Chapter -7 STRUCTURAL EQUATION MODELLING

Transcription

1 Chapter -7 STRUCTURAL EQUATION MODELLING

2 STRUCTURAL EQUATION MODELLING Chapter Introduction There is an increasing trend in usage of structural equation modelling (SEM) in management research. Conceptual and methodological basis of using SEM is not new. Popularity of SEM has mainly grown due to the availability of software packages like LISREL, AMOS, and EQS. Structural equation models aid in assessing relationships between variables and are based on the principles of multiple regression and factor analysis (Bacon & Bacon, 1997). Problems of multicollinearity and unreliability of data are duly addressed by SEM application. SEMs analyses mostly involve two types of variables (observed and latent). Observed variables are those variables which have a numeric response corresponding to a given rating scale format (e.g., height). Observed variables in SEMs are usually continuous. On the other hand, latent variables are those variables which can not be directly observed and in theoretical terms, can have infinite number of values. For examples, some of the latent variables/constructs in organizational behavior include job satisfaction, commitment, and organizational citizenship behaviors (OCBs) and others. There are varieties of SEMs however, majority of SEMs are based on linear relationships between variables. SEMs use logic similar to regression and factor analysis in assessing relationships between variables. In SEMs variables are expressed in terms of weighted linear combinations of the other variables under examination. In SEMs there are endogenous and exogenous variables. Endogenous variables are those variables that depend on other variables and are also referred to as dependent variables. Exogenous variables refer to those variables which do not depend on other variables and are also called independent variables in the model. SEMs are also called simultaneous equation models. SEMs are multivariate in nature as they involve multi-equation regression models (Fox, 2002). It is pertinent to note that in SEMs, a response variable in one regression equation may be treated as predictor variable in another equation. Further, in SEMs there could be reciprocal relationship between variables (either direct or indirect) through other variable in the model.

3 Furthermore, it is relevant to note that SEM approach has advantages over the traditional regression method. As SEMs include latent variable approach it helps in minimizing measurement error. This approach aids in accurate estimation of the relationship between variables in the SEM models. However, regression uses manifest variable models that are imperfectly measured, thus is susceptible to the risk of overestimating the relationship between variables (Byrne, 1994; Hoyle, 1995). As discussed in SEM, one dependent variable in one equation can be an independent variable in another equation. This reciprocal role helps SEM to provide causal explanation between variables (Gunzler et al., 2013). In general SEMs are made up of two components (measurement model and structural model). The portion of SEM that estimates relationship between latent and observed variables it is called measurement model. Whereas, the portion of SEM that involves relationship assessment between endogenous and exogenous variables, in terms of their direction and strength, it is referred as the structural model. Measurement model component generally uses the maximum likelihood method in estimating variables. The structural equation model parameters are estimated through methods like unweighted least squares (ULS), weighted least squares (WLS), and generalized least squares (GLS). 7.2 Model Development As discussed in chapter 1, one of the primary objectives of this research is to examine the relationship of PsyCap (predictor variable) with performance, job satisfaction, stress symptoms, and job insecurity (dependent variables). The current chapter s aim is to test the conceptual model with help of SEM procedure. Conceptual model was developed by reviewing relevant literature. Theoretical rationale in support of the relationship between the predictor variable and the dependent variables are described in the literature review chapter. The proposed model was tested with the help of data collected from 312 respondents belonging to three private life insurance companies. Detailed description on study design, sample selection, sample description, data collection procedure, and the measures used are provided in chapter

4 7.3 Preconditions for SEM Analysis Before proceeding for SEM analysis it is important to assess the multivariate data normality, theoretical rationale of the model, and examine the covariance input matrix (Hair et al., 2006). Following sub-sections discuss on how the said conditions of SEM analysis were satisfied for testing the conceptual model Multivariate Data Normality Bollen (1989) and Kaplan (2000) suggest that before undertaking SEM analysis, it is imperative to check multivariate normality of data. Table 7.1 provides an assessment of the multivariate data normality. It can be observed that, all study variables are normally distributed as skewness values are ranging from to and kurtosis values are ranging from to These skewness and kurtosis values indicate that the sample data satisfy the assumption of multivariate data normality. Table 7.1 Assessment of the Data Normality Variables Minimum Maximum Skewness Kurtosis Statistic Statistic Statistic Std. Error Statistic Std. Error Self-Efficacy (1-6 scale) Hope (1-6 scale) Optimism (1-6 scale) Resilience (1-6 scale) Performance ( 1-9 scale) Job Satisfaction( 1-6 scale) Stress Symptoms (0-3 scale) Job Insecurity (1-5 scale) Theoretical Support: An Essential Condition for Model Building It is important to note that no model should be developed for the use in SEM without some underlying theory (Hair et al., 2006). In this research the hypothesized measurement model (PsyCap as a second higher order construct) is supported by Hobfoll s (2002) psychological resource theory, multiple-component resource theories of 136

5 Antonovsky (1979) and Kobasa (1979).Further, Fredrickson s (1998, 2001) broaden-andbuild theory of positivity also supports the higher order structure of PsyCap. Detailed discussion on these theoretical foundations of PsyCap can be found in the literature review chapter. Similarly, theoretical support for the structural component of the model (relationship of PsyCap with performance, job satisfaction, stress symptoms, and job insecurity) has been discussed in the literature review chapter. Therefore, both the measurement and structural components of the proposed model are supported with firm theoretical foundation Covariance Input Matrix Bollen (1989) and Kline (1998) opine that covariance matrix has more advantage than correlation matrix in SEM. It helps to find out the covariances of a variable with itself. Table 7.2 shows the covariance matrix of the study variables. Table 7.2 Covariance Matrix Variable Self-efficacy Hope Optimism Resiliency Performance Job Satisfaction Stress Symptoms Job Insecurity Note: n = Model Description In the proposed structural equation model, the observed variables are the 4 subconstructs of PsyCap (self-efficacy, hope, optimism and resilience). Each of the subconstructs is measured by 6 items. In structural model PsyCap is the exogenous latent second order construct and is derived from the four sub-constructs namely self-efficacy, 137

6 hope, optimism, and resilience. Evidence of PsyCap being a latent second order construct is found in study conducted by Luthans et al. (2007). Further, manager-rated performance, job satisfaction, stress symptoms, and job insecurity are the endogenous constructs in this model. Manager-rated performance is measured by five-item, job satisfaction is measured by three-item, stress symptoms by seven-item, and job insecurity by four-item. These endogenous constructs are well established in organizational behavior literature and have demonstrated adequate psychometric validities. For example, evidence towards validity of job satisfaction can be found in Hackman and Oldham (1980), manager-rated performance in Heilman et al. (1992), stress symptoms in Lovibond and Lovibond (1995), job insecurity in Vander et al. (2014).The hypothesized structural model aims to examine the relationship of PsyCap with performance, job satisfaction, job insecurity, and stress symptoms. After identifying all the unobserved latent variables and observed variables, path diagrams were drawn and analyzed. As evident in Figure 7.1, the arrows show dependencies in the models. Single headed arrows reflect the regression weights. Single headed arrow starting from PsyCap towards performance indicates a significant positive relationship of PsyCap with performance. Similarly, single headed arrow coming from PsyCap towards job satisfaction indicates a significant positive relationship of PsyCap with job satisfaction. In contrast, single headed arrow beginning from PsyCap towards job insecurity, marked with a (-) sign, indicates a significant negative relationship of PsyCap with job insecurity. Likewise, single headed arrow marked with a (-) sign originating from PsyCap towards stress symptoms indicates a significant negative relationship of PsyCap with stress symptoms. 138

7 e1 Hope Performance e5 e2 Self-efficacy PsyCap Job Satisfaction e6.47 e3 e4 Resilience Optimism Job Insecurity Stress Symptoms e7 e8.86 Figure 7.1 Structural Equatation Model 7.5 Model Results and Test of Goodness of Fit This section of the chapter reports findings related to the mode testing. First subsection describes the findings related to the measurement model and the second sub-section describes the findings concerning to the structural model Measurement Model Test Results Chi-square = ** (DF = 18) ** p < 0.01 The measurement model specifies the relations between latent (unobserved) and indicator (observed) variables. The measurement model also represents confirmatory factor analysis (CFA). As discussed earlier the PsyCap construct has four dimensions (hope, selfefficacy, resilience, and optimism) and each dimension is measured by 6 items. It was found that each of the 6 items loadings for their respective dimensions (e.g., hope, selfefficacy, resilience, and optimism) were significant (p<.01).furthermore, each of the dimensions loaded significantly high on the second order latent factor PsyCap with very high statistical significance ( p<.01). As seen in Table 7.3 following CFA results were obtained (Chi-square = , DF=2 p<.01); (CFI=0.996); (RMSEA=0.078); (NFI=0.995); (RFI=0.977); (IFI=0.996); (TLI=0.979). These model fit indices suggest satisfactory overall model fit as per Hair et al. (2006). These model fit indices also confirm external validity of the four dimensional structure of PsyCap construct in Indian context 139

8 and also support the results of the previous studies conducted in Western countries (e.g., Luthans et al.,2007; Luthans et al.,2010; Peterson et al.,2011). Table 7.3 Psychological Capital Measurement Model Fit Values Fit Indices Fit Value Chi-square ** (DF= 2) CFI RMSEA NFI RFI IFI TLI Notes: **p < Structural Model Test Results The structural model refers to relationship among exogenous and endogenous variables. In SEM, these variables are also called constructs. As seen in Figure 7.1 PsyCap is the exogenous construct and performance, job satisfaction, stress symptoms, and job insecurity are the endogenous constructs. In the measurement model discussion, it was found that PsyCap emerged as the second order latent construct. Now let us discuss on the structural component of the model. The hypothesized relationships were tested through structural equation modelling using AMOS (v.4). As seen in Table 7.4 there is existence of a positive and significant relationship between PsyCap and performance with path estimate (0.218, p <.01). Similarly, it can be observed from Table 7.4 that there a positive and significant relationship between PsyCap and job satisfaction with path estimate (0.230, p <.01). Further, Figure 7.1 also depicts that there is significant positive relationship of PsyCap with performance and job satisfaction. These findings further support H 1. It can be seen in Table 7.4 there is a significant negative relationship between PsyCap and job insecurity with path estimate (-.059, p <.01). In the same way, it can be observed in Table 7.4 that there is a significant negative relationship between PsyCap and stress symptoms having a path estimate (-.042, p <.01). Moreover, Figure 7.1 also shows 140

9 that there is significant negative relationship of PsyCap with job insecurity and stress symptoms. These significant negative relationships of PsyCap with stress symptoms and job insecurity provide supportive evidence towards H 6. As seen in Table 7.5, the fit indices of the structural model are as follows: (Chisquare= , DF=18, p <.01); (CFI=0.990); (NFI=0.098); (RMSEA= 0.095); (RFI=0.097); (IFI=0.990); (TLI=0.981). These model fit indices support an overall good fit with the data as per Hair et al. (2006). Hence, the model is valid. Table 7.4 Path Estimates of the Structural Model Hypothesized Paths Direction Path Estimates PsyCap Performance ** PsyCap Job Satisfaction ** PsyCap Job Insecurity ** PsyCap Stress Symptoms ** Notes: PsyCap = Psychological Capital; Unstandardized Path Estimates. **p <.01 Fit Indices Table 7.5 Structural Models Fit Values Fit Value Chi-square ** (DF= 18) CFI RMSEA NFI RFI IFI TLI Notes: **p <

10 7.6 Summary This chapter discussed on the usage of structural equation modelling (SEM) to measure PsyCap and also examined the relationship of PsyCap with performance, job satisfaction, job insecurity and stress symptoms. In the development of this model, PsyCap was treated as the exogenous second order latent construct and was derived from the 4 subconstructs namely self-efficacy, hope, optimism, and resilience. Manager-rated performance, job satisfaction, stress symptoms, and job insecurity were the endogenous constructs in this model. Firstly, factor structure of PsyCap was found in the measurement model and thereafter, structural model depicting the relationship of PsyCap with performance, job satisfaction, job insecurity, and stress symptoms, were derived through appropriate path diagrams with firm theoretical linkages. All the test measures of goodness of fit were obtained through AMOS (v.4) software. The structural model identified positive relationship of PsyCap with performance and job satisfaction, and on the other hand, it was found that PsyCap had significant negative relationship with job insecurity and stress symptoms. Finally, overall model fit indices support a good fit with the data and the conceptual model was validated. References [1] Antonovsky, A. (1979). Health, stress, and coping. San Francisco: Jossey-Bass. [2] Bollen, K.A. (1989). Structural Equations with Latent Variables, New York, NY: Wiley. [3] Byrne, B. M. (1994). Structural equation modelling with EQS and EQS/Windows: Basic concepts, applications, and programming. Thousand Oaks, CA: Sage Publications. [4] Bacon, L. D., & Bacon, L. (1997). Using Amos for structural equation modelling in market research. U.S.A, Lynd Bacon & Associates Limited and SPSS Incorporated. [5] Fredrickson, B. L. (1998).What good are positive emotions? Review of General Psychology, 2(3),

11 [6] Fredrickson, B. L. (2001). The role of positive emotions in positive psychology: The broaden and-build theory of positive emotions. American Psychologist, 56(3), [7] Fox, J. (2002). Structural Equation Models, Appendix to an R and S-PLUS Companion to Applied Regression Retrieved from [8] Gunzler, D., Chen, T., Wu, P., & Zhang, H. (2013). Introduction to mediation analysis with structural equation modeling. Shanghai Archives of Psychiatry,25(6), [9] Hackman, J.R., & Oldham, G.R. (1980). Work redesign. Reading, MA: Addison- Wesley. [10] Hair, J. F., Black, W. C., Babin, B. J., Anderson, R. E., & Tatham, R. L.(2006).Multivariate data analysis. New Delhi, Pearson Prentice Hall. [11] Heilman, M. E., Block, C. J., & Lucas, J. A. (1992). Presumed incompetent? Stigmatization and affirmative action efforts. Journal of Applied Psychology,77(4), [12] Hobfoll, S. (2002).Social and psychological resources and adaptation. Review of General Psychology, 6(4), [13] Hoyle, R. H. (1995). Structural equation modeling: Concepts, issues, and application. Thousand Oaks, CA: Sage Publications. [14] Kaplan, D. (2000). Structural Equation Modeling, Thousand Oaks, CA: Sage. [15] Kobasa, S. (1979). Stressful life events, personality and health: An inquiry into hardiness. Journal of Personality and Social Psychology, 37(1), [16] Kline, R.B. (1998). Principles and Practice of Structural Equation Modeling, New York, NY: Guilford Press. [17] Lovibond, P. F., & Lovibond, S. H. (1995). The structure of negative emotional stress: Comparison of the Depression Anxiety Stress Scales (DASS) with the Beck 143

12 depression and anxiety inventories. Behaviour, Research and Therapy, 33(3), [18] Luthans, F., Avolio, B. J., Avey, J. B., & Norman, S. M. (2007).Positive psychological capital: Measurement and relationship with performance and satisfaction. Personnel Psychology, 60(3), [19] Luthans, F., Avey, J. B., Avolio, B. J., & Peterson, S. J. (2010). The development and resulting performance impact of positive psychological capital. Human Resource Development Quarterly, 21(1), [20] Peterson, S. J., Luthans, F., Avolio, B. J., Walumbwa, F. O., & Zheng, Z. (2011). Psychological capital and employee performance: A latent growth modeling approach. Personnel Psychology, 64(2), [21] Vander Elst, T., De Witte, H., & De Cuyper, N. (2014). The Job Insecurity Scale: A psychometric evaluation across five European countries. European Journal of Work and Organizational Psychology, 23(3),