ANALYSIS USING STRUCTURAL EQUATION MODELING (SEM)

Transcription

1 CHAPTER V ANALYSIS USING STRUCTURAL EQUATION MODELING (SEM) 5.1 Nature of SEM The model grows out of and serves purposes similar to multiple regression, but in a more powerful way which takes into account multiple latent independents each measured by multiple indicators, one or more latent dependents also each with multiple indicators, the modeling of mediators as both causes and effects, modeling of interactions, nonlinearities, correlated independents, measurement error, and correlated error terms. SEM is a very powerful multivariate analysis deals with samples in which for each unit examined there are observations on two or more stochastically related measurements. 5.2 Earlier Studies on SEM Bollen (1990) and Bollen & Ting (1993, 2000) observed that all modelimplied tetrads equal 0 (a "vanishing tetrad") in a fully reflective model (a model with fully reflects the data). They proposed CTA as a means of distinguishing between causal and effect indicators in SEM models. A Study on Perceived Risk in Investment with reference to Investor of Stocks, Mutual Funds& ULIPs 216

2 Jaccard and Wan (1996: 80) state that regression may be preferred to structural equation modeling when there are substantial departures from the SEM assumptions of multivariate normality of the indicators and/or small sample sizes, and when measurement error is less of a concern because the measures have high reliability. Discussed by Kline (1998a: ) for the case of two-points-in-time longitudinal data, the researcher repeats the structural relationship twice in the same model, with the second set being the indicators and latent variables at time. 5.3 Analysis of Investment Risk Perception Factors using SEM The SEM approach was adopted in the data analysis to presents the results of the revised model with standardized path coefficients between constructs and indicated that the endogenous variables, as explained with the three factor in Table 5.1. The higher loading components selected for the table extracted from rotated component matrix solutions and sorted Varimax solutions. Those three investment risk perception factors (measurement model) then analyzed through assessment criterion such as CMIN, GFI, NFI, RMR, AGFI and IFI in SEM approach. A Study on Perceived Risk in Investment with reference to Investor of Stocks, Mutual Funds& ULIPs 217

3 Table 5.1 Higher loading Components adopted for Structural Equation Modeling with Identified Factor names Factor Variables Components Factor 1 Facing Investment Risk Factor 2 Observing Investment Factor 3 Perceiving Investment Protection C25 C3 C17 C21 C24 C7 C19 C9 C14 C8 C22 C5 C11 C16 Risk on investment will go down as well as up Facing risk voluntarily Risk of value of money may not rise Investor spend time in monitoring the investment Risk of investment might fall below expectation Risk of losing the money Differences in the risk of other different products Losses observed by individual investor Observe charges levied by provider Understand the performance of investment Access information about product before purchase Risk in investment known to experts Easy to retrieve money if needed Investment Provider protect investments C2 *Extracted from rotated factor higher loadings Consequences of owning the product A Study on Perceived Risk in Investment with reference to Investor of Stocks, Mutual Funds& ULIPs 218

4 5.4 Validities of Convergent, Discriminant, Content and Composite Reliability Table 5.2 and Table 5.3 shows the calculated values of Composite Reliability and AVE value to support Convergent Validity, Discriminant Validity and Content Validity of the measurement model. According to Fornell & Larcker (1981), average variance extracted (AVE) should be more than the correlation squared of the two constructs to support discriminant validity Table 5.2 Convergent Validity and Composite Reliability for the extracted Factors Convergent Validity Observed Variables Factor Loadings Reliability AVE Composite Reliability Facing Investment Risk Observing Investment Perceiving Investment Protection *Computed Values Composite reliability is also used to check the internal consistency, which should be greater than the benchmark of 0.7 and AVE should be greater than 0.5 to be considered adequate (Fornell and Larcker 1981). Since the calculated value of composite reliability is and the AVE value of which shows an adequate result for the present model. A Study on Perceived Risk in Investment with reference to Investor of Stocks, Mutual Funds& ULIPs 219

5 Table 5.3 Discriminant and Content Validity for the model Indicator Observed Value Fit Indices AVE Discriminant Validity > Content Validity >= *Computed Values To evaluate Discriminant validity, the average variance extracted (AVE) is used. All constructs have an AVE of at least 0.5 (Fornell and Larcker 1981). It is clear from the above table the observed value for Discriminant is which shows the adequate validity of the model. The fit value for content should be greater than 0.7 also established by the model. 5.5 Goodness of Fit Comparison between Default and Independent Model using Standardized Solutions The goodness of fit of a statistical model describes how well it fits a set of observations. Here the measures of goodness of fit typically summarize the discrepancy between observed values and the values expected under the investment risk perception model in question. The fig 5.1 shows the standardized solutions of the model. A Study on Perceived Risk in Investment with reference to Investor of Stocks, Mutual Funds& ULIPs 220

6 Figure 5.1 Model Showing Standardized Solution of Investment Risk Perception Components Components in the below model are extracted from the higher factor loadings mentioned in Table 5.1. The components depending three factors were identified and named as, Facing Investment Risk as Factor 1, Observing Investment as Factor 2 and Perceiving Investment Protection as Factor F1 F2 F3.93 C C C C21.62 C24.12 C C C C14.18 C8.66 C C C C16.07 C2 e1 e2 e3 e4 e5 e6 e7 e8 e9 e10 e11 e12 e13 e14 e15 Standardized solution computed through Amos, output A Study on Perceived Risk in Investment with reference to Investor of Stocks, Mutual Funds& ULIPs 221

7 The Figure 5.1 shows the standardized solution for the variables under risk perception in investment from investor point of view computed through structural equation modeling. The result values were interpreted and exhibit in Table 5.4. Table 5.4 Goodness of Fit Best Fit Indices from the Model Index Default Model Independent Model CMIN GFI CFI NFI RMR AGFI IFI *Computed through Amos, output CMIN: (called Chi square in Amos): Smaller chi-square values indicate better fit. Ideally, the chi-square would be non-significant indicating no significant discrepancy between model and data. Also, slight discrepancies between model and the data may result in a statistically significant chi square. It A Study on Perceived Risk in Investment with reference to Investor of Stocks, Mutual Funds& ULIPs 222

8 is clear from the above table the value of CMIN is less than 5 which shows better fit of the investment risk perception model. GFI: The GFI (goodness-of-fit index) was devised by Jöreskog and Sörbom (1984). The GFI indicates the proportion of the observed covariance explained by the model covariance. GFI is always less than or equal to 1. GFI = 1 indicates a perfect fit. It is clear from the above table the value of GFI is less than 1 which denotes the best fit of the risk perception variables model. CFI: The CFI (comparative fit index) is directly based on the non-centrality measure. The CFI is also known as the Bentler Comparative Fit Index. CFI is not too sensitive to sample size (Fan, Thompson, and Wang, 1999). It is clear from the above table the value of CFI is greater than 0.9 which shows good fit of the model. NFI: The NFI (normed fit index) was developed as an alternative to CFI, but one which did not require making chi-square assumptions. It varies from 0 to 1, with 1 = perfect fit. It is clear from the above table the value of NFI is equal to one which proves the fit of the model. NFI reflects the proportion by which the researcher's model improves fit compared to the null model (random variables). NFI is also similar to preceding model fit indices, telling how big discrepancy A Study on Perceived Risk in Investment with reference to Investor of Stocks, Mutual Funds& ULIPs 223

9 there is between the model being evaluated (default model) and the baseline model (terribly fitting independence model ). RMR: The RMR (root mean square residual) is an absolute measure of fit and here is defined as the standardized difference between the observed and predicted correlation. A value less than 0.8 is generally considered a good fit (Hu and Bentler, 1999). It is clear from the above table the Value of RMR is which is less than 0.8 shows the best fit of risk perception model. AGFI: The AGFI (adjusted goodness of fit index) is a sensible fit index in association with the sample size (Sharma, mukherjee and dilon, 2005). The norms of AGFI should be between 0 to 1 and it was proved by the above table shows the model fit. IFI: The IFI (Incremental Fit Index) by convention, IFI should be equal to or greater than 0.90 to accept the model. To compute the IFI, first the difference between the chi square of the independence model in which variables are uncorrelated and the chi-square of the target model is calculated. Next, the difference between the chi-square of the target model and the degrees of freedom for the target model is calculated. The ratio of these values represents the IFI. It is clear from the above table the value of IFI is 1 which shows the acceptance of risk perception model. A Study on Perceived Risk in Investment with reference to Investor of Stocks, Mutual Funds& ULIPs 224

10 Table 5.5 Path Co-efficient in Extracted Model Un- Hypothesis Relationship between Variables standardized Coefficient Estimate S.E Standardized Coefficient(β) C.R p value H1 F1 F H2 F2 F H3 F3 F Showing Covariance for different factors Source: Amos 16.0 version, output Notes: S.E-Standard error, C.R-Critical ratio, P- Estimated probability It is clear from the table 5.5 shows the hypothetical variables, standardized coefficient with p values. Standardized values for the variables facing investment risk (f1) and observing investment (f2) is (p>0.05) which shows those relationship were not significant and not supported each other. The value for observing investment (f2) and perceiving investment protection (f3) is (p<0.05) which shows those relationship is significant and for the variables perceiving investment protection (f3) and facing investment risk (f1) the value is (p<0.05) which shows those relationship was significant with each other. A Study on Perceived Risk in Investment with reference to Investor of Stocks, Mutual Funds& ULIPs 225

11 5.6 Model Fit Fitness of the Risk Perception Components Table 5.6 Model Result - Default Result(Default Model) Minimum was achieved Probability level =.000 *Amos result Fit refers to the ability of a model to reproduce the data (i.e., usually the variance-covariance matrix). From the table 5.6 the model result computed through Amos version shows the minimum was achieved with the probability level of elucidate the perfect fit of the risk perception s adopted by the SEM. A good-fitting model is one that is reasonably consistent with the data and so does not require respecification. Also a good-fitting measurement model is required before interpreting the causal paths of the structural model. It should be noted that a good-fitting model is not necessarily a valid model. For instance, a model all of whose parameters are zero is of a "good-fitting" model. Parameter estimates must be carefully examined to determine if one has a good model as well as a good-fitting model. A Study on Perceived Risk in Investment with reference to Investor of Stocks, Mutual Funds& ULIPs 226