Selection of SEM Methodology

Partial least square (PLS) is considered as a suitable method for research in busi- ness studies. PLS is a regression based approach and has fewer identification is- sues besides it works well both with smaller and larger samples. It also estimates both reflective and formative indicators152_{. On the other hand, covariance based} (CB) structural modeling approach does not explain variance and also does not focus on prediction. CB estimates the parameters of a model such that the dis- crepancy between the sample covariance matrix and the implied covariance ma- trix is minimal. The choice of either PLS-SEM or CB-SEM depends on a number of considerations like purpose of research, nature of indicators, nature of inner model, data characteristics, sample size, and purpose of model evaluation153_. These considerations are used alternatively to select the estimation method.

4.6.1 Purpose of Research

The first criteria is to consider the purpose of research as either theory building or theory testing. For theory testing or confirmation CB method is preferred. However in case where theory confirmation is not the primary concern and as- sessing prediction of a causal model is the major objective, PLS is the preferred method. The reason is that CB does not focus on prediction as mentioned earli- er154_{. The supply chain resilience model is primarily concerned with the nature of} predictors that determine the resilience of processes and global resilience of sup- ply chains. Theory testing or confirmation is a secondary purpose that has been worked out in the study. PLS is considered as a preferred choice for the study in the light of first criteria for choosing between the two methodologies, for the purpose of testing causal model for predictability.

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4.6.2 Nature of Indicators

The second recommendation is that in case of formative indicators use PLS methodology. With CB methodology, formative indicators can also be estimated but it asks for relatively complex and stringent specification rules155_{. As dis-} cussed in the preceding section, all the indicators are formative in nature, there- fore PLS is considered appropriate for estimation.

4.6.3 Nature of Inner model

It is also suggested that PLS is suitable estimation method in case the inner mod- el is having many constructs and many indicators156_{. Supply chain resilience} model has twenty three indicators and eight construct that is pretty complex. In this context, PLS is considered appropriate for estimation of the model.

4.6.4 Data Characteristics

Covariance based structural equation modeling assumes normality of data, mini- mum sample size rule, and other characteristics of data. Normality assumes that the data is evenly distributed and shows a normal curve shape, without skewness and kurtosis. Normality shows that data is evenly distributed with normal curve. Skewness is deviation from normality with lack of symmetry where the most of the data is clustered around a point. Kurtosis is also deviation from normality and the data is grouped at an end of the curve. Data with normality, skewness, or kur- tosis issues causes problem in analysis. The sample size rule needs that the num- ber of observations are required to be equal to ten times of the number of varia- bles in the model. Supply chain resilience model with around thirty variables will need at least 300 observations whereas the sample size of data collected in the survey is short of 150 that is far below. PLS assumption for distribution of data and sample size are different than CB method. The sample size required by PLS

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is ten times of the largest number of formative indicators or ten times of the larg- est number of structural paths directed at a construct in model157_{. The largest} number of formative indicators in supply chain resilience model is five for manu- facturing disruption vulnerability, manufacturing adaptive capability or transpor- tation disruption vulnerability constructs. The strict data requirements for covari- ance based method and the fact that the sample size is small, PLS method for model estimation is used.

4.6.5 Purpose of Model Evaluation

The purpose of evaluation is to assess the relationship among constructs for pre- diction and not the global goodness-of-fit or test of invariance of outer model158_. Supply chain resilience model is interested to assess the relationship between indicators and constructs and among constructs for predictability. In this case, PLS method is considered appropriate for estimation of the model.

Looking in to the goal of research, nature of indicators, characteristics of data, sample size, and purpose of model evaluation, PLS has been identified as pre- ferred method for the analysis of supply chain resilience. The following section presents the evaluation of outer model by assuming the indicators as formative and using PLS method for estimation of the model.

4.7 Summary

The research paradigm in this study is logical empiricism that adapts quantitative method to analyze the research question. In deductive approach, theory is tested through hypothesis with the help of empirical data collected from the population of interest. The design of research is explanatory to explain causal relationship among constructs. The research strategy is survey carried over countries and

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supply chain firms. The study is cross sectional for which data was collected through structured questionnaire, filled in person, at a specific point in time. The framework is to be tested for conformity across countries for finding the role of locational factors in supply chain resilience. PLS SEM methodology has been selected for testing of the extended model of supply chain resilience. The next chapter presents the setting for international garments supply chain spread over Germany, Pakistan and Turkey.