Multilevel analyses in PLS-SEM: An anchor-factorial with variation diffusion approach

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Data Analysis Perspectives Journal, 1(2), 1-6, July 2020

Multilevel analyses in PLS-SEM:

An anchor-factorial with variation diffusion approach

Ned Kock

Texas A&M International University, USA

Abstract

A multilevel analysis, in the context of structural equation modeling via partial least squares

(PLS-SEM), can be seen as an analysis in which: (a) data is collected at the individual level from

multiple groups, and (b) group membership is expected to influence data analysis results. In this

paper we illustrate such an analysis employing WarpPLS, a leading PLS-SEM software tool. The

analysis employs an anchor-factorial with variation diffusion approach.

Keywords: Multilevel Analysis; Instrumental Variable, Structural Equation Modeling; Partial

Least Squares; WarpPLS.

Introduction

A multilevel analysis employing structural equation modeling via partial least squares (PLS-

SEM) is characterized by data being collected at the individual level from multiple groups,

where group membership is expected to influence data analysis results (Kock et al, 2017);

notably path coefficients. In this paper we exemplify and discuss such an analysis utilizing

WarpPLS 7.0 (Kock, 2020a; 2020b). The analysis employs an “anchor-factorial with variation

diffusion” approach (Kock, 2020a).

Illustrative model and data

Figure 1 shows the illustrative model that is used as a basis for our discussion. It contains four

latent variables: the degree to which individuals in a company uses task-specific technologies

(TU); the education level of the individuals (ED); the problem-solving ability of the individuals

(PS); and the job performance of the individuals (JP).

We employed the Monte Carlo simulation method (Kock, 2016) to create data: 300 cases, each

case referring to an individual in a company. The existence of three companies was assumed in

the data creation process, each of the companies representing a business area: farming,

manufacturing, and technology. That is, even though the unit of analysis is the individual, the

individuals came from three separate companies.

The model incorporates three predictions, which are based on past empirical research on

related topics. The predictions are that job performance (JP) is significantly and positively

associated with technology use (TU), education level (ED), and problem-solving ability (PS).

Increases in these three variables are hypothesized to cause increases in JP.

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Data Analysis Perspectives Journal, 1(2), 1-6, July 2020

Figure 1: Illustrative model used

Note: model notation used is the same as that employed by Kock (2020b).

What characterizes a multilevel analysis?

A multilevel analysis is characterized by data being collected at the individual level from

multiple groups, where group membership is expected to influence path coefficients. Consider

our illustrative data. Each of the three companies from which data was collected consists of a

group of individuals, with the data collected at the individual level. Since each company is of a

different type (farming, manufacturing, or technology), company membership is expected to

influence analysis results.

This situation creates an endogeneity problem (Kock et al, 2017), where a hidden variable is

expected to influence an endogenous variable indirectly through its predictors. Figure 2

illustrates this problem. The hidden variable is company type (CO), which influences each of the

three predictors: TU, ED and PS. As such, variation from CO flows indirectly into the

endogenous variable JP. This effect, if strong, could significantly bias the path coefficients

associated with the links: TU > JP, ED > JP, and PS > JP.

To solve this problem, we need to create an instrumental variable that incorporates the

variation in CO that ends up in JP; via the intermediate effects on TU, ED, and PS. We then need

to control for the effect of this instrumental variable with respect to JP. That is, we will add this

instrumental variable into the model by making it point at JP.

An anchor-factorial with variation diffusion approach

In our example, the company type variable is categorical, and is stored as a data label column

using three identifiers: “FARM”, “MANU” and “TECH”. These refer respectively to farming,

manufacturing, and technology. We need to use the menu option “Explore categorical-numeric-

categorical conversion”, under the “Explore” menu options of WarpPLS, to perform a

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Data Analysis Perspectives Journal, 1(2), 1-6, July 2020

categorical-to-numeric conversion and obtain the indicator for the instrumental variable CO. For

this to be done, we first need to analyze the model without CO being added to it.

Figure 2: Multilevel model with endogeneity

The conversion mode “anchor-factorial with variation diffusion” should be employed in cases

like this, when the new instrumental variable is expected to be included in the model as a control

variable. As noted by Kock (2020a), this option is a more sophisticated alternative to perform

multilevel analyses than the group mean variable approach discussed by Kock & Hadaya (2018)

in Appendix F of their article (see also: Kock et al, 2017).

Figure 3 shows the options chosen for categorical-to-numeric conversion in our illustrative

example. The anchor latent variables are ED, TU, and PS. The correlation signs associated with

each of these anchor latent variables reflect the expected signs of their relative relationships with

the categorical variable. In this case, the signs are all set as positive, because technology use

(TU), education level (ED), and problem-solving ability (PS) are all expected to be influenced in

the same direction by company type. For example, “TECH” companies are expected to be

associated with higher scores in these three variables than “MANU” and “FARM”, and

“MANU” associated with higher scores than “FARM”. These expectations are based on theory

and prior research.

The absolute correlations with the categorical variable, shown on the screen, are meant to give

the researcher an idea of the strength of the associations among the quantified categorical

variable, the anchor variables (ED, TU, and PS), and the endogenous variable that is indirectly

affected (JP). The new instrumental variable will be created with a name like “c2n_CO”, where

the “c2n” part indicates that this new variable is the result of a categorical-to-numeric conversion

of the data label variable noted as CO.

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Data Analysis Perspectives Journal, 1(2), 1-6, July 2020

Figure 3: Categorical-to-numeric conversion

Once this new variable is created, it will be added to the dataset as a new standardized

indicator. The scores of this new variable can be inspected through the option “View or save raw

indicator data”, under the “Data” menu option. Unlike raw scores obtained from unstandardized

scales, these raw scores are created directly in standardized format. The scores can be inspected

side-by-side with the corresponding data label values; the latter can be viewed through the “View

or save data labels” option.

In our example this side-by-side inspection yields the following scores: -1.352 for “FARM”,

0.096 for “MANU”, and 1.246 for “TECH”. Since these scores are standardized, they usually

vary from -2 to 2, with a mean of 0 (zero). Therefore, we can see that the quantified categorical

variable has an intuitively appealing relationship with the underlying company type, which

ultimately influences the job performance of the individuals (JP) in the company: low for the

farming company, average for the manufacturing company, and high for the technology

company. This could be interpreted as job performance being higher in the technology company,

average in the manufacturing company, and low in the farming company.

The next step in the analysis is to add a new latent variable to the model, which we refer to as

“CO”, with the new indicator “c2n_CO” as its sole indicator. This new latent variable is added to

the model pointing at job performance (JP). We then run the analysis again. Figure 4 summarizes

the results for our illustrative model.

The results control for multilevel effects via the latent variable CO, which quantifies the

categorical variable that stores information about company type membership for the individuals

from whom data was collected. Note that the path coefficient for the link CO > JP is small (with

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Data Analysis Perspectives Journal, 1(2), 1-6, July 2020

a value of -0.06) and statistically non-significant. This means that the multilevel effects do not

have a sizeable effect on the path coefficients for the links TU > JP, ED > JP, and PS > JP.

Figure 4: Results controlling for multilevel effects

Conclusion

In this paper we illustrate a multilevel analysis with one categorical variable and one

endogenous variable. The same procedure should be conducted in models with more than one

categorical or endogenous variable, where expectations exist that each categorial variable

influences one or more endogenous variables. These expectations should be based on theory and

past research.

Acknowledgments

The author is the developer of WarpPLS, which has over 7,000 users in more than 33

countries at the time of this writing. He is grateful to those users for questions, comments, and

discussions on topics related to the use of WarpPLS.

References

Kock, N. (2016). Non-normality propagation among latent variables and indicators in PLS-SEM

simulations. Journal of Modern Applied Statistical Methods, 15(1), 299-315.

Kock, N. (2020a). WarpPLS User Manual: Version 7.0. Laredo, TX: ScriptWarp Systems.

Kock, N. (2020b). Full latent growth and its use in PLS-SEM: Testing moderating relationships.

Data Analysis Perspectives Journal, 1(1), 1-5.

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Kock, N., & Hadaya, P. (2018). Minimum sample size estimation in PLS-SEM: The inverse

square root and gamma-exponential methods. Information Systems Journal, 28(1), 227–

261.

Kock, N., Avison, D., & Malaurent, J. (2017). Positivist information systems action research:

Methodological issues. Journal of Management Information Systems, 34(3), 754-767.