Assignment Exercise 17B and Chapter 17A and 19A for Reference
Complete both Path Analysis Multiple Regression and Structural Equation Modeling techniques and complete only the Path Analysis technique exercises using SPSS.
Download the Data File named Exercise and load it into SPSS.
Complete the Path Analysis exercises.
Write a 1,050- to 1,400-word paper that includes the major elements, concepts, or components. Address the following issues:
See Practice Exercises for 17B on page 2
· Analyze and explain similarities and differences in the path analysis multiple regression model and the structural equation model.
· Evaluate the assumptions used in path analysis and the process for inclusion of values for the variables in path analysis.
· Analyze how the path structure evolves and the indirect and total effects of the variables in the path analysis model.
· Replicate the major tables for the path analysis model. After each of the primary tables explain (from your own understanding) the primary results that are shown in certain table columns that lead to the interpretation of the test results. Evaluate the strengths and weaknesses or limitations of the model.
· Draw conclusions about how the path analysis approach and techniques might provide considerations for a projected dissertation study.
· Expand conclusions about how the path analysis approach might lead to structural equation modeling.
See Chapter Reference Material 17A (page 10) and 19A (page 23) for Practice Exercises of 17B
Practice Exercises 17B
Path Analysis: Multiple Regression Using IBM SPSS
17B.1 The Data Set and Model Used in Our Example
This chapter describes how to perform a path analysis using multiple regression. The path model that represents our fictional study is shown in Figure 17b.1. The outcome variable is the amount of exercise engaged in by college students during a semester (named exercise in the data file). The amount of exercise in which they engage is hypothesized to be directly predictable from the degree to which students maintain a healthy diet (named diet in the data file), the tendency to portray themselves in a socially desirable way (named desire in the data file), and their levels of self-esteem (named selfesteem in the data file) and body-esteem (named bodyesteem in the data file). Social desirability and acceptance of others (named acceptance in the data file), self-esteem, and body-esteem are also hypothesized to exert an indirect effect on exercise through diet. In addition, self-esteem and body-esteem were hypothesized to affect social desirability and acceptance of others. Finally, it was hypothesized that acceptance of others influenced the degree of social desirability.
The data file for this example is named Exercise. It contains 415 cases. Because there are no missing data, all of the regression analyses will be performed on data from the same cases, and the path coefficients from separate analyses may be appropriately placed in the model as a whole.
17B.2 Specifying the Variables in Each Analysis
The multiple regression approach to path analysis requires us to perform as many analyses as there are endogenous variables in the model. In our example shown in Figure 17b.1, there are four such variables, and so we must perform (in any order) the following four regression analyses:
Figure 17b.1 The Path Model Predicting the Amount of Exercise in Which Students Engaged During a Semeste
· Exercise will be predicted from diet, social desirability, self-esteem, and body-esteem.
· Diet will be predicted from self-esteem, social desirability, acceptance, and body-esteem.
· Social desirability will be predicted from self-esteem, body-esteem, and acceptance.
· Acceptance will be predicted from self-esteem and body-esteem.
We have described the steps to perform and how to interpret the output of ordinary least squares regression in Section 7B.1; readers are advised to consult that material to refresh their memories as we will assume here that the basics of the procedure are already familiar.
Figure 17b.2 The Main Regression Window
17B.3 Predicting Exercise
17B.3.1 Predicting Exercise: Analysis Setup
Open the Exercise data file and select Analyze Regression Linear. As shown in Figure 17b.2, we specify exercise as the Dependent variable and diet, desire, selfesteem, and bodyesteem as the Independent variables. Keep the Method as Enter.
In the Statistics window, check Estimates in the Regression Coefficients panel. Also check Model fit, R squared change, Descriptives, and Part and partial co
elations. This is shown in Figure 17b.3. Click Continue to return to the main dialog screen and click OK to produce the analysis.
17B.3.2 Predicting Exercise: Output
The output of interest is shown in Figure 17b.4. As can be seen in the top table of Model Summary, 35% of the variance of exercise was explained by the prediction model. Tested with 4 and 410 degrees of freedom, the F ratio of XXXXXXXXXXevaluating the value of the R2 was statistically significant.
The standardized regression coefficients are presented in the lower table of Figure 17b.4. Both diet and bodyesteem were significant predictors of exercise with standardized regression weights of .429 and .338, respectively (rounded to .43 and .34, respectively, in Figure 17b.5). The coefficients of −.018 for desire and .058 for selfesteem (rounded to −.02 and .06, respectively, in Figure 17b.5) were not statistically significant. We show the path model at this stage of the analysis in Figure 17b.5 with the values of the path coefficients and the R2 for exercise included.
Figure 17b.3 The Statistics Window
Figure 17b.4 The R2, Test of Significance of the Model, and the Coefficients Predicting Exercise
Figure 17b.5 The Path Model With Exercise and Diet Predicted
17B.4 Predicting Diet
17B.4.1 Predicting Diet: Analysis Setup
In this second analysis, specify diet as the Dependent variable and selfesteem, bodyesteem, desire, and acceptance as the Independent variables. Use the setup for the Statistics window as described in Section 17B.3.1.
Figure 17b.6 The R2, Test of Significance of the Model, and the Coefficients Predicting Diet
17B.4.2 Predicting Diet: Output
The output of interest is shown in Figure 17b.6. As can be seen in the top table of Model Summary, approximately 9% of the variance of diet was explained by the prediction model. Tested with 4 and 410 degrees of freedom, the F ratio of 9.789 evaluating the value of the R2 was statistically significant.
The standardized regression coefficients are presented in the lower table of Figure 17b.6. Both desire and acceptance were significant predictors of diet with standardized regression weights of .165 and .211, respectively. The coefficients of −.095 and .071 for selfesteem and bodyesteem, respectively, were not statistically significant. We show the path model at this stage of the analysis in Figure 17b.7 with the values of the path coefficients and the R2 for diet added to our model.
17B.5 Predicting Social Desirability
17B.5.1 Predicting Social Desirability: Analysis Setup
In this third analysis, specify desire as the Dependent variable and selfesteem, bodyesteem, and acceptance as the Independent variables. Use the same setup for the Statistics window as described in Section 17B.3.1.
17B.5.2 Predicting Social Desirability: Output
The output of interest is shown in Figure 17b.8. As can be seen in the top table of Model Summary, approximately 16% of the variance of desire was explained by the prediction model. Tested with 3 and 411 degrees of freedom, the F ratio of XXXXXXXXXXevaluating the value of the R2 was statistically significant.
Figure 17b.7 The Path Model With Exercise and Diet Predicted
The standardized regression coefficients are presented in the lower table of Figure 17b.8. Both selfesteem and acceptance were significant predictors of desire with standardized regression weights of .221 and .211, respectively. The coefficient of .086 for selfesteem and bodyesteem was not statistically significant. We show the path model at this stage of the analysis in Figure 17b.9 with the values of the path coefficients and the R2 for desire added to our model.
17B.6 Predicting Acceptance
17B.6.1 Predicting Acceptance: Analysis Setup
In this fourth analysis, specify acceptance as the Dependent variable and selfesteem and bodyesteem as the Independent variables. Use the same setup for the Statistics window as described in Section 17B.3.1.
Figure 17b.8 The R2, Test of Significance of the Model, and the Coefficients Predicting Desire
Figure 17b.9 The Path Model With Exercise, Diet, and Social Desirability Predicted
Figure 17b.10 The R2, Test of Significance of the Model, and the Coefficients Predicting Acceptance
17B.6.2 Predicting Acceptance: Output
The output of interest is shown in Figure 17b.10. As can be seen in the top table of Model Summary, approximately 13% of the variance of acceptance was explained by the prediction model. Tested with 2 and 412 degrees of freedom, the F ratio of XXXXXXXXXXevaluating the value of the R2 was statistically significant. The standardized regression coefficients are presented in the lower table of Figure 17b.10. Selfesteem with a standardized regression weight of .334 was statistically significant; acceptance with a standardized regression weight of .026 was not significant.
We show the path model at this final stage of the analysis in Figure 17b.11 with the values of the path coefficients and the R2 for acceptance added to our model. As mentioned in Section 17A.13.1, it is possible to more completely explore mediation effects, principally with respect to the outcome variable (Exercise in this example) once the model is in its completed form. Here, we note that neither of the two exogenous variables (Body-Esteem and Self-Esteem) exhibit a statistically significant path to the potential mediator variable of Diet; as a consequence of this, a mediation analysis of those variables would not make sense (e.g., Body-Esteem cannot produce an indirect on Exercise through Diet if it is not related to Diet) in this context.
17B.7 Mediation Effects in the Larger Model
17B.7.1 Overview
With the overall model in place, it is possible to explore on a post hoc basis portions of the model in order to explicate simple mediation relationships if there are appropriate theoretical, research-based, or practical rationales for doing so. We will use the designations shown previously in Figure 8a.2 where X is the predictor variable, M is the mediator variable, and Y is the outcome variable. For such an analysis to make any sense, the following conditions (bo
owed from Section 8A.7.2 and applied to this example) must be met:
Figure 17b.11 The Path Model With Exercise, Diet, Social Desirability, and Acceptance Predicted
· X must significantly predict Y in isolation. That is, it makes no sense to speak of a mediated effect of X on Y if X and Y are not co
elated when considering only those two variables apart from the larger model.
· If X is going to “act through” M to influence Y, then X must significantly predict M in the larger model. If there is no significant prediction, X cannot “act through” a