Empirical studies attempt to measure variables of interest and assess the assumed relationship among these variables. The supply chain resilience model suggests relationship between indicators and constructs and among constructs shown in Figure 14. Survey instrument has been devised and used to conduct survey to collect data. The next step is to find suitable statistical method for estimation of the model for relationships among variables. The model of supply chain resili- ence presented in Figure 14 has unobserved variables with each represented by a set of measured variables. Structural equation model is a state of the art method to assess the relationship among unobserved variables and observed variables. It
is a statistical method to model, measure and test variables for such relations125. It is based on statistical methods like analysis of variance, factor analysis, multiple regression analysis and path analysis. It has been applied in psychology, man- agement, economics, sociology, political science, marketing and education since 1980s.
Structural equation modeling has the ability to model and estimate the unob- served variables on the basis of observed variables. It is also capable of capturing the causal relationship among unobserved variables where the variables adapt the roles of dependent and independent variables126. Casual relationships among var- iables are drawn from theory and structural equation modeling has the ability to test the hypothesized model of relations among observed and unobserved varia- bles. It uses number of measurements to see how well the model is represented by the observed data. However, structural equation modeling only shows the sta- tistical significance of the proposed hypothesis and therefore a statistically signif- icant model does not necessarily mean that the theory of the model is true. It is primarily related to the fit of model to data and not to be used to confirm the the- oretical basis of the model127. The hypothesized structure model rather needs to be based on sufficient knowledge and sound theoretical foundations.
Structural equation modeling can be used for theory development, theory testing and testing of causal relationship among variables. Theory development is the process of exploring relevant indicator variables of unobserved variables. The unobserved variables are also termed as constructs. The approach does not im- pose structure of relations among variables. Indicators variables are tested freely without being assigned to a construct. The significantly related indicator varia- bles are grouped together and are named under a suitable common heading as a construct. It is necessary that a construct sufficiently represents the indicators
125 Hoyle, 2012, p. 3
126 DiLalla, 2000, p. 439
because factors are used in place of the individual indicator variables for further analysis. As a result theoretical models are developed that consist of factors and the respective indicator variables. This approach is known as exploratory analy- sis. Unlike theory building, theory testing proposes a theory at first that is mod- eled and tested for soundness statistically. Constructs are derived from theory and respective determinants and specifics are developed as indicator variables. Theoretically proposed models consists of constructs along with assigned indica- tors. The indicators of constructs are tested for soundness to identify whether a construct represents the indicator variables adequately as reflective model or the indicator sufficiently captures the concept as formative model. This approach is called as confirmatory analysis. Furthermore, the constructs assume roles of in- dependent and dependent variables and develops in a causal model. Independent variable, in causal model, adapts the role of predictor variables that determine dependent variable. Dependent variable is the outcome variable. Variables, in such relations, are developed as structural equation models that are tested for cause and effect relations128. As the construct is an unobserved variable that is estimated through the shared covariance among the observed variables129. There- fore, structural equation modeling is also termed as latent variable modeling, co- variance structural modeling and causal modeling130.
Structural equation modeling is well suited statistical method to estimate the causal relationship proposed in this study. There are unobserved variables name- ly manufacturing adaptive capability, manufacturing disruption vulnerability, transportation adaptive capability, transportation disruption vulnerability, manu- facturing resilience, transportation resilience, supply chain global resilience, and supply chain risk costs. These are the constructs that are supposedly representing group of certain measurement variables called indicators. The indicators are to be tested for validity and the causal relationship among the constructs is to be exam-
128 DiLalla, 2000, p. 439
129 Hoyle, 2012, p. 3
ined. The purpose of measuring the relationship is to help describing, differenti- ating, explaining, predicting, diagnosing and deciding on problems. A theory helps either implicitly or explicitly to identify the relevant variables to be studied about their operations or relations among themselves131. In order to study the rel- evant variables numbers are assigned to aspects of objects or events according to the practices. Advanced mathematical or statistical tools are applied to measure and examine aspects and relationship among objects132. Structural equation mod- eling has been considered as appropriate tool for the measurement and evaluation of supply chain resilience model in this study.
For analysis purpose it is important to differentiate that structural equation model comprising of inner model and outer model. Inner model is the part that has con- structs and respective indicators. Outer model has the constructs that are related in a directional way having cause and effect relationship. The inner model is test- ed for validation in order to establish that the indicators and constructs are suffi- ciently related. The inner model is tested for theoretical relationships for signifi- cance.
Once structural equation model modeling is determined as an estimation method, further decisions are to be made regarding the nature of indicators as reflective or formative and selection of estimation approach as partial least square method (PLS) or covariance based (CB) structural equation modeling.