Structural Equation Modeling - Research Paper Example

Structural equation modeling Structural equation modeling (SEM) holds its essential focus on the examination of a set of regression equations concurrently and is thus an expansion of general linear model since As compared to multiple regression, the SEM holds an advantage of higher flexibility in area of assumptions. This benefit of SEM is seen particularly in the light of multicollinearity. Another important advantage of SEM involves the exploitation of confirmatory factor analysis. This advantage results in reduction in the measurement error by making use of multiple indicators per latent variable. In addition, the SEM holds the capability to test models with multiple dependent variables. It also holds the capability to model mediators and residuals. It is essential to consider here that since the model and data have been given prior to the assignment, only model testing, results and interpretation shall seek the attention of performance here. The data therefore shall be put in the Amos software and the model shall be tested to obtain the results. The results obtained can be utilized for the modification of the model. However, it is essential to consider here that a change can result in a change in model's meaning. It is therefore essential to consider whether or not the changes hold consistency with the theory. If the results reveal the need for change in the model then it should be done. However, since theory was not provided for the practical assignment, the changes should be performed in the light of cautious steps. The essential task is to find out as to what extent does the independent variable (reputation, skill, information exchange, power and flexibility) predict trust (independent variable). In addition, it is also required to find whether or not trust is a mediator to long-term orientation. ' It is important to note that all the variables have been presented in an oral shape in the figure above. The oral shape on the variables represents the fact that they are latent variables. Since all the variables were provided in the data set, it can be assumed that these were provided on the basis of factor scores and therefore these variables no longer remains latent variables, but become observed variables. Therefore one should conceptualize them as observable variables from this point of time. The presented model above has no covariance shown between the five independent variables. Since the task of assignment is to specify that the above model is based on covariance, there exists a dominant need to add bi-directional arrows between the five independent variables. It is important to note here that the five independent variables are exogenous because they have no prior casual variable. In addition, it is essential to understand that trust is a mediating variable and is an effect of other five mentioned exogenous variables, and it results in long-term orientation, a dependent variable. It is essential to note here that both trust and long-term orientation are endogenous variables. The model shows no residuals, so they are required to be allocated to endogenous variables. This is because the residuals are unobserved and thus have to be depicted as ovals. Normality and sample size Evaluation of absolute model fit can be done by means of probability of chi-square test. However, it is important to consider here that the probability of chi-square test if highly sensitive to both sample size and non-normality in distribution of variables. It is therefore essential to find out whether or not the variables are distributed in normal pattern and eliminate all outliers. It is important to note here that based on ordinary least squares multiple regression analysis, the rule of thumb is to have at least 15 cases per predictor. It is also important to note that since there are 229 cases there exists no problem as far as the sample size is concerned. In order to know whether or not the variables are distributed in normal patterns, it is essential to consider two figures: skewness and kurtosis. The distribution can be considered to be skewed if there former measure is higher than 1 and latter one is higher than 4. However, if non-formality is found then it is essential to identify outliers. This can be done by considering the observations that are farthest from the centroid. It is important to note here that all cases in which probability for D value is lower than 0.05 can be considered as outliers. In the process of removing the outliers, it was found that there exists 16 outliers, and the cases were as follows: 96, 91, 173, 89, 156, 138, 143, 169, 70, 83, 30, 103, 206, 162, 129, and 125. Assessment of normality (Group number 1) Variable min max skew c.r. kurtosis c.r. POWER 1.250 7.000 -.445 -2.747 -.335 -1.034 FLEX 1.000 7.000 .775 4.786 .689 2.127 FOREX 1.000 7.000 .513 3.167 .141 .437 SKILL 1.000 6.167 .473 2.922 .640 1.976 REP 1.000 6.250 .389 2.406 -.150 -.464 TRUST 1.000 6.643 .719 4.444 .485 1.498 LTO 1.000 6.333 1.041 6.429 1.457 4.502 Multivariate 12.806 8.632 It was found that there exists no kurtosis in distribution but there exists skewness in distribution for long-term orientation. In addition, it was found that there were outliers. The case 96 was deleted because the p2 measure indicated that this case was an outlier. Observation number Mahalanobis d-squared p1 p2 147 27.534 .000 .059 109 26.178 .000 .005 96 26.112 .000 .000 91 25.099 .001 .000 89 24.963 .001 .000 175 24.557 .001 .000 30 23.581 .001 .000 141 21.429 .003 .000 159 21.175 .004 .000 84 19.520 .007 .000 10 17.739 .013 .000 7 17.488 .015 .000 33 16.896 .018 .000 70 16.728 .019 .000 38 16.181 .024 .000 176 16.142 .024 .000 174 14.497 .043 .021 68 13.907 .053 .062 139 13.541 .060 .096 88 13.534 .060 .061 134 13.482 .061 .043 114 13.318 .065 .042 82 13.233 .067 .033 228 12.584 .083 .141 153 12.584 .083 .097 118 12.394 .088 .112 42 12.293 .091 .103 98 12.285 .092 .072 69 12.047 .099 .101 208 11.889 .104 .114 71 11.875 .105 .084 9 11.416 .121 .225 162 11.330 .125 .215 137 11.308 .126 .173 127 11.132 .133 .213 203 10.913 .142 .288 222 10.913 .142 .228 179 10.814 .147 .233 206 10.805 .147 .186 78 10.644 .155 .228 132 10.460 .164 .295 215 10.248 .175 .395 136 10.190 .178 .377 158 10.131 .181 .360 135 10.120 .182 .308 192 10.085 .184 .277 172 10.063 .185 .238 8 9.974 .190 .248 213 9.867 .196 .273 36 9.696 .206 .354 52 9.615 .211 .364 50 9.612 .212 .308 209 9.253 .235 .576 18 9.137 .243 .625 106 8.833 .265 .821 148 8.809 .267 .796 4 8.569 .285 .902 27 8.390 .299 .947 171 8.383 .300 .931 131 8.227 .313 .960 59 8.186 .316 .957 81 8.102 .324 .964 19 8.000 .333 .974 212 7.999 .333 .964 108 7.975 .335 .957 210 7.807 .350 .980 100 7.776 .353 .977 151 7.767 .354 .970 226 7.767 .354 .959 199 7.752 .355 .949 218 7.752 .355 .933 112 7.615 .368 .961 150 7.613 .368 .948 225 7.613 .368 .931 93 7.442 .384 .968 75 7.437 .385 .958 169 7.334 .395 .971 217 7.324 .396 .963 146 7.320 .396 .952 43 7.295 .399 .946 111 7.288 .399 .932 185 7.233 .405 .936 67 7.177 .411 .940 165 7.100 .418 .952 113 7.083 .420 .943 83 6.996 .429 .957 205 6.995 .429 .944 51 6.928 .436 .952 154 6.921 .437 .940 229 6.921 .437 .922 214 6.877 .442 .923 160 6.866 .443 .907 163 6.792 .451 .923 177 6.690 .462 .948 61 6.686 .462 .934 191 6.466 .487 .983 161 6.437 .490 .981 140 6.356 .499 .987 121 6.295 .506 .989 12 6.279 .508 .987 An exploitation of this procedure shall result in the achievement of a point, where there shall exist neither kurtosis nor skewness. Assessment of normality (Group number 1) Variable min max skew c.r. kurtosis c.r. POWER 1.250 7.000 -.442 -2.713 -.338 -1.038 FLEX 1.000 7.000 .709 4.353 .559 1.716 FOREX 1.000 7.000 .518 3.180 .207 .636 SKILL 1.000 6.167 .472 2.895 .669 2.052 REP 1.000 6.250 .420 2.578 -.063 -.193 TRUST 1.000 6.643 .671 4.118 .443 1.361 LTO 1.000 6.333 .938 5.757 1.140 3.497 Multivariate 10.344 6.926 At this point of time we shall hold the focus of our attention on cases, which have the biggest distance from centroid (i.e. outliers). In addition, the cases with p2 values lower than 0.05 shall be removed in the following manner: 1. cases with lowest p2 values 2. if there exist more number of cases with the same p2 values that have to be removed the priority is required to be projected to the ones that are above the other cases. In addition, it is important to throw light again on the last step. The last step shall be removing the last outlier, which in this case is 125. After the removal of all outliers, the measures for normality and outliers are as follows: Assessment of normality (Group number 1) Variable min max skew c.r. kurtosis c.r. POWER 1.250 7.000 -.437 -2.602 -.352 -1.050 FLEX 1.000 6.667 .567 3.380 .218 .649 FOREX 1.000 7.000 .387 2.307 .209 .624 SKILL 1.000 5.167 .255 1.522 -.009 -.027 REP 1.000 6.250 .297 1.771 -.360 -1.072 TRUST 1.000 5.686 .484 2.886 -.005 -.014 LTO 1.000 5.333 .592 3.527 -.038 -.114 Multivariate 3.692 2.400 Observations farthest from the centroid (Mahalanobis distance) (Group number 1) Observation number Mahalanobis d-squared p1 p2 32 23.250 .002 .280 10 20.757 .004 .221 7 19.092 .008 .238 37 18.437 .010 .172 130 17.194 .016 .264 85 16.744 .019 .225 107 16.343 .022 .196 161 16.164 .024 .135 67 15.422 .031 .217 80 15.012 .036 .236 69 14.676 .040 .245 68 14.539 .042 .196 92 14.369 .045 .166 212 14.285 .046 .121 142 14.285 .046 .072 126 14.161 .048 .056 111 13.970 .052 .052 193 13.317 .065 .151 9 13.251 .066 .116 177 13.098 .070 .109 41 12.947 .073 .104 191 12.758 .078 .111 198 12.756 .078 .073 200 12.433 .087 .118 128 12.095 .097 .192 127 12.037 .099 .160 147 11.876 .105 .173 76 11.866 .105 .128 164 11.829 .106 .099 150 11.683 .111 .107 188 11.470 .119 .142 206 11.470 .119 .102 159 11.419 .121 .085 120 11.394 .122 .064 100 11.304 .126 .060 8 11.250 .128 .050 184 11.134 .133 .053 35 10.788 .148 .127 137 10.775 .149 .097 18 10.677 .153 .099 51 10.622 .156 .087 79 10.525 .161 .090 4 10.183 .178 .208 49 9.893 .195 .357 194 9.491 .219 .638 94 9.471 .221 .591 88 9.278 .233 .694 195 9.276 .233 .636 157 9.138 .243 .694 27 9.118 .244 .653 124 9.071 .248 .634 66 8.959 .256 .675 140 8.943 .257 .630 210 8.943 .257 .569 202 8.860 .263 .588 199 8.794 .268 .590 58 8.777 .269 .546 197 8.769 .270 .492 190 8.662 .278 .537 42 8.566 .285 .572 19 8.543 .287 .535 153 8.540 .287 .478 73 8.349 .303 .614 105 8.309 .306 .597 102 8.144 .320 .703 136 8.115 .323 .678 60 8.100 .324 .639 162 8.082 .325 .602 209 8.040 .329 .588 139 8.040 .329 .531 12 7.908 .341 .615 148 7.834 .347 .638 104 7.802 .350 .618 143 7.786 .352 .580 213 7.786 .352 .523 43 7.740 .356 .516 50 7.714 .359 .490 106 7.646 .365 .509 151 7.530 .376 .585 114 7.518 .377 .542 176 7.496 .379 .511 81 7.470 .382 .486 149 7.464 .382 .437 170 7.416 .387 .437 65 7.268 .401 .555 131 7.163 .412 .623 74 7.119 .417 .621 64 6.948 .434 .755 156 6.909 .438 .749 208 6.852 .444 .762 138 6.852 .444 .717 189 6.836 .446 .686 207 6.836 .446 .635 16 6.776 .453 .654 3 6.708 .460 .683 181 6.698 .461 .644 13 6.674 .464 .621 61 6.665 .465 .578 99 6.623 .469 .578 167 6.588 .473 .568 Removing and adding pathways In the next step it is essential to find out whether or not in the chi-square test of absolute fit model fits the data. The probability value of the chi-square test is equal to 0.00, which represented that the null hypothesis shall be required to be removed. The alternative hypothesis states that the model fails to fit the data. The above procedure is followed by the testing of the relative fit, which means the measurement of the following three measures for analysis: GFI, AGFI and RMSEA. The first measure is required to be higher than 0.9, the second one should be higher than 0.8 and the last one should be smaller than 0.08. If this is not being present it means that some pathways are missing or are inappropriate. RMR, GFI Model RMR GFI AGFI PGFI Default model .074 .947 .702 .169 Saturated model .000 1.000 Independence model .391 .468 .291 .351 RMSEA Model RMSEA LO 90 HI 90 PCLOSE Default model .198 .148 .252 .000 Independence model .365 .340 .390 .000 Since the AGFI and RMSEA measures have failed to meet the criteria, there arises a need to analyze the critical rate in estimates. It is important to consider here that if the figures are smaller than 1.645 then it means that the pathway is not significant and therefore should be removed. In addition, in this case the pathway trust and skills fail to meet the criteria and therefore hold the reason to be removed from the model. Regression Weights: (Group number 1 - Default model) Estimate S.E. C.R. P Label TRUST Read More