estimating outer weights. Correspondingly, Jakobowicz and Derquenne (2007, p. 3668) point out that “when working with continuous data […], PLS does not face any problems, but when working with nominal or binary
data it is not possible to suppose there is any underlying continuous distribution.” In a similar vein, Lohmöller (1989) argues that standard procedures for applying linear equations cannot be used for categorical variables. Based on Lohmöller’s (1989) early efforts to include categorical variables, Jakobowicz and Derquenne (2007) developed a modified version of the PLS-SEM algorithm based on generalized linear models that is, however, restricted to reflective measures. The standard PLS-SEM algorithm’s application does not account for these extensions and thus often violates fundamental OLS principles when used on categorical variables. As a consequence, researchers should not use categorical variables in endogenous constructs and should carefully interpret the meaning of categorical variables in exogenous constructs. Alternatively, categorical variables can be used to split the data set for PLS multigroup comparisons (Sarstedt et al. 2011b).”

(Joe F. Hair & Marko Sarstedt & Christian M. Ringle & Jeannette A. Mena (2012): An assessment of the use of partial least squares structural equation modeling in marketing research, in: J. of the Acad. Mark. Sci. (2012) 40:414-433.



Therefore you should split your data and perform a multgroup comparison if possible.

Best,

Christian

[syho1976]

Dear Christian and others,

Thank you for the reply.

It seems to me that, if I have a binary variable as the only endogenous variable, the problematic part is the last path (the path between the output variable (which is binary) and its antecedent). Except the last path, the path significance and the coefficients for the rest of the model (assuming that all other constructs are made up of continuous variables) is alright. Am I correct?

In my research, I use the model to do a prediction (to see whether a path is significant) and the coefficients are unimportant. In this case, if I use PLS to test the full model (which has a binary variable as the endogenous variable) and then I perform a separate logistic regression to relate the endogenous variable to composite scores of its antecedents for double-checking the path significance. Do you think that this approach is making sense?

Thanks a lot.

Regards,
Susanna

[Singh]

Dear Friends

My endogenous LV 'Innovation' is made up three aspects as following (referring to the measurement model):

1. Process - consists of 6 binary (Yes = 1 and NO= 0) items that will give me a score of 6 if all the respondents answer yes
2. Organizational - consists of 3 binary (Yes = 1 and NO= 0) items that will give me a score of 3 if all the respondents answer yes
3. Product - consists of 3 binary (Yes = 1 and NO= 0) items that will give me a score of 3 if all the respondents answer yes

Question
1. By adding up the items in each aspect can i treat then as score i.e ratio scale.
2. When i use them as items to measure 'innovation' (LV) do i need to do any changes because aspect 1 consists of 6 items and aspect 2 & 3 consists of 3 items each? or i can just used this scores directly. Do i like need to balance the items in each aspects?

Thanks!

Keshminder

[Hengkov]

Hi,

PLS algorithm is quite difficult to run for the dependent variable is binary.
You may be able to use programs such as Stata to this problem.

Best