Quantitative Data Analysis and Partial least square Structural Equation Modelling (PLS-SEM)

6 min readJun 19, 2021

In this article, I will be showing how we can measure the behavior of a latent variable in data analysis. A latent variable is not directly observed but is rather inferred from other variables that are observed. And this article is based on my own research and self-study, I highly appreciate your feedback and I consider it as a learning opportunity for me.

Partial Least Square Structural Equation Modelling (PLS-SEM) is the SEM technique mostly used in IS research, PLS does not require a larger sample size, and when the research area is comparatively new. (Kante, et al, 2018)

Reasons for choosing PLS-SEM

Small sample sizes (However many researchers argue that the minimum sample size should be 200)
Exploratory research objective/ predictive purposes
Non normality
Analyze formative and reflective constructs
Number of interaction terms
Mediated Models

In order to analyze the moderating effect of a latent variable, we can use the SmartPLS3 software. For instance, Let’s build the hypothesis as Gamification has an effect on the relationship between Employee rewarding and employee performance.

Conceptual Framework

Hypothesis

We will have three hypotheses to test such as,

H1: Gamification has a moderating effect on the relationship between Employee rewarding and Employee performance

H2: Gamification has a positive effect on the Employee’s Performance

H3: Employee rewarding has a positive effect on employee performance.

According to the previous similar research, there are two types of measurement models named, formative and reflective used in the partial least square structural equation model. (Kante, et al., 2018) . And in the first stage, it will be tested the fitness of the measurement model known as the outer model. Then in the second stage, the structural model also known as the inner model will be evaluated with the significance of path coefficients.

Outer model fit evaluation

In the partial least square method, when evaluating the reliability of the outer model, the researcher has to determine the outer model is reflective or informative. This specifies the relationship between the latent constructs and the observed variables. In the reflective model, changes in the construct are reflected in shifts in all of its indicators, and the direction of causality is from the construct to the indicators. In Formative models, the direction of causality is from the indicators to the construct, and the weights of formative indicators represent the importance of each indicator in explaining the variance of the construct. In the diagram below I have shown how a reflective measurement model will look like for my hypothesis testing.

To test the fitness of the Reflective outer model, we can use the internal consistency reliability, indicator reliability, convergent validity, and discriminant validity. Let’s look at how to validate the test results.

Internal consistency Reliability

The internal consistency reliability can be assessed using Cronbach’s alpha which calculates the extent to which MVs load simultaneously when the LV increases. (Urbach & Ahlemann, 2010). If the alpha value of the variables is above 0.8 and scales are good for the internal consistency reliability test.

Composite reliability

According to the gathered information by Kante et al (2018) (Urbach & Ahlemann, 2010) composite reliability is attempting to measure the sum of latent variable’s factor loading relative to the sum of the factor loadings plus error variance. This leads to values between 0 (completely unreliable) and 1 (perfectly reliable). Values should be more than 0.6 and all variables in the study should have higher values than the threshold which indicating sufficient reliability.

Indicator reliability

An indicator loading test carried out to check the contribution of the indicators to the definition of its latent variable. (Urbach & Ahlemann, 2010). The threshold value should be more than 0.600.

Convergent validity

The average variance extracted should be > 0.5 and it involves the degree to which individual items reflecting construct coverage in comparison to items measuring different constructs (Bartelt & Dennis, 2014).

Average variance Extracted (AVE)

The convergent validity of the reflective construct is analyzed with the average communality or AVE (Average variance extracted). It should be higher than 0.5 and thus are appropriate.

Heterotrait Menotrait Ration (HTMT)

It is the correlations of indicators measuring different phenomena which are the correlation of indicators within the same construct. (Kante, et al., 2018). With the use of Smart PLS3 software, the Heterotrait Menotrait Ration (HTMT ) rates can be calculated, and the threshold value should be less than 1 (Garson, 2016).

Inner model fit evaluation

To test the fitness of the Inner model or reject or approve the hypothesis, we can use the Coefficient of Determination (R2), predictive relevance (Q2), Standardized Root Mean Square Residual (SRMR), and path coefficients (Kante, et al., 2018). Let’s look at each of the validity types.

Predictive relevance (Q2)

Blindfolding can be used to assess the predictive strength of the structural equation model (Ringle, et al., 2018) Figure above shows the criteria to measure the predictive relevance of the model. Here we can systematically assume that a certain number of cases are missing from the sample, the model parameters are estimated and used to predict the omitted values. Q2 measures the extent to which this prediction is successful.

R2 — Coefficient of Determination

R2 the measure which is used to calculate the proportion of the variance of the dependent variable which is Employee performance in this case and its means that is explained by the independent variables such as employee rewarding and gamification. The R square value should be greater than 0.100. (Ringle, et al., 2018). Values approximately, 0.670 are substantial and values around 0.333 average and values of 0.190 are weak. (Ringle, et al., 2018) . The path coefficient significance test and p-value should be done using the bootstrapping technique. Critical t-values for a two-tailed test is 1.65 (significance level = 10 percent), 1.96 (significance level = 5 percent), and 2.58 (significance level = 1 percent).

Standardized root mean square residual (SRMR)

Eventually, the model fitness should be assessed using SRMR and a model has a good fit when this value is less than 0.100.

In conclusion, based on the model evaluation results, we can determine and report the results of these validity criteria. Then the PLS-SEM analysis provides important insights into the strength and signiﬁcance of the hypothesized model relationships.

Cheers!

Reference

Bartelt, V. & Dennis, A., 2014. Nature and Nurture: The Impact of Automaticity and the Structuration of Communication on Virtual Team Behavior and Performance. Psychology, Computer Science, 38(2), p. 521–538.

Garson, G. D., 2016. Partial Least Squares: Regression & Structural Equation Models. s.l.:Statistical Associates Publishing.

Kante, M., Chepken, C. & Oboko, . R., 2018. Partial Least Square Structural Equation Modelling’ use in Information Systems: An Updated Guideline of Practices in Exploratory Settings. Kabarak Journal of Research & Innovation, Volume 6.

Ludviga, I. & Ērgle, D., 2018. USE OF GAMIFICATION IN HUMAN RESOURCE MANAGEMENT: IMPACT ON ENGAGEMENT AND SATISFACTION. Business and Management 2018.

Ringle, C. M., Sarstedt, M., Mitchell, R. & P. Gudergan, S., 2018. Partial least squares structural equation modeling in HRM. THE INTERNATIONAL JOURNAL OF HUMAN RESOURCE MANAGEMENT,

Urbach, N. & Ahlemann, F., 2010. Structural Equation Modeling In Information Systems Research Using Partial Least Squares. Journal Of Information Technology Theory And Application, 11(2), p. 5–40.