Structural Equation Modeling (SEM) PDF

Structural Equation Modeling (SEM): A Detailed Guide Structural Equation Modeling (SEM) is a comprehensive statistical approach used to test hypotheses about relationships among observed and latent variables. It combines factor analysis and multiple regression analysis, allowing researchers to mode...

Structural Equation Modeling (SEM): A Detailed Guide Structural Equation Modeling (SEM) is a comprehensive statistical approach used to test hypotheses about relationships among observed and latent variables. It combines factor analysis and multiple regression analysis, allowing researchers to model complex relationships between variables. Key Concepts in SEM 1. Observed and Latent Variables: Observed Variables: These are variables that are directly measured (e.g., survey responses, test scores). rectangles represent observed variables. Latent Variables: Variables that are not directly measured but inferred from observed variables (e.g., intelligence, satisfaction, motivation). Ovals or circles represent latent variables. Single-Headed Arrows: These indicate a causal relationship or a direction of influence from one variable to another (e.g., from a latent variable to an observed variable). Double-Headed Arrows: These represent correlations or covariance’s between two variables, without implying causation. 2. Measurement Model: This part of the SEM represents the relationship between observed variables and their underlying latent variables. It is essentially a confirmatory factor analysis (CFA) where observed indicators are used to define latent constructs.  3. Structural Model: The structural model specifies the causal relationships among latent variables. It shows the directional paths and explains the relationships hypothesized in the research. 4. Path Diagrams: SEM models are often represented visually using path diagrams. Ovals or circles represent latent variables, rectangles represent observed variables, arrows indicate causal paths, and double-headed arrows indicate covariance’s or correlations. Steps in Conducting SEM 1. Model Specification: o Define the hypothesized relationships among variables based on theoretical or empirical knowledge. Specify paths and relationships, deciding which variables are observed and which are latent. 2. Model Identification: o Determine whether the model can be estimated uniquely based on the data. This often depends on the number of parameters versus the available data points. A model is identified if the number of known values is greater than or equal to the number of parameters to be estimated. 3. Model Estimation: o Estimate the parameters of the model using software such as AMOS, LISREL, or Mplus. Common estimation methods include Maximum Likelihood Estimation (MLE) and Weighted Least Squares (WLS). 4. Model Testing and Evaluation (Model Fit): o Fit Indices: Evaluate model fit to check how well the specified model matches the observed data.   CMIN/DF (Chi-Square/Degrees of Freedom Ratio): This is a relative measure of model fit, showing how well the model fits the data while considering its complexity.  RMSEA (Root Mean Square Error of Approximation): Measures how much error is in the model; a value of 0.08 or less means the fit is acceptable.  CFI (Comparative Fit Index): Compares your model with a baseline model, with values above 0.90 showing a good fit.  GFI (Goodness of Fit Index): Indicates how much of the data variability is explained by your model, where higher values suggest better fit. o Modification Indices: Identify areas for improvement, suggesting paths or covariance’s that may improve the model. 5. Model Re-specification: o Based on fit indices and modification suggestions, refine the model by adding or removing paths to improve fit. Be cautious to keep changes theoretically justified. 6. Model Interpretation: o Interpret the path coefficients, which show the strength and direction of relationships among variables. o Assess the overall structural model’s explanatory power by examining R² values for endogenous variables. Types of Models in SEM 1. Confirmatory Factor Analysis (CFA): o A model that specifies the relationships between observed variables and their underlying latent constructs. It is used to validate the measurement model. 2. Path Analysis: o A simpler form of SEM without latent variables, focusing on causal relationships between observed variables. 3. Full SEM: o Combines both the measurement and structural models, allowing the researcher to test the full network of relationships among observed and latent variables. Common Applications of SEM 1. Psychology and Education: Testing theories related to cognitive abilities, personality, and educational achievement. 2. Marketing and Consumer Behavior: Analyzing customer satisfaction, brand loyalty, and purchase intentions. 3. Healthcare: Examining the relationships between patient attitudes, behaviors, and health outcomes. 4. Social Sciences: Exploring social phenomena like attitudes, perceptions, and behaviors in society. SEM Software Tools  AMOS: User-friendly for beginners, integrates well with SPSS.  LISREL: Robust software with extensive modeling options.  Mplus: Advanced capabilities, supports a wide range of models including complex latent variable interactions.  R (lavaan package): Free and powerful for SEM, with high flexibility for model customization. Confirmatory Factor Analysis (CFA): Confirmatory Factor Analysis (CFA) is a statistical technique used within Structural Equation Modeling (SEM) to test the hypothesis that the relationships between observed variables and their underlying latent constructs are consistent with a researcher’s theoretical model. CFA is primarily used to verify the measurement model in SEM, specifying how observed variables represent underlying latent factors. Key Concepts in CFA Latent Variables (Factors): Latent variables are unobserved constructs inferred from observed variables. In CFA, we aim to confirm that a set of observed variables loads onto specific latent variables, as hypothesized. Observed Variables (Indicators): These are the directly measured items or indicators that load onto latent variables (e.g., survey items). Each latent variable typically has multiple observed variables associated with it to capture its essence accurately. Factor Loadings: Factor loadings represent the strength of the relationship between each observed variable and its respective latent variable. Higher loadings (preferably >0.5) indicate a stronger association between the observed variable and the latent factor. Measurement Error: Measurement errors, denoted by the unique variance of each observed variable, are accounted for in CFA. This allows for a more accurate measurement of the latent variables. Steps in Conducting CFA Using SPSS AMOS 1. Data Preparation: o Ensure data is clean, reliable ad variables should be continuous or ordinal, as AMOS handles these types best in CFA. 2. Model Specification in AMOS: o Define the model structure based on theoretical expectations. Identify which observed variables load onto which latent variables. o In AMOS, open a new project and use the Draw tool to create the model diagram:   Ovals represent latent variables.  Rectangles represent observed variables.  Single-headed arrows indicate the hypothesized direction of influence (from latent to observed variable), while double-headed arrows represent error covariance’s or correlations between latent variables. o Connect observed variables to their respective latent variables as per your hypothesized model. 3. Model Identification: o Ensure that the model is identified, meaning there are enough data points to estimate all parameters. A rule of thumb is having at least three indicators per latent factor, as models with fewer indicators can be under-identified. 4. Model Estimation: o Run the analysis using Maximum Likelihood Estimation (MLE) in AMOS, which is suitable if the data are reasonably normally distributed. o Click on Calculate Estimates to obtain factor loadings, error terms, and model fit indices. 5. Model Evaluation (Fit Indices): o Evaluate model fit to determine if the specified CFA model is consistent with the observed data. Common fit indices include:  CMIN/DF (Chi-Square/Degrees of Freedom Ratio): This is a relative measure of model fit, showing how well the model fits the data while considering its complexity. A CMIN/DF value between 1 and 3 indicates a good model fit, while values below 5 may still be acceptable in some cases. Lower values are generally better as they suggest a more parsimonious model.  RMSEA (Root Mean Square Error of Approximation): Measures how much error is in the model; a value of 0.08 or less means the fit is acceptable.  CFI (Comparative Fit Index): Compares your model with a baseline model, with values above 0.90 showing a good fit.  GFI (Goodness of Fit Index): Indicates how much of the data variability is explained by your model, where higher values suggest better fit. Generally, value above 0.90 o In AMOS, these indices are displayed in the Output window under Model Fit Summary. 6. Examine Factor Loadings: o Confirm that all factor loadings are significant and sufficiently high (usually > 0.5). Low loadings indicate that the observed variable does not strongly represent the latent construct. o Factor loadings can be found in the Standardized Estimates output in AMOS. 7. Modification Indices: o Check modification indices to see if model fit can be improved. AMOS provides suggestions on freeing specific parameters (e.g., adding covariance’s between errors). o Be cautious when making modifications; ensure that changes are theoretically justified and do not lead to overfitting.  8. Model Re-specification (if needed): o Based on the modification indices, consider adding paths or correlations between error terms only if they make theoretical sense. Re-run the model and evaluate if these changes improve the fit. 9. Interpreting Results: o Interpret factor loadings, variances, and covariance’s. Higher factor loadings indicate stronger representation of the latent factor by the observed variable. Example of CFA Workflow in AMOS 1. Defining the Model: Suppose we have four latent variables (e.g., Organizational support, Task significance, Employee Tenure and Work Engagement) with three observed variables each. 2. Drawing the Model in AMOS: o Use ovals for Organizational support, Task significance, Employee Tenure and Work Engagement. o Use rectangles for each observed variable and connect them to their respective latent variable. o Draw error terms for each observed variable (automatically added by AMOS). 3. Running the Model: o Run Calculate Estimates in AMOS to obtain factor loadings and fit indices. 4. Checking Fit Indices: o Check RMSEA, CFI, and GFI to determine if the model fits well. 5. Evaluating Factor Loadings: o Ensure all loadings are above 0.5 and statistically significant. 6. Modifications (if necessary): o Based on modification indices, add covariance’s between error terms if theoretically justified, and re-run the model. 7. Final Interpretation: o If the model fits well, interpret factor loadings and evaluate construct reliability and validity. Confirmatory Factor Analysis: This Confirmatory Factor Analysis (CFA) model represents the relationships between latent constructs and their corresponding observed variables, as well as the relationships among the latent constructs. Latent Constructs and Observed Variables: 1. Organizational Support (OS): o Observed variables: OS1, OS2, OS3, OS4 o Standardized factor loadings:  OS1: 0.79  OS2: 0.67  OS3: 0.78  OS4: 0.78  oThese loadings indicate how well each observed variable represents the latent construct (OS). Values above 0.6 generally show good reliability. 2. Task Significance (TS): o Observed variables: TS1, TS2, TS3 o Standardized factor loadings:  TS1: 0.85  TS2: 0.66  TS3: 0.68 o TS1 has the strongest relationship with TS, while TS2 and TS3 have moderate loadings. 3. Employee Tenure (ET): o Observed variables: ET1, ET2, ET3 o Standardized factor loadings:  ET1: 0.80  ET2: 0.67  ET3: 0.70 o All three observed variables have acceptable loadings for representing ET. 4. Work Engagement (WE): o Observed variables: WE1, WE2, WE3, WE4 o Standardized factor loadings:  WE1: 0.84  WE2: 0.77  WE3: 0.71  WE4: 0.89 o WE4 has the highest loading, suggesting it is the best indicator of WE among the four. Correlations Among Latent Constructs:  OS and TS: 0.36  OS and ET: 0.42  OS and WE: 0.46  TS and ET: 0.38  TS and WE: 0.26  ET and WE: 0.35 These correlations reflect the strength and direction of relationships among the latent constructs. For example:  OS and WE have a moderately strong positive relationship (0.46).  TS and WE have a weaker positive relationship (0.26). This model shows a strong measurement structure for the constructs of Organizational Support, Task Significance, Employee Tenure, and Work Engagement, with reliable observed variables for each latent construct. Covariance’s: Estimate S.E. C.R. P OS TS.310.058 5.367 *** TS ET.476.088 5.425 *** WE ET.569.086 6.626 *** OS ET.397.067 5.930 *** WE TS.391.072 5.391 *** WE OS.219.052 4.178 *** The covariance table provides information on the relationships (covariance’s) between pairs of latent variables in the model Columns Explained: 1. Estimate: The covariance value between two latent constructs. 2. S.E.: The standard error of the estimate, indicating the variability or uncertainty in the covariance value. 3. C.R.: The critical ratio, which is the covariance estimate divided by the standard error (Estimate/S.E.). This value follows a standard normal distribution. 4. P: The p-value, showing the statistical significance of the covariance. A p-value less than 0.05 (or *** indicates p < 0.001) suggests a significant relationship between the constructs. Interpretation of Each Row: 1. OS TS: o Estimate: 0.310 o S.E.: 0.058 o C.R.: 5.367 o P: *** (p < 0.001) Interpretation: There is a significant positive covariance (0.310) between Organizational Support (OS) and Task Significance (TS). This indicates that higher levels of OS are associated with higher levels of TS, and the relationship is statistically significant. 2. TS ET: o Estimate: 0.476  o S.E.: 0.088 o C.R.: 5.425 o P: *** (p < 0.001) Interpretation: There is a significant positive covariance (0.476) between Task Significance (TS) and Employee Tenure (ET). This suggests that as TS increases, ET also tends to increase, and the relationship is statistically significant. 3. WE ET: o Estimate: 0.569 o S.E.: 0.086 o C.R.: 6.626 o P: *** (p < 0.001) Interpretation: There is a significant positive covariance (0.569) between Work Engagement (WE) and Employee Tenure (ET). This shows that higher levels of ET are strongly associated with higher levels of WE, with high statistical significance. 4. OS ET: o Estimate: 0.397 o S.E.: 0.067 o C.R.: 5.930 o P: *** (p < 0.001) Interpretation: A significant positive covariance (0.397) exists between Organizational Support (OS) and Employee Tenure (ET). This implies that higher organizational support is associated with longer employee tenure, with a significant relationship. 5. WE TS: o Estimate: 0.391 o S.E.: 0.072 o C.R.: 5.391 o P: *** (p < 0.001) Interpretation: There is a significant positive covariance (0.391) between Work Engagement (WE) and Task Significance (TS). This means higher task significance is linked to greater work engagement, with a statistically significant relationship. 6. WE OS: o Estimate: 0.219 o S.E.: 0.052  o C.R.: 4.178 o P: *** (p < 0.001) Interpretation: A significant positive covariance (0.219) exists between Work Engagement (WE) and Organizational Support (OS). This indicates that better organizational support is moderately associated with higher work engagement, with a statistically significant relationship. Overall Summary:  All covariance’s between the latent variables are positive and statistically significant (p < 0.001).  The strongest relationship is between WE and ET (covariance = 0.569), indicating that employee tenure is highly associated with work engagement.  The weakest relationship is between WE and OS (covariance = 0.219), which still indicates a moderate association between these two variables.  This covariance’s confirm the interconnections among the latent constructs, supporting the hypothesized relationships in the model. Model Fit in SEM: Model fit in Structural Equation Modeling (SEM) refers to how well a specified model reproduces the observed data. SPSS AMOS offers a variety of fit indices to assess this alignment. Understanding these indices helps researchers confirm that their model accurately represents the theoretical constructs and relationships. Categories of Fit Indices in AMOS AMOS provides several categories of fit indices, each capturing a different aspect of model fit: 1. Absolute Fit Indices: Indicate how well the proposed model fits the data without comparing it to any other model. 2. Incremental (Comparative) Fit Indices: Compare the fit of the specified model to a baseline (null) model that assumes no relationships between variables. 3. Parsimonious Fit Indices: Account for model complexity, preferring simpler models if they fit nearly as well as more complex ones. Fit Indices in SPSS AMOS: 1. Chi-Square (χ²) Test: o Description: The chi-square test measures the discrepancy between the observed and expected covariance matrices. A non-significant chi-square (p > 0.05) indicates that the model fits well. However, chi-square is highly sensitive to sample size; in large samples, even well-fitting models may yield significant chi-square values. o χ²/df (Coefficient of Discrepancy): A small chi-square value relative to degrees of freedom (χ²/df) is generally preferred. Coefficient of Discrepancy ratio of 3  to 5 are considered acceptable, while values less than 3 indicate an excellent fit. 2. Root Mean Square Error of Approximation (RMSEA): o Description: RMSEA estimates the discrepancy per degree of freedom, adjusting for sample size and penalizing model complexity. It provides a confidence interval, with a lower bound ideally close to 0. o Interpretation: RMSEA ≤ 0.05 indicates a close fit, values between 0.05 and 0.08 indicate an acceptable fit, and values above 0.10 suggest a poor fit. 3. Goodness-of-Fit Index (GFI): o Description: GFI reflects the proportion of variance in the observed data explained by the model. It ranges from 0 to 1, with higher values indicating better fit. o Interpretation: GFI ≥ 0.90 is typically considered an acceptable fit, although values closer to 1 are preferred. 4. Comparative Fit Index (CFI): o Description: CFI compares the fit of the target model with the null model, accounting for model complexity. It is one of the most commonly used fit indices in SEM due to its reliability across different sample sizes. o Interpretation: CFI ≥ 0.90 indicates an acceptable fit, while CFI ≥ 0.95 suggests a very good fit. 5. Normed Fit Index (NFI): o Description: NFI compares the proposed model to a null model, providing a measure of improvement in fit. It ranges from 0 to 1, with higher values indicating better fit. o Interpretation: NFI ≥ 0.90 suggests an acceptable fit, but values closer to 1 are preferred. Model Fit Summary CMIN Model NPAR CMIN DF P CMIN/DF Default model 34 95.390 71.028 1.344 Saturated model 105.000 0 Independence model 14 2301.403 91.000 25.290 RMR, GFI Model RMR GFI AGFI PGFI Default model.053.965.948.652 Saturated model.000 1.000 Independence model.452.423.334.366 Baseline Comparisons NFI RFI IFI TLI Model CFI Delta1 rho1 Delta2 rho2 Default model.959.947.989.986.989 Saturated model 1.000 1.000 1.000 Independence model.000.000.000.000.000 Parsimony-Adjusted Measures Model PRATIO PNFI PCFI Default model.780.748.772 Saturated model.000.000.000 Independence model 1.000.000.000 NCP Model NCP LO 90 HI 90 Default model 24.390 2.895 53.955 Saturated model.000.000.000 Independence model 2210.403 2057.781 2370.380 FMIN Model FMIN F0 LO 90 HI 90 Default model.249.064.008.141 Saturated model.000.000.000.000 Independence model 6.009 5.771 5.373 6.189 RMSEA Model RMSEA LO 90 HI 90 PCLOSE Default model.030.010.045.990 Independence model.252.243.261.000 AIC Model AIC BCC BIC CAIC Default model 163.390 166.161 297.712 331.712 Saturated model 210.000 218.560 624.817 729.817 Independence model 2329.403 2330.544 2384.712 2398.712 ECVI Model ECVI LO 90 HI 90 MECVI Default model.427.370.504.434 Saturated model.548.548.548.571 Independence model 6.082 5.684 6.500 6.085 HOELTER HOELTER HOELTER Model.05.01 Default model 369 409 Independence model 20 21 Model fit indices for CFA model: 1. Chi-Square (CMIN) and Degrees of Freedom (DF)  Default model: o CMIN (Chi-Square): 95.390 o DF: 71 o P-value: 0.028 (less than 0.05) o CMIN/DF: 1.344 Interpretation: While the p-value is significant (indicating potential model misfit), this is expected in large samples because even small differences from the ideal model can lead to significant p-values. The ratio of CMIN/DF = 1.344 is well below the acceptable threshold of 3, suggesting a good fit. 2. Root Mean Square Error of Approximation (RMSEA)  RMSEA: 0.030  90% Confidence Interval (CI): [0.010, 0.045]  PCLOSE: 0.990 Interpretation:  RMSEA values below 0.06 indicate excellent model fit. The value of 0.030 is well within the acceptable range.  The 90% CI is very narrow, indicating stability in the estimate.   The PCLOSE value (probability of RMSEA being less than 0.05) of 0.990 is excellent, confirming a close model fit. 3. Goodness of Fit Index (GFI) and Adjusted GFI (AGFI)  GFI: 0.965  AGFI: 0.948 Interpretation:  GFI and AGFI values above 0.90 are considered good. Both GFI (0.965) and AGFI (0.948) indicate an excellent fit.  AGFI adjusts the GFI for the degrees of freedom in the model and remains high, confirming good fit. 4. Comparative Fit Index (CFI)  CFI: 0.989 Interpretation:  CFI values above 0.95 indicate excellent fit. A value of 0.989 confirms that the model fits the data exceptionally well compared to a null/independence model. 5. Normed Fit Index (NFI) and Relative Fit Index (RFI)  NFI: 0.959  RFI: 0.947 Interpretation:  NFI values above 0.90 are acceptable, and values above 0.95 indicate excellent fit. Here, NFI = 0.959 suggests a very good fit.  RFI (adjusted for model complexity) is also close to 0.95, further supporting good fit. Structural Equation Modeling (SEM) – Path Analysis Using AMOS Path Analysis is a specialized form of Structural Equation Modeling (SEM) that focuses on the direct and indirect relationships between observed (measured) variables. In SEM, Path Analysis is used to test causal relationships and explore how multiple variables impact one another within a system. AMOS (Analysis of Moment Structures), a software within SPSS, provides a visual way to conduct Path Analysis, enabling researchers to estimate relationships between variables, test hypotheses, and understand complex dependency structures. Key Concepts in Path Analysis 1. Observed Variables: o Unlike CFA, which includes latent (unobserved) variables, Path Analysis typically only involves observed (measured) variables. These variables are represented as rectangles in AMOS path diagrams. 2. Causal Paths and Arrows: o In Path Analysis, single-headed arrows represent causal relationships, indicating the direction and influence from one variable to another. o Double-headed arrows represent covariance’s or correlations between variables without implying causation. 3. Direct and Indirect Effects: o Direct Effects: The impact of one variable directly on another, represented by a single-headed arrow. o Indirect Effects: When one variable influences another through an intermediary variable, resulting in a sequence of relationships. 4. Mediating Variables: o Mediating variables explain the relationship between two other variables, often revealing the indirect pathways within the model. Mediation analysis is common in Path Analysis to understand the mechanism through which one variable affects another. 5. Endogenous and Exogenous Variables: o Exogenous Variables: Variables that are independent and not influenced by any other variable within the model. o Endogenous Variables: Variables that are dependent on or influenced by other variables within the model. Advantages and Limitations of Path Analysis in AMOS Advantages:  Simple Visualization: AMOS provides an easy-to-understand path diagram interface, making model specification intuitive.  Ability to Estimate Indirect Effects: AMOS calculates both direct and indirect effects, making it easy to understand mediation relationships.  Fit Indices and Statistical Testing: AMOS provides a comprehensive range of fit indices and statistical tests, allowing thorough model evaluation. Limitations:  Limited to Observed Variables: Path Analysis typically does not include latent variables, which can restrict the complexity of the model.  Sample Size Sensitivity: Path Analysis can yield biased results with small sample sizes, particularly for chi-square testing.  Assumptions of Linearity and Normality: Path Analysis assumes linear relationships and normally distributed data, which may not always be realistic. Steps to Conduct Path Analysis in AMOS Step 1: Specify the Model 1. Define Variables and Hypothesized Relationships: o Identify the observed variables and hypothesize how they influence one another based on theory or prior research. o Determine which variables are exogenous and which are endogenous in your model. 2. Draw the Path Diagram in AMOS: o Open AMOS and select New Model to start. o Use the Draw Variable Tool to add observed variables (rectangles) to the canvas. o Use the Draw Path Tool to create single-headed arrows representing hypothesized causal relationships. o Double-headed arrows can be added between exogenous variables if there is a theoretical reason to assume they are correlated. 3. Specify Measurement Scales: o Ensure that each observed variable is defined by the correct measurement scale (e.g., continuous, ordinal), as this affects the estimation process. Step 2: Model Identification 1. Identify Parameters: o Ensure the model is identified, meaning there are enough data points to estimate all paths (parameters). 2. Check for Degrees of Freedom: o A positive number of degrees of freedom (df) indicates that the model is over- identified and suitable for estimation. Step 3: Estimate the Model 1. Select the Estimation Method: o In AMOS, Maximum Likelihood Estimation (MLE) is the default method. 2. Run the Analysis: o Click on Calculate Estimates to run the path analysis and estimate the parameters. AMOS will produce estimates for path coefficients, variances, and covariance’s in the output. Step 4: Evaluate Model Fit 1. Interpret Path Coefficients: o Path coefficients represent the strength and direction of relationships. Standardized coefficients (ranging from -1 to 1) are typically used for easier interpretation. o For each path, check if the coefficient is statistically significant (p < 0.05), as this indicates a meaningful relationship between the variables. 2. Assess Model Fit Using Fit Indices:  CMIN/DF (Chi-Square/Degrees of Freedom Ratio): This is a relative measure of model fit, showing how well the model fits the data while considering its complexity. A CMIN/DF value between 1 and 3 indicates a good model fit, while values below 5 may still be acceptable in some cases. Lower values are generally better as they suggest a more parsimonious model.  RMSEA (Root Mean Square Error of Approximation): Measures how much error is in the model; a value of 0.08 or less means the fit is acceptable.  CFI (Comparative Fit Index): Compares your model with a baseline model, with values above 0.90 showing a good fit.  GFI (Goodness of Fit Index): Indicates how much of the data variability is explained by your model, where higher values suggest better fit. Generally, value above 0.90 Step 5: Interpret and Report Results: o Interpret the path coefficients, which show the strength and direction of relationships among variables. Practical Example of Path Analysis in AMOS We are studying the influence of Organizational Support (OS), Task Significant (TS), and Employee Tenure (TE) on Work Engagement(WE). Structural Equation Modeling (SEM) output from AMOS, representing the relationships between Organizational Support (OS), Task Significance (TS), Employee Tenure (ET), and their influence on Work Engagement (WE). Interpretation of the model: Model Interpretation 1. Latent Variables and Indicators: o Organizational Support (OS):  Measured by four observed variables: OS1, OS2, OS3, and OS4.  The factor loadings are strong, ranging from 0.67 to 0.79, indicating that these indicators reliably measure OS. o Task Significance (TS):  Measured by three observed variables: TS1, TS2, and TS3.  Factor loadings range from 0.66 to 0.85, with TS1 having the highest contribution to TS. o Employee Tenure (ET):   Measured by three observed variables: ET1, ET2, and ET3.  Factor loadings are moderate, ranging from 0.67 to 0.80, with ET1 contributing the most. o Work Engagement (WE):  Measured by four observed variables: WE1, WE2, WE3, and WE4.  Factor loadings are very strong, ranging from 0.71 to 0.89, indicating reliable measurement of WE. 2. Direct Effects on Work Engagement (WE): o OS → WE (0.03):  The path coefficient from Organizational Support to Work Engagement is very small (0.03), suggesting that OS has a negligible direct effect on WE. o TS → WE (0.19):  The path coefficient from Task Significance to Work Engagement is positive but moderate (0.19), indicating a weak direct relationship. o ET → WE (0.37):  The path coefficient from Employee Tenure to Work Engagement is significant and moderate (0.37), showing that ET has the strongest influence among the three predictors. 3. Relationships Among Predictors: o OS ↔ TS (0.36):  There is a moderate positive correlation between Organizational Support and Task Significance, indicating some shared variance. o TS ↔ ET (0.38):  A moderate positive correlation exists between Task Significance and Employee Tenure. o OS ↔ ET (0.42):  Organizational Support and Employee Tenure are moderately correlated, showing a stronger relationship than the other two pairs. Regression Weights: (Group number 1 - Default model) Estimate S.E. C.R. P WE