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Similarities and Differences
The use of the multiple regression model and the structural equation model as approaches to path analysis have some similarities and differences. The first similarity is that both models apply linear statistical models such as regression, correlation, and analysis of variance to path analysis for they provide path coefficients (Field, 2013). The second similarity is that these models are valid if data meet the assumptions of independence of observation, the linearity of relationship, multivariate normality, and homoscedasticity (Harlow, 2014). The third similarity is that these models allow post hoc analysis to cross-validate outcomes and enhance their accuracy. Nevertheless, a major difference between these models is that the structural equation model offers comprehensive path analysis because it does not limit the number of relationships, while multiple regression analysis relies on default settings that restrict path analysis to a stepwise process (Harlow, 2014). Another difference between these models is that the structural equation model can assess the relationships between latent variables, whereas multiple regression analysis can assess the relationship between measured variables.
Assumptions of Path Analysis
For one to undertake path analysis and obtain valid outcomes, variables should meet some assumptions. Path analysis assumes that variables should have linear and causal relationships, errors of endogenous variables should not correlate, a one-way causal relationship must exist between variables, the scale of variables should be an interval, and errors ought to be absent in measured variables (Meyers, Gamst, & Guarino, 2013). The values of variables are included in the model if they meet these assumptions but are excluded from the model if they do not meet them. Included variables can be exogenous or endogenous depending on their contribution to the model. Exogenous variables are independent variables because they are not under the influence of variables within the model but outside the model, while endogenous variables are dependent variables because they are under the influence of exogenous variables within the model. Thus, assumptions and contributions of variables determine their inclusion in path analysis.
Evolution of Path Structure
Path analysis evolved from multiple regression analyses for they both predict the influence of independent variables on a dependent variable. The need to determine the nature of multiple relationships and make multiple predictions led to the emergence of path analysis (Field, 2013). A simple path structure that illustrates the direct and indirect effects of variables comprises two endogenous and two exogenous variables. As an independent variable that is subject to extraneous variables, an exogenous variable can influence endogenous variables directly or indirectly via another endogenous variable (Meyers et al., 2013). In an indirect effect, endogenous variables mediate the influence of exogenous variables on an endogenous variable.
Replicated Tables for Path Analysis
Prediction of Exercise
Table 1.
The regression model is statistically significant in predicting the influence of body-esteem, diet, desire, and self-esteem on exercise, F(4,410) = 55.082, p = 0.000. Predictors of the model (Table 1) account for 35% (R2 = 0.350) of variation in the magnitude of exercise that students perform.
Table 2.
The path coefficients in Table 2 indicate that diet (β = 0.429) and body-esteem (β = 0.338) are statistically significant predictors of exercise, while desire (β = -0.018) and self-esteem (β = 0.058) are statistically insignificant predictors of exercise.
Prediction of Diet
Table 3.
The model summary (Table 3) shows the regression model is statistically significant in predicting the effects of body-esteem, acceptance, desire, and self-esteem on diet level, F(4,410) = 9.789, p = 0.000. These predictors account for 8.7% (R2 = 0.087) of the variation in diet level among students.
Table 4.
Path coefficients in Table 4 reveal that desire (β = 0.165) and acceptance (β = 0.211) are statistically significant predictors of the level of diet, whereas self-esteem (β = -0.95) and body-esteem (β = 0.071) are not statistically significant predictors of the level of diet.
Prediction of Social Desirability
Table 5.
The regression analysis depicted in Table 5 reveals that the regression model is statistically significant in predicting the influence of body-esteem, acceptance, and self-esteem on social desirability among students, F(3,411) = 26.205, p = 0.000. These predictors account for 16.1% (R2 = 0.161) of the variation in the level of social desirability.
Table 6.
The examination of path coefficients in Table 6 shows that acceptance (β = 0.211) and self-esteem (β = 0.221) are statistically significant predictors of social desirability, while body-esteem (β = 0.086) is a statistically insignificant predictor of social desirability.
Prediction of Acceptance
Table 7.
In the prediction of acceptance by body-esteem and self-esteem, the model summary (Table 7) shows that the regression model is statistically significant, F(2,412) = 29.357, p = 0.000. Body-esteem and self-esteem account for 12.5% (R2 = 0.125) of the variation in the level of acceptance among students.
Table 8.
Path analysis (Table 8) depicts that self-esteem (β = 0.339) is a statistically significant predictor of acceptance, whereas body-esteem (β = 0.026) is a statistically insignificant predictor of acceptance.
Strengths and Weaknesses
The strength of path analysis is that it decomposes correlation coefficients into path coefficients, which indicate the extent of direct and indirect effects. An additional strength is that path analysis allows multiple analyses of the relationship between exogenous variables and between exogenous and endogenous variables. However, a weakness of path analysis is that although it can assess the causal relationship, it provides a one-way causal relationship and rules out the existence of reciprocal causation (Jeon, 2015). Another weakness is that the assumptions of multivariate correlation and the absence of errors in variables are not feasible in social sciences (Jeon, 2015). The existence of multicollinearity in data is a weakness because it reduces the accuracy and validity of path coefficients. Other weaknesses are the existence of extraneous variables that influence the model and the requirement of a large sample size.
Conclusion
The approach and techniques of path analysis are central to a dissertation study because they define and elucidate the nature of relationships between diverse variables. Furthermore, regression analysis describes the direct and indirect effects of independent variables on dependent variables using R-square and beta coefficients. As an expanded conclusion, path analysis provides structural relationships among variables. Path coefficients delineate structural relationship, and thus, form the basis of the structural equation modeling.
References
Field, A. (2013). Discovering statistics using IBM SPSS statistics (4th ed.). Los Angeles, CA: SAGE Publications.
Harlow, L. (2014). The essence of multivariate thinking: Basic themes and methods. New York, NY: Routledge.
Jeon, J. (2015). Strengths and limitations of the statistical modelling of complex social phenomenon: Focusing on SEM, path analysis, or multiple regression models. International Journal of Social, Behavioral, Educational, Economic, Business and Industrial Engineering, 9(5), 1634-142.
Meyers, L. S., Gamst, G., & Guarino, A. J. (2013). Applied multivariate research: Design and interpretation. Los Angeles, CA: SAGE Publications.
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